Capacitor Equations

Question 1

Capacitance Definition

Answer 1

C=Q / delta V

Question 2

Parallel Plate Capacitence

Answer 2

C = E0 A K / d

Question 3

Capacitors in Parallel

Answer 3

Capacitance adds in parallel, with total capaitance greater then greatest individual.

V is same for all capacitors in parallel.

Question 4

Capacitors in Series

Answer 4

Capacitance decreases in series, with total capacitance lesser then least.

Q is same for all capacitors in series.

Question 5

Energy Stored

Answer 5

= 1/2 CV^2

Question 6

Charging RC Voltage

Answer 6

Emf (1-e^(-t/Tau) )

Question 7

Charging & Discharging RC Current

Answer 7

Emf/R (e^-t/Tau)

Question 8

Charging RC Charge

Answer 8

C*Emf (1-e^(-t/Tau))

Question 9

Discharging RC Voltage

Answer 9

Emf e^-t/Tau

Question 10

Discharging RC Charge

Answer 10

C*Emf e^-t/Tau

Question 11

General RC (Capacitor)

Answer 11

Tau = RC. Voltage on charging capacitor goes to a limit, along with charge. Voltage & charge on discharging capacitor decay.

I always decays, either from capacitor turning into a gap or from losing the steady source of voltage.

Question 12

Power on Capacitor

Answer 12

P=IV=V^2 / R = I^2 R. Instaneous is annoying.

Question 13

Electric Field from One Plane

Answer 13

Using Gaussian Surface of a subdivided cylinder, and qenc = density * area,
E = density/ 2*epsilon

Double for capacitor.

Question 14

Kappa

Answer 14

Electric Permativity = Kappa * E0 (free space permativity)

Question 15

Capacitance, Spherical

Answer 15

By integrating Potential E=kQ/r over a sphere with Edr,

C=Q/V = (1) / (k (1/ra - 1/rb) ), where ra is the smaller sphere and r/b the larger.

Question 16

Capacitance, Cylindrical

Answer 16

By finding E = 2kQ / L *r, and integrating 1/s for voltage into ln,

C = Q/deltaV = L / (2k) (ln b/a)