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Chapter 27 Current amp Resistance
Current Dead or Alive DEATH bull NEUROLOGIC CRITERIA An individual with
irreversible cessation of all brain function including the brain stem is dead
bull CARDIOPULMONARY CRITERIA An individual with irreversible cessation of circulatory and respiratory function is dead
Positive Charges move from HI to LOW potential
HI V LOW V
Negative Charges move from LOW to HI potential
HI V LOW V
HOW FAST DO ELECTRONS MOVE IN A CURRENT
CARRYING CONDUCTING WIRE
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Current Dead or Alive DEATH bull NEUROLOGIC CRITERIA An individual with
irreversible cessation of all brain function including the brain stem is dead
bull CARDIOPULMONARY CRITERIA An individual with irreversible cessation of circulatory and respiratory function is dead
Positive Charges move from HI to LOW potential
HI V LOW V
Negative Charges move from LOW to HI potential
HI V LOW V
HOW FAST DO ELECTRONS MOVE IN A CURRENT
CARRYING CONDUCTING WIRE
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Positive Charges move from HI to LOW potential
HI V LOW V
Negative Charges move from LOW to HI potential
HI V LOW V
HOW FAST DO ELECTRONS MOVE IN A CURRENT
CARRYING CONDUCTING WIRE
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Negative Charges move from LOW to HI potential
HI V LOW V
HOW FAST DO ELECTRONS MOVE IN A CURRENT
CARRYING CONDUCTING WIRE
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
HOW FAST DO ELECTRONS MOVE IN A CURRENT
CARRYING CONDUCTING WIRE
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Electron Speed is called the DRIFT Velocity
Drift velocity ~ 001 ms
Electric Fields travel at the speed of light
d
qEv
mv = pm=Ftm = qEtm
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull Current flows from a higher potential to a
lower potential (electrons flow the opposite
way) Current carrying wires are neutral
bull DC current flows in one direction
bull AC current oscillates back and forth
bull Electrons have a drift velocity of 001ms
bull Electric Fields travel at speed of light
I = Coulombsecond = Ampere
Current dQI
dt
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
(a) Current is defined as I = Qt so the
charge delivered in time t is
Q = It = (150 A)(080 s) = 120 C
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Current is charge in motion
bull Charge eg electrons exists in conductors with a
number density ne (ne approx 1029 m-3)
bull Current density J is given by J = qenevd = qnv
ndash unit of J is Cm2sec or Am2 (A equiv Ampere) and 1A equiv 1Cs
ndash current I is J times cross sectional area I = J pr2
ndash for 10 Amp in 1mm x 1mm area J = 10+7 Am2 and ve is about 10-3
ms (Yes the average velocity is only 1mms)
d
qEv
mv = pm=Ftm = qEtm
IJ qnv
A
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Engine Current Problem Again
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
a How much charge passes through the starter motor
b What is the drift speed of the electrons Show how the units work out
28 3electron number density 85 10 m
4
d 22 28 3 19
150 A5617 10 ms
00025 m 85 10 m 160 10 C
J I A Iv
nq ne r nep p
IJ qnv
A
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Fuses If the current drawn exceeds safe levels the fuse melts and the
circuit lsquobreaksrdquo ndash most house have switches not fuses
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Fuse Problem You need to design a 10 A fuse that lsquoblowsrsquo if the current exceeds 10 A The fuse material in your stockroom melts at a current density of 500 Acm2 What diameter wire of
this material will do the job
J I A
2
2
4 10 A40050 cm 050 mm
4 500 Acm
D I IA D
J J
p
p p
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Atomic Model
bull E-field in conductor provided by a battery
bull Charges are put in motion but scatter in a very short
time from things that get in the way
ndash itrsquos crowded inside that metal
ndash defects lattice vibrations (phonons) etc
bull Typical scattering time = 10-14 sec
bull Charges ballistically accelerated for this time and then
randomly scattered
bull Average velocity attained in this time is v = Ftm = qEm
bull Current density is J = qnv so current is proportional to E
which is proportional to Voltage
bull OHMrsquos LAW J = s E s = conductivity
2q n
m
s
d
qEv
m
IJ E qnv
As
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Resistivity
where E = electric field and
J = current density in conductor
L A
E
j
Property of bulk matter related to resistance of a sample is the resistivity (r) defined as
Jr
E 1r
s
eg for a copper wire r ~ 10-8 W-m 1mm radius 1 m long then R 01W
for glass r ~ 10+12 W-m for semiconductors r ~ 1 W-m
So in fact we can compute the resistance if we know a bit about the material and YES the property belongs to the material
For uniform case IJ
A ELV
Jr r
I ρLV EL L L I
A A
A
LR rwhere IRV
2q n
m
s J Es
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull The LONGER the wire the GREATER the R
