Question

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.

Answer 1

c. doubled

Step-by-step 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