A capacitor consists of two parallel plates of area A separated by a distance d. The capacitor carries a charge Q. If the separation between the plates is doubled while keeping the plates insulated so that no charge is lost, then the energy stored in the capacitor is.

a. will quadruple.
b. be cut in fourth.
c. double.
d. be cut in half.
e. not change.

c. doubled

Explanation:

The Energy stored in a capacitor is given as,

E = 1/2Q²/C Equation 1

Where E = Energy stored in the capacitor, C = Capacitance of the capacitor, Q = Charge.

Also,

C = εA/d Equation 2

Where A = cross sectional area of the plate, d = distance of separation between the plate, ε = Permitivity of the material.

Substitute equation 1 into Equation 2

E = 1/2Q²/( εA/d)

E = 1/2Q²d/εA Equation 3

If the distance of separation of the plates is doubled,

distance = 2d

Substitute the distance into equation 3

E' = 1/2Q²(2d)/εA

E' = Q²d/εA Equation 4

Comparing equation 3 and equation 4, It can be seen that,

E' = 2×E

Hence the Energy is doubled when the distance of separation of the plates is doubled.

The right option is c. doubled

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