Question

In the given circuit diagram. Find the heat generated on closing the switch $S$ (Initially the capacitor of capacitance $C$ is uncharged) -

• A. $\frac{3}{2}CV^{2}$
• B. $C V^{2}$
• C. $\frac{1}{2}C V^{2}$
• D. $2 \, C V^{2}$

Answer 1

Answer: (C)

Before closing switch $U_{i}=\frac{1}{2} \, \times \, \frac{3 C \times 2 C}{3 C + 2 C}\times \, V^{2}$
$=\frac{3}{5}C V^{2}$
After closing switch $U_{f}=\frac{1}{2} \, CV^{2}+\frac{3}{5}CV^{2}$
$Energy \, supply \, by \, battery=CV \, \times \, V=C V^{2}$
$C V^{2}=U_{f}- \, U_{i}+\Delta H$
$CV^{2}=\frac{1}{2} \, CV^{2}+\Delta H$
$\Delta H=\frac{1}{2} \, C V^{2}$