bull The THINNER the wire the GREATER the R
bull The HOTTER the wire the GREATER the R
Resistance Resistivity
A
LR r
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
The HOTTER the wire the GREATER the R
Resistance Dependence on
Temperature
0(1 )R R T
0 original resistance
temperature coefficient of resistivity
temperature change (lt100 C)
R
T
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
When are light bulbs more likely
to blow
When hot or cold
0(1 )R R T
The HOTTER the wire the GREATER the R
At lower Resistance the bulb draws more
current and it blows the filament
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Resistivity Values
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Engine Current Problem
The starter motor of a car engine draws a current of 150 A from the battery The copper wire to the motor is 50 mm in diameter and 12 m long The starter motor runs for 080 s until the car engine starts
c What is the resistance in the copper wire
8 3
2 2
124 17 10 104 10
(005 )
4
l l mR x m x
DA mr r
pp
W W
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Problem
If the magnitude of the drift velocity of free electrons in a
copper wire is 784 times 10^ ndash4 ms what is the electric field
in the conductor The number density for copper is
849 times 10^28 electronsm3 What is the collision time
0181 V mE
IJ E qnv
As
qnvE qnvr
s
2q n
m
s
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
1 1 2 2 1 1 2 2
21 2
RA A d
r r r r
3 3
23
400 10 m 0250 m 600 10 m 0400 m378
300 10 m
R
W W W
A rod is made of two materials The figure is not drawn to scale Each conductor has a square cross section 300 mm on a side The first material has a resistivity of 400 times 10ndash3 Ω middot m and is 250 cm long while the second material has a resistivity of 600 times 10ndash3 Ω middot m and is 400 cm long What is the resistance between the ends of the rod
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Radial Resistance of a Coaxial
Cable Leakage bull Assume the silicon
between the conductors to
be concentric elements of
thickness dr
bull The resistance of the
hollow cylinder of silicon
is
bull The total radial resistance
is
2
ρdR dr
πrL
A
LR r
2ln
b
a
ρ bR dR
πL a
This is fairly high which is desirable since you want the current to
flow along the cable and not radially out of it
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Resistors
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Ohms Law J Es
V = IR
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Resistance QUESTION
How much current will flow
through a lamp that has a
resistance of 60 Ohms when
12 Volts are impressed
across it
USE OHMS LAW V = IR
12 122
60 60
V V VI A
R V A
W
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
What makes
the wires
Glow
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Electrical Power bull As a charge moves from a to b the electric
potential energy of the system increases by QV The chemical energy in the battery must decrease by this same amount
bull As the charge moves through the resistor (c to d) the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor
bull This energy is transformed into internal energy in the resistor as increased vibrational motion of the atoms in the resistor
bull The resistor emits thermal radiation which can
make it glow
U q V
dU dq V dqP V I V
dt dt dt
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull You pay for ENERGY not for ELECTRONS
bull Kilowatt-hour is the energy consumed in one
hour [kWh]=J NOT TIME Power x Time
POWER
2V VP I V V
R R
WattEnergy J
Ptime s
2( )P I V I IR I R
P I V
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
If V = 120V What is I
USE P = IV=gt I = PV
Appliance _ Power Current (A)
Hair Dryer 1600 Watts 133 A
Electric Iron 1200 Watts 10 A
TV 100 Watts 83 A
Computer 45 Watts 38 A
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts
Electric Iron 1200 Watts
TV 100 Watts
Computer 45 Watts
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Electric Bill
Cost to run for 1 hr
$05 per 1 kw-hr
Cost = Power x Time x Rate Appliance _ Power Cost______
Hair Dryer 1600 Watts $008
Electric Iron 1200 Watts $006
TV 100 Watts $0005
Computer 45 Watts $0003
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
QUESTION
The voltage and power on a light bulb read
ldquo120 V 60 Wrdquo How much current will flow
through the bulb
USE P = I V
I = PV = 60 W120 V = 12 Amp
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
QUESTION
The power and voltage on a light bulb read
ldquo120 V 60 Wrdquo What is the resistance of the
filament (I = 5 A)
Hint USE OHMS LAW V = IR
R = VI = 120 V 5 A = 240 W
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull The voltage of each device is the
full voltage of the EMF source
(the battery)
bull The total current is divided
between each path
Parallel Circuits
1 2
1 2 1 2
1 1( )
P
V V VI I I V
R R R R R
1 2 3
1 1 1 1
PR R R R
Equivalent Resistance
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
1 2 1 2 1 2( + ) + + I R R IR IR V V
total totalV IR
