Question

If the charge on the parallel plate capacitor is increased by 3 C, the energy stored in it increases by 44%. The original charge on the capacitor is ______.

Options

• 10 C

• 15 C

• 20 C

• 25 C

Answer 1

If the charge on the parallel plate capacitor is increased by 3 C, the energy stored in it increases by 44%. The original charge on the capacitor is 15 C.

Explanation:

The energy stored in a capacitor with charge Q and capacitance C is:

U = `Q^2/(2 C)`

Since capacitance C remains constant, U ∝ Q²

As per the given condition, when,

Q₂ = (Q₁ + 3)

∴ `U_2 = 44%  "of"  U_1 = 144/100 U_1`

∴ `(Q_2^2)/(2 C) = 144/100 xx Q_2^1/(2 C)`

∴ `Q_1 = 10/12 Q_2`

∴ `Q_1 = 5/6 (Q_1 + 3)`

∴ 6Q₁ = 5Q₁ + 15

∴ Q₁ = 15 C