Capacitors and Dielectrics — Formula Sheet

C = Q/V

1 farad = 1 coulomb/volt

C = 4π ε0 a

C_K = 4π ε0 K a

Dimensions of capacitance = M^-1 L^-2 T^4 A^2

U = (1/2)(Q^2/C) = (1/2)CV^2

V = (Q1 + Q2)/(C1 + C2) = (C1V1 + C2V2)/(C1 + C2)

U - U' = [C1C2/(2(C1 + C2))](V1 - V2)^2

Charge transferred = [C1C2(V1 - V2)]/(C1 + C2)

C0 = ε0A/d

C = Kε0A/d

C = ε0A/(d - t + t/K)

C = ε0A/(t1/K1 + t2/K2 + t3/K3 + ... )

When a conductor of capacitance C is charged to Q, its potential is V = Q/C.

Potential energy of a charged conductor is U = (1/2)Q^2/C = (1/2)CV^2.

C = Q / V is the defining relation.

U = (1/2) Q^2 / C = (1/2) C V^2.

The capacitance of an isolated spherical conductor is C = 4πε0a, where a is the radius.