A 4μF conductor is charged to 400 volts and then its plates are joined through a resistance of 1kΩ. The heat produced in the resistance is ?

A 4μF conductor is charged to 400 volts and then its plates are joined through a resistance of 1kΩ. The heat produced in the resistance is ?

(a) 0.16 J

(b) 1.28 J

(c) 0.64 J

(d) 0.32 J

Answer :  (d) 0.32 J

\( H = i^2 R t \)

\( \quad = \frac{V^2}{R} \cdot t \)

This cannot be used because as \( q \) reduces, \( V \downarrow \ i \downarrow \). So it is not constant.

Energy stored in a capacitor is converted as heat energy.

Energy stored \( = \frac{1}{2} C V^2 \)

\( = \frac{1}{2} (4 \mu) \cdot 400^2 \)

\( = \frac{1}{2} \cdot 4 \times 10^{-6} \cdot 4^2 \times 10^4 \)

\( = 0.32\, \text{J} \)