Question

If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.

Options

• increases to 3 times its initial value

• increases to 9 times its initial value

• increases to 27 times its initial value

• decreases to 1/3 times its initial value

Answer 1

If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor increases to 9 times its initial value.

Explanation:

`"E"_1 = 1/2 "CV"_1^2, "E"_2 = 1/2 "CV"_2^2`

`therefore "E"_1/"E"_2 = "V"_1^2/"V"_2^2`

`therefore "E"_2 = "V"_2^2/"V"_1^2  "E"_1`

`= 900/100 xx "E"_1`

`= 9  "E"_1`