Question

Find the increase in energy of a condenser of capacity \(6\, \text{pF}\) on changing the potential difference from 10 V to 20 V.

Hint:

Energy stored in capacitor is proportional to the square of the voltage.

Answer 1

The energy stored in a condenser (capacitor) is given by \[ U = \frac{1}{2} C V^2, \] where \(C\) is the capacitance and \(V\) is the potential difference. Initial energy: \[ U_1 = \frac{1}{2} \times 6 \times 10^{-12} \times (10)^2 = 3 \times 10^{-10} \text{ J}. \] Final energy: \[ U_2 = \frac{1}{2} \times 6 \times 10^{-12} \times (20)^2 = 1.2 \times 10^{-9} \text{ J}. \] Increase in energy: \[ \Delta U = U_2 - U_1 = 1.2 \times 10^{-9} - 3 \times 10^{-10} = 9 \times 10^{-10} \text{ J} = 6 \times 10^{-7} \text{ J}. \]