Capacitors

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Capacitors
Physics 102 Lecture 04
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Recall from last lecture..Electric Fields,
Electric Potential
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ComparisonElectric Potential Energy vs.
Electric Potential

• DVAB the difference in electric potential
  between points B and A
• DUAB the change in electric potential energy of
  a charge q when moved from A to B
• DUAB q DVAB

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Electric Potential Summary

• E field lines point from higher to lower
  potential
• For positive charges, going from higher to lower
  potential is downhill
• For negative charges, going from lower to higher
  potential is downhill
• For a battery, the terminal is at a higher
  potential than the terminal
• Positive charges tend to go downhill, from to
  -
• Negative charges go in the opposite direction,
  from - to

DUAB q DVAB
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Important Special CaseUniform Electric Field
- - - - -

• Two large parallel conducting plates of area A
• Q on one plate
• - Q on other plate
• Then E is
• uniform between the two plates E4?kQ/A
• zero everywhere else
• This result is independent of plate separation
• This is call a parallel plate capacitor

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Parallel Plate CapacitorPotential Difference
Charge Q on plates
Charge 2Q on plates
V VA VB E0 d
V VA VB 2E0 d
E2 E0
EE0
- - - - -

- - - - -


- - - - -
A
B
d
d
Potential difference is proportional to charge
Double Q ? Double V
E04?kQ/A
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Capacitance The ability to store separated
charge C?Q/V

• Any pair conductors separated by a small
  distance. (e.g. two metal plates)
• Capacitor stores separated charge
• Positive Q on one conductor, negative Q on other
• Net charge is zero

QCV
U (½) Q V

• Stores Energy

Units 1 C/Volt 1 Farad (F)
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Why Separate Charge?

• Camera Flash
• Defibrillatorsee ex. 17.12 in text
• AC -gt DC
• Tuners
• Radio
• Cell phones

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Capacitance Practice
Example

• How much charge is on a 0.9 F capacitor which has
  a potential difference of 200 Volts?

How much energy is stored in this capacitor?
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Capacitance Practice
Example

• How much charge is on a 0.9 F capacitor which has
  a potential difference of 200 Volts?

Q CV
(0.9)(200) 180 Coulombs
How much energy is stored in this capacitor?
U ½ Q V
½ (180) (200) 18,000 Joules!
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Capacitance of Parallel Plate Capacitor

• V Ed E4?kQ/A
• (Between two large plates)
• So V 4?kQd/A
• Recall C?Q/V
• So C A/(4?kd)
• Define
• e01/(4pk)8.85x10-12 C2/Nm2

V
E

-
A
A
d
C e0A/d Parallel plate capacitor
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Parallel Plate CapacitorC e0A/d

• Calculate the capacitance of a parallel plate
  capacitor made from two large square metal sheets
  1.3 m on a side, separated by 0.1 m.

Example
A
A
d
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Parallel Plate CapacitorC e0A/d

• Calculate the capacitance of a parallel plate
  capacitor made from two large square metal sheets
  1.3 m on a side, separated by 0.1 m.

Example
A
A
d
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Dielectric

• Placing a dielectric between the plates increases
  the capacitance.
• C k C0

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ACT Parallel Plates
A parallel plate capacitor given a charge q. The
plates are then pulled a small distance further
apart. What happens to the charge q on each plate
of the capacitor?
1) Increases 2) Constant 3) Decreases
Remember charge is real/physical. There is no
place for the charges to go.
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Preflight 4.1
A parallel plate capacitor given a charge q. The
plates are then pulled a small distance further
apart. Which of the following apply to the
situation after the plates have been moved?
1)The capacitance increases True
False 2)The electric field increases
True False 3)The voltage between the plates
increases True False
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C e0A/d C decreases!
E Q/(e0A) Constant
V Ed
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ACT/Preflight 4.1
A parallel plate capacitor given a charge q. The
plates are then pulled a small distance further
apart. Which of the following apply to the
situation after the plates have been moved?
The energy stored in the capacitor
A) increases B) constant C) decreases
U ½ QV Q constant, V increased
Plates are attracted to each other, you must pull
them apart, so the potential energy of the plates
increases.
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ACT/Preflight 4.2
Two identical parallel plate capacitors are shown
in end-view in A) of the figure. Each has a
capacitance of C.
B
)
A
)
If the two are joined as in (B) of the figure,
forming a single capacitor, what is the final
capacitance?
63 7 30
1) 2C 2) C 3) C/2
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Voltage in Circuits

• Elements are connected by wires.
• Any connected region of wire has the same
  potential.

