circuit elements. conventional current: widely known as ohm’s law resistance of a long wire:...
TRANSCRIPT
![Page 1: Circuit Elements. Conventional current: Widely known as Ohm’s law Resistance of a long wire: Units: Ohm, George Ohm (1789-1854) Resistance Resistance](https://reader035.vdocuments.site/reader035/viewer/2022081515/56649da15503460f94a8d776/html5/thumbnails/1.jpg)
Circuit Elements
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Conventional current: Widely known as Ohm’s law
Resistance of a long wire:
Units: Ohm, George Ohm(1789-1854)
Resistance
Resistance combines conductivity and geometry!
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Microscopic Macroscopic
Can we write V=IR ?
Microscopic and Macroscopic View
Current flows in response to a DV
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L=5 mm
A = 0.002 mm2
Conductivity of Carbon: = 3.104 (A/m2)/(V/m)
What is its resistance R?
(V/A)
What would be the current through this resistor if connected to a 1.5 V battery?
Exercise: Carbon Resistor
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Mobility of electrons: depends on temperature
Conductivity and resistance depend on temperature.
Conductivity may also depend on the magnitude of current.
Constant and Varying Conductivity
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Ohmic resistor: resistor made of ohmic material
Ohmic materials: materials in which conductivity is independent of the amount of current flowing through
not a function of current
Examples of ohmic materials:metal, carbon (at constant T!)
Ohmic Resistors
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Tungsten: mobility at room temperature is larger than at ‘glowing’ temperature (~3000 K)
V-A dependence:3 V 100 mA1.5 V 80 mA0.05 V 6 mA
R30 19 8
V
I
Is a Light Bulb an Ohmic Resistor?
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Metals, mobile electrons: slightest V produces current.
If electrons were bound – we would need to apply some field to free some of them in order for current to flow. Metals do not behave like this!
Semiconductors: n depends exponentially on E
Conductivity depends exponentially on E
Conductivity rises (resistance drops)with rising temperature
Semiconductors
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Capacitors |V|=Q/C, function of time
Batteries: double current, but |V|emf, hardly changes
has limited validity!Ohmic when R is indep-pendent of I!
Conventional symbols:
Nonohmic Circuit Elements
Semiconductors
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Vbatt + V1 + V2 + V3 = 0
emf - R1I - R2I - R3I = 0
emf = R1I + R2I + R3I
emf = (R1 + R2 + R3) I
emf = Requivalent I , where Requivalent = R1 + R2 + R3
Series Resistance
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Know R , find V1,2
Solution:
1) Find current:
2) Find voltage:
3) Check:
Exercise: Voltage Divider
R1
R2
V1
V2
emf
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I = I1 + I2 + I3
Parallel Resistance
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R1 = 30
R2 = 10
What is the equivalent resistance?
What is the total current?
Alternative way:
Two Light Bulbs in Parallel
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What would you expect if one is unscrewed?
Two Light Bulbs in Parallel
A) The single bulb is brighterB) No differenceC) The single bulb is dimmer
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Current: charges are moving work is done
Work = change in electric potential energy of charges
Power = work per unit time:
I
Power for any kind of circuit component:
Work and Power in a Circuit
Units:
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emf RKnow V, find P
Know I, find P
In practice: need to know P to select right size resistor – capable of dissipating thermal energy created by current.
Power Dissipated by a Resistor
What is the power output of the battery?
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Electric field in a capacitor:0
/
AQ
E
E
s
+Q-Q
f
i
ldEV
EsV
sAQ
V0
/
V
s
AQ 0
VQ ~In general:
Definition of capacitance:VCQ
Capacitance
Capacitance of a parallel-plate capacitor:
s
AC 0
Capacitance
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Capacitance
Michael Faraday
(1791 - 1867)
VCQ
Units: C/V, Farads (F)
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This 1 Farad capacitor is equivalent to a large two-disk capacitor
s=1 mm
D
How large would it be?
s
AC 0
0
CsA
A 1 F 0.001 m
9 10 12 C2 /N m2 A 1.1108 m2
D ~ 10 km (6 miles)
Exercise
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Alternative approach:
Energy density:
Energy:
Energy Stored in a Capacitor
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Capacitor: Charging and Discharging
Charging Discharging
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Positive and negative charges are attracted to each other: how can they leave the plates?
Fringe field is not zero!
How is Discharging Possible?
Electrons in the wire near the negative plate feel a force thatmoves them away from the negative plate.
Electrons near the positive plate are attracted towards it.
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Initial moment: brighter?
Will it glow longer?
Parallel Capacitors
Fringe field:R
sAQE
01 2
/
Capacitors in parallel effectively increase A
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Will it glow at all?How do electrons flow throughthe bulb?
An Isolated Light Bulb
Why do we show charges nearbulb as - on the left and + onthe right?
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Ammeter: measures current I
Voltmeter: measures voltage difference V
Ohmmeter: measures resistance R
Ammeters, Voltmeters and Ohmmeters
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0.150
Connecting ammeter:
Conventional current must flow into the ‘+’ terminal and emerge from the ‘-’ terminal to result in positive reading.
Using an Ammeter
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Simple commercialammeter
Ammeter Design
Want tiny resistance in coil so current isn’t affected
What happens if not connected correctly?
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VAB – add a series resistor to ammeter
R
VI
Measure I and convert to VAB=IR
Connecting Voltmeter:
Higher potential must be connected to the ‘+’ socket and lower one to the ‘-’ socket to result in positive reading.
VoltmeterVoltmeters measure potential difference
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R
How would you measure R?
A
Ohmmeter
R
emfI
I
emf
Ohmmeter
Ammeter with a small voltage source
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0_ Ctripround VRIemfV
C
QVC
0C
QRIemf
I dQ
dt
emf Q / C
R
Initial situation: Q=0R
emfI 0
Q and I are changing in timedt
d
RC
Q
dt
d
R
emf
dt
d
dt
dIdt
dQ
RCdt
dI 1 I
RCdt
dI 1
Quantitative Analysis of an RC Circuit
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IRCdt
dI 1
dtRC
dII
11
tI
I
dtRC
dII 0
11
0
RC
tII 0lnln
RC
t
I
I
0
ln
RC
t
eI
I
0
RCteII /0
Current in an RC circuit
What is I0 ?
RCteR
emfI /
Current in an RC circuit
RC Circuit: Current
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What about charge Q?
RCteR
emfI /
Current in an RC circuit
dt
dQI
IdtdQ
t
RCtt
dteR
emfIdtQ
0
/
0
Q C emf 1 e t / RC
RC Circuit: Charge and Voltage
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RCteR
emfI /
Current in an RC circuit
Charge in an RC circuit
Q C emf 1 e t / RC
Voltage in an RC circuit
V emf 1 e t / RC
RC Circuit: Summary
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RCteR
emfI /
Current in an RC circuit
When time t = RC, the current I drops by a factor of e.
RC is the ‘time constant’ of an RC circuit.
37.0718.2
11/ ee RCt
The RC Time Constant
A rough measurement of how long it takes to reach final equilibrium
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What is the value of RC?
About 9 seconds
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Question
A 0.5 farad capacitor isconnected to a 1.5 voltbattery and a bulb, andcurrent runs until the bulbgoes out. What is theabsolute value of thecharge on one plate of thecapacitor?
A) 0.33 CB) 0.5 CC) 0.75 CD) 1.5 CE) 3.0 C