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
bull The current is the same in each device
bull The equivalent resistance of the circuit is the sum
of the individual resistances R=R1+R2
Series Circuits
1 2 1 2 3+ SV V V R R R R
To find the current use the total voltage and equivalent resistance
S
VI
R
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Circuits ProblemBulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240W light bulbs
In which circuit does each bulb burn brighter
RULE THE MORE POWER DISSIPATED IN A BULB THE
BRIGHTER IT IS
Find the power in each bulb when in series and in parallel
P IV
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
In Series
The Voltage is divided in series each bulb gets half V = 24V
2 2(24 )24
240
V V VP IV V W
R R
W
Circuits ProblemBulbs in Series vs Parallel
In Parallel
Voltage is the same in each bulb 48V
2 2(48 )96
240
V VP W
R
W
Parallel Bulbs Burn Brighter
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Circuits Problem3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the series circuit the bulbs DIM WHY
22 2
singlebulb 3 1
9 9
PVV VP
R R R
1 2 3V V V V
In series each of the three equal bulbs gets one third of the Voltage
(V3) that a single bulb would get
Note P=VI but I is due to the equivalent Resistance I = VRs =V3R
So the Current through each is 13 the current through a single bulb and
P=VI=V3 x I3 = VI9 = P9 The bulbs burn 19 as bright
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Circuits Problem3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total) how does the brightness
of the bulbs change Or not
In the parallel circuit the bulbs DO NOT DIM
WHY
2
singlebulb
VP P
R
In parallel each of the three equal
bulbs gets the full voltage of the battery source
Is this getting something for nothing
NO Parallel circuits drain the battery faster
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Parallel Circuits
bullAs the number of branches is increased the
overall resistance of the circuit is DECREASED
bullOverall resistance is lowered with each added
path between any two points of the circuit
bullThis means the overall resistance of the circuit is
less than the resistance of any one of the
branches (Weird)
bullAs overall resistance is lowered more current is
drawn This is how you blow fuses
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Circuits ProblemBulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit Does it go out Is it brighter Dimmer Or
In the series circuit the burned out bulb will short the circuit and
the other bulb will go out
In the parallel circuit the other bulb will have the same brightness
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
QUESTION
The power rating for two light bulbs read
30W and 60W Which bulb has the greatest
resistance at 120V
2 2 P V R R V P
2(120 ) 30 480R V W W
2(120 ) 60 240R V W W
Which burns brighter and why
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Quick Quiz
For the two lightbulbs shown in this figure
rank the current values at the points from
greatest to least
Ia = Ib gt Ic = Id gt Ie = If
The 60 W bulb has the lowest
resistance and therefore draws the
most current and burns brightest
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Resistance Question
bull The resistivity of both resistors is the same (r) bull Therefore the resistances are related as
1
1
1
1
1
2
22 88
)4(
2R
A
L
A
L
A
LR rrr
bull The resistors have the same voltage across them therefore
1
12
28
1
8I
R
V
R
VI
bull Two cylindrical resistors R1 and R2 are made of identical material R2 has twice the length of R1 but half the radius of R1
ndash These resistors are then connected to a battery V as shown
V I1 I2
ndash What is the relation between I1 the current flowing in R1 and I2 the current flowing in R2
(a) I1 lt I2 (b) I1 = I2 (c) I1 gt I2
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1911 H K Onnes who had figured
out how to make liquid helium used it
to cool mercury to 42 K and looked at
its resistance
bull 1957 Bardeen (UIUC) Cooper and Schrieffer (ldquoBCSrdquo)
publish theoretical explanation for which they get the
Nobel prize in 1972
ndash It was Bardeenrsquos second Nobel prize (1956 ndash transistor)
ndashCurrent can flow even if E=0
ndashCurrent in superconducting rings can flow for years with no
decrease
bull At low temperatures the resistance of
some metals0 measured to be less
than 10-16bullρconductor (ie ρlt10-24 Ωm)
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
Superconductivity
bull 1986 ldquoHighrdquo temperature superconductors are
discovered (Tc=77K)
ndash Important because liquid nitrogen (77 K) is much cheaper than
liquid helium
ndash Highest critical temperature to date 138 K (-135˚ C = -211˚ F)
bull Today Superconducting loops are used to produce
ldquolosslessrdquo electromagnets (only need to cool them not
fight dissipation of current) for particle physics
[Fermilab accelerator IL]
bull The Future Smaller motors ldquolosslessrdquo power
transmission lines magnetic levitation trains
quantum computers
top related