• The potential difference across an element is the
  elements voltage.

Example
C1
C2
C3
VC1 5-0 V 5 V
VC3 15-12 V 3 V
VC2 12-5 V 7 V
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Capacitors in Parallel

• Both ends connected together by wire

• Add Areas Ceq C1C2 remember C?0A/d
• Share Charge Qeq Q1Q2

Veq

• Same voltage V1 V2

15 V
15 V
C1
C2
10 V
10 V
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Parallel Practice

• A 4 mF capacitor and 6 mF capacitor are connected
  in parallel and charged to 5 volts. Calculate
  Ceq, and the charge on each capacitor.

Example
4 mF6 mF 10 mF
Ceq C4C6
Q4 C4 V4
(4 mF)(5 V) 20 mC
Q6 C6 V6
(6 mF)(5 V) 30 mC
Qeq Ceq Veq
(10 mF)(5 V) 50 mC
Q4Q6
V 5 V
5 V
5 V
5 V
C4
C6
Ceq
0 V
0 V
0 V
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Capacitors in Series

• Connected end-to-end with NO other exits
• Same Charge Q1 Q2 Qeq

• Add d

• Share VoltageV1V2Veq

Q


C1


-




C2
-Q
-

-


36

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Series Practice

• A 4 mF capacitor and 6 mF capacitor are connected
  in series and charged to 5 volts. Calculate Ceq,
  and the charge on the 4 mF capacitor.

Example
Q CV
5 V

C4
Ceq
-

C6
-
0 V
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ComparisonSeries vs. Parallel

• Series
• Can follow a wire from one element to the other
  with no branches in between.

• Parallel
• Can find a loop of wire containing both elements
  but no others (may have branches).

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Electromotive Force

-

• Battery
• Maintains constant potential difference V
• Does NOT produce or supply charges, just pushes
  them.

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Preflight 4.4
A circuit consists of three initially uncharged
capacitors C1, C2, and C3, which are then
connected to a battery of emf E. The
capacitors obtain charges q1, q2,q3, and have
voltages across their plates V1, V2, and V3.
Which of these are true?

• q1 q2
• q2 q3
• V2 V3
• E V1
• V1 lt V2
• Ceq gt C1

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ACT/Preflight 4.4 Which is true?
A circuit consists of three initially uncharged
capacitors C1, C2, and C3, which are then
connected to a battery of emf E. The
capacitors obtain charges q1, q2,q3, and have
voltages across their plates V1, V2, and V3.
1) q1 q2
Not necessarily C1 and C2 are NOT in series.
2) q2 q3
Yes! C2 and C3 are in series.
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ACT/Preflight 4.4 Which is true?
A circuit consists of three initially uncharged
capacitors C1, C2, and C3, which are then
connected to a battery of emf E. The
capacitors obtain charges q1, q2,q3, and have
voltages across their plates V1, V2, and V3.
1) V2 V3
Not necessarily, only if C1 C2
2) E V1
Yes! Both ends are connected by wires
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ACT/Preflight 4.4 Which is true?
A circuit consists of three initially uncharged
capacitors C1, C2, and C3, which are then
connected to a battery of emf E. The
capacitors obtain charges q1, q2,q3, and have
voltages across their plates V1, V2, and V3.
1) V1 lt V2
Nope, V1 gt V2. (E.g. V1 10-0, V2 10-7
2) Ceq gt C1
Yes! C1 is in parallel with C23
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Recap of Todays Lecture

• Capacitance C Q/V
• Parallel Plate C ?0A/d
• Capacitors in parallel Ceq C1C2
• Capacitors in series Ceq 1/(1/C11/C2)
• Batteries provide fixed potential difference