Question

In the given circuit, switch $S$ is open initially. If $C=2\, \mu F$ and $V=3\, V$, then find the heat produced (in $\mu J$ ) in the circuit after closing the switch.

Answer 1

$U_{i}=\frac{1}{2} C \cdot\left(\frac{V}{2}\right)^{2} \cdot 2 ; U_{f}=\frac{1}{2} C V^{2}=\frac{C V^{2}}{2}$
$W_{\text {Cell }}=V \cdot \Delta q=V \cdot\left(C V-\frac{C V}{2}\right)=\frac{C V^{2}}{2}$
Now, $U_{i}+W_{\text {cell }}=U_{f}+H$
$\therefore H=\frac{C V^{2}}{4}=\frac{2 \times 9}{4}=4.50$