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CurrentCurrent• Electric Current (I)
– T he rate at which charge flows through a perpe ndicular surface
dQI
dt
C/s or Ampere, A
T he current has the same direction as the flow of positive charge.
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CurrentCurrent• Direct Current (DC)
– The constant current in magnitude and direction
• Alternating Current (AC)– The current changing in magnitude and
direction all the time
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CurrentCurrent
( )dQ nAv t q
( )dav d
nAv t qQI nqv A
t t
vd : drift speed of charge q
n : number of mobile charge carriers per unit volume
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Quiz #1Quiz #1
• Consider positive and negative charges movin g horizontally through the four regions shown i n the figure . Rank the current in these four reg
ions, from lowest to highest.
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current density current density• The current density (J)
– the current per unit area
d
IJ nqv
A
dJ nqv
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current density current density• A current density J and an electric field E are establi
shed in a conductor whenever a potential differenc e is maintained across the conductor
J E
Ohm’s law
: conductivity
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ResistanceResistance
b a
J I lV V V El l l I IR
A A
= 1/ : Resi st i vi ty
lR
A Resi st ance (.m)
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RResistivityesistivity
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ResistResistorsors
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ResistanceResistance
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ResistanceResistance and Temperature
0 01 ( )T T
0 T
0 01 ( )R R T T
temperature coefficient of resistivity
Conductor
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Resistance and Temperature Resistance and Temperature
Semiconductor
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superconductorsuperconductor
• a class of metals and com pounds whose resistance
decreases to zero when th ey are below a certain tem
perature Tc , known as the critical temperature
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superconductorsuperconductor
• A small permanent magnet levitated a
bove a disk of the s uperconductor Ba
2Cu3O7 , which is at77 K.
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Electrical Power Electrical Power ((PP))
• T he rate at which energy is delivered to a r esi st or
22( )V
P I V I RR
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Example #7Example #7
• For t he t wo l i ght bul b s shown in f igure, rank t
he cur r ent val ues at p oi nt s a t hr ough f , from
gr eat est t o l east
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Direct Current Circuits Direct Current Circuits
• Electromotive Force• Resistors in Series and Parallel• Kirchhoff’s Rules• RC Circuits• Electrical Meters
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Electromotive Force Electromotive Force
• Describing not a force but rather a potential difference in volts
• A battery is called either a source of electromotive force, or more commonly, a source of emf
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Electromotive Force Electromotive Force
• The emf of a battery is the maximum possible voltage that the battery can provide between its terminals
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Circuit Diagram
2 2Power I I R I r
a bV V V Ir
IR Ir IR r
r = internal resistance
R = load resistance
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Example #8Example #8
• A battery has an emf of 12.0 V and an internal resistance of 0.05 . Its terminals are connected to a load resistance of 3.00 .
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Resistors in Series
1 2 1 2( ) eqV IR IR I R R IR 1 2eqR R R
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Resistors in Parallel
1 21 2 eq
V V VI I I
R R R
1 2
1 1 1
eqR R R
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Example #9Example #9
• Four resistors are connected as shown in the figure, – Find the equivalent
resistance between points a and c
– What is the current in each resistor if a potential difference
of 42 V is maintained between a and c
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Example #10Example #10
• Three resistors are connected in parallel as shown in the figure 28.11 . A potential difference of 18.0 V is maintained between points a and b– Find the current in each resistor– Calculate the power delivered to
each resistor and the total power delivered to the combination of resistors
– Calculate the equivalent resistance of the circuit
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Kirchhoff’s Rules• Junction rule.
– The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction
in outI I
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Kirchhoff’s Rules• Loop rule.
– The sum of the potential differences across all elements around any closed circuit loop must be zero
0CosedLoop
V
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Example #11Example #11
• A single-loop circuit contains two resistors and two batteries, as shown in the figure (Neglect the internal resistances of the batteries.– Find the current in the circuit.– What power is delivered to each
resistor? – What power is delivered by the 12-V
battery?
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Solution #11Solution #11
The 12-V battery delivers power
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Example #12Example #12
• Find the currents I1, I2, and I3 in the circuit shown in the figure.
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Solution #12Solution #12
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RC Circuits• Charging a Capacitor
0q
IRC
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RC Circuits• Charging a Capacitor
0
t
RCI I e
Q C
0IR
current at t = 0
maximum charge
( ) 1t
RCq t Q e
time constant of the circuit
RC
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RC Circuits• Discharging a Capacitor
( 0)q t Q 0q
IRC
Charge at t = 0
( )t
RCq t Qe
0
( )( )
t t
RC RCdq t QI t e I e
dt RC
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Electrical Meters• The Galvanometer
– the main component in analog meters for measuring current and voltage
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Electrical Meters• The Ammeter
– A device that measures current
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Electrical Meters• The Voltmeter
– A device that measures potential difference
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Quiz #2Quiz #2• Find the equivalent resis
tance between points a and b i n the fi gur e
• If a pot ent i al di ff er en ce of 34.0 V i s appl i ed
between points a and b. c alculate the current in e
ach resistor.