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Capacitors, Multimeters, Circuit Analysis. Capacitor: Charging and Discharging. Charging. Discharging. Capacitor: Construction and Symbols. The capacitor in your set is similar to a large two-disk capacitor. D. s. There is no connecting path through a capacitor. - PowerPoint PPT Presentation
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Capacitors, Multimeters, Circuit Analysis
Capacitor: Charging and Discharging
Charging Discharging
The capacitor in your set is similar to a large two-disk capacitor
s
D
Capacitor: Construction and Symbols
There is no connecting path through a capacitor
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.
Capacitor: Charging
Ultimately, the fringe field of the capacitor and the fielddue to charges on the wire are such that E=0 inside the wire. At this point, i=0.
Why does current ultimately stop flowing in the circuit?
Thick filamentThin filament
Which light bulb will glow longer?
Why?1) Round is brighter capacitor gets charged more?
2) Long bulb glows longer capacitor gets charged more?
The Effect of Different Light Bulbs
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?
Electric field in a capacitor:0
/
AQE
E
s
+Q-Q
f
i
ldEV
EsV
sAQV0
/
VsAQ 0
VQ ~In general:
Definition of capacitance:VCQ
Capacitance
Capacitance of a parallel-plate capacitor:
sAC 0
Capacitance
Capacitance
Michael Faraday(1791 - 1867)
VCQ
Units: C/V, Farads (F)
The capacitor in your set is equivalent to a large two-disk capacitor
s=1 mm
D
How large would it be?
sAC 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
A capacitor is formed by two rectangular plates 50 cm by 30 cm, and the gap between the plates is 0.25 mm. What is its capacitance?
sAC 0
C 0A
s
9 10 12 C2 /N m2 0.15 m2 2.5 10 4 m
5.4 10 9 F 5.4 nF
Exercise
s
D
No insulator:
0
/
AQE
EsV
sAQV0
/
VsAQ 0
sAC 0
With insulator:
0
/KAQE
EsV
sK
AQV0
/
Vs
AKQ 0
sAKC 0
A Capacitor With an Insulator Between the Plates
Ammeter: measures current I
Voltmeter: measures voltage difference V
Ohmmeter: measures resistance R
Ammeters, Voltmeters and Ohmmeters
0.150
Connecting ammeter:
Conventional current must flow into the ‘+’ terminal and emerge from the ‘-’ terminal to result in positive reading.
Using an Ammeter
Simple ammeter using your lab kit:
Simple commercialammeter
Digital ammeters: uses semiconductor elements.ADC – analog-to-digital converter(Combination of comparator and DAC)
Ammeter Design
VAB – add a series resistor to ammeter
RVI
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
R
How would you measure R?
A
Ohmmeter
RemfI
Iemf
Ohmmeter
Ammeter with a small voltage source
0_ Ctripround VRIemfV
CQVC
0CQRIemf
I dQdt
emf Q / C
R
Initial situation: Q=0R
emfI 0
Q and I are changing in time dtd
RCQ
dtd
Remf
dtd
dtdI
dtdQ
RCdtdI 1
IRCdt
dI 1
Quantitative Analysis of an RC Circuit
IRCdt
dI 1
dtRC
dII
11
tI
I
dtRC
dII 0
11
0
RCtII 0lnln
RCt
II
0
ln
RCt
eII
0
RCteII /0
Current in an RC circuit
What is I0 ?
RCteR
emfI /
Current in an RC circuit
RC Circuit: Current
What about charge Q?
RCteR
emfI /
Current in an RC circuit
dtdQI
IdtdQ
t
RCtt
dteR
emfIdtQ0
/
0
Q C emf 1 e t / RC
RC Circuit: Charge and Voltage
RCteR
emfI /
Current in an RC circuit
Charge in an RC circuit
Q C emf 1 e t / RC
Voltage in an RC circuitV emf 1 e t / RC
RC Circuit: Summary
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.
37.0718.211/ ee RCt
The RC Time Constant
A rough measurement of how long it takes to reach final equilibrium
What is the value of RC?
About 9 seconds
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
A B
C D
What is the final charge on a 1 F capacitor connected to a 1.5V battery through resistor 100 ?
C 5.1 VCQ
Can you apply the RC equations to the circuit below?
RCteR
emfI /
Current in an RC circuit
No! Resistance depends on current.
Exercise
Find currents through resistors
Loop 1
Loop 2
Loop 3
Loop 4
I1
I2
I3
I5I4
loop 1:017441111 IRIRIRIremf
loop 2:033262222 IRIRemfIrIR
loop 3:0553344 IRIRIR
nodes:04321 IIII
0523 III0154 III
Five independent equations and five unknowns
Exercise: A Complicated Resistive Circuit
