1. General Physics L14_capacitance A device storing electrical energy
Capacitors
A device storing electrical energy

2. Capacitor
A potential across connected plates causes charge migration until equilibrium
Charge stored
q = CDV
C = capacitance
Unit = C/V = farad= F DV
– – –
+ + + –q +q

3. Field Around Infinite Plate
With uniform charge density s = Q/A s e0 1 2
E =
e0 = 8.8510–12 C2
N m2

4. Infinite ||-Plate capacitor
Individually
Together –q
1/2 s/e0 +q −q
s/e0 +q
1/2 s/e0

5. General Physics L14_capacitance
Finite Capacitor
Parallel plates of opposite charge
Charge density s = Q/A – +
Fields cancel outside
s/e0
Potential DV = d s/e0
= d Q/(Ae0)
Capacitance C = Q/V
= e0 A/d d

6. Parallel Plate Capacitance
Plate area A, plate separation d d A
Field E = s e0 = Q
Ae0
Potential DV = Ed = Qd
Ae0
Capacitance Q/DV =
Q Ae0 Qd
Ae0 d =

7. Circuit Element Symbols
+ – DV
Potential Source
Conductor
Capacitor or
Resistor

8. General Physics L14_capacitance
At Equilibrium
Capacitor charges to potential DV
Capacitor charge Q = CDV
+ – DV DV C
+ –

9. Energy in a Capacitor C = Q/V so V = Q/C Work to push charge Q
To push DQ increases as Q increases V Q
slope = 1/C

10. Energy in a Capacitor
Work to charge to Q is area of triangle W = 1/2 Q(Q/C) = 1/2 Q2/C
Work to charge to V W = 1/2 V (CV) = 1/2 C(V)2 V Q
Q/C
CDV

11. Combining Capacitors
Parallel
and
Series

12. Parallel Capacitors All have the same potential difference
Capacitances add
(conceptually add A’s)

13. Series Capacitors All have the same charge separation
Reciprocals of C are additive
(conceptually add d’s)

14. Capacitor with a Dielectric
Fill the space between the plates with a polarizable insulator (dielectric)
Reduces E field between plates
Stabilizes charge on plates
− − − − − − − − − − + −

15. Capacitor with a Dielectric
If capacitance without dielectric is C, capacitance with dielectric is kC.
k = dielectric constant k

16. Dielectric Insulator Polarizes in field
Effectively reduces plate separation d
Reduces field between plates
Dielectric constant = relative permittivity e = ke0
Capacitance C = Ae/d

17. Dielectric breakdown Strong field can separate charges
Ejects electrons from their orbitals
Dielectric becomes a conductor
Damage usually permanent
Limits practical thinness of dielectric layer

18. Some Dielectrics Material k Strength (kV/mm) Air 1.0006 3 Paper 3.8516
Teflon
2.1
19.7
Mica
3–6
118
TiO2
86–173 4
Silica
470–670

19. RC Circuits
resistor + capacitor

20. Charging a Capacitor e Initial charge Q = 0 Close switch at t = 0
+ – R
Initial charge Q = 0
Close switch at t = 0
Uncharged capacitor acts as a conductor
Charged capacitor acts as a break in the circuit
Q = Ce (1 − e−t/t)
I = e /R e−t/t

21. Time Constant t Characteristic time of the circuit
At current e/R, time to transfer charge Q
Value t = RC
Units = WF
= s

22. Discharging a Capacitor
+Q0
−Q0
Initial charge Q = Q0
Initial voltage V0 = Q0/C
Close switch at t = 0 C R
Q = Q0 e−t/t
I = V0/R e−t/t