Question

A capacitor of capacitance 5$\mu$F is charged by a battery of emf 10V. At an instant of time, the potential difference across the capacitors is 4V and the time rate of change of potential difference across the capacitor is 0.6 V/s. Then the time rate at which energy is stored in the capacitor at the instant is

• A. 12$\mu$W
• B. 3$\mu$W
• C. Zero
• D. 30$\mu$W

Answer 1

The Correct Option is A

The energy stored in a capacitor is given by:
\( U = \frac{1}{2} C V^2 \)
where \( C = 5 \mu F \) and \( V = 4 \, \text{V} \). 

The rate at which energy is stored in the capacitor is the derivative of the energy with respect to time:
\( \frac{dU}{dt} = C V \frac{dV}{dt} \) 
Substituting the known values:\( \frac{dU}{dt} = 5 \times 10^{-6} \times 4 \times 0.6 = 12 \times 10^{-6} \text{W} = 12 \mu \text{W} \) 

Thus, the rate at which energy is stored in the capacitor is 12$\mu$W.