Question

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

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

Answer 1

Answer: (C)

Before closing switch $U_i=\frac{1}{2}\times \frac{3C\times 2C}{3C+2C}\times V^2$
$=\frac{3}{5}C{V}^2$
After closing switch $U_f=\frac{1}{2}C{V}^2+\frac{3}{5}C{V}^2$
$Energysupplybybattery=CV\times V=C{V}^2$
$C{V}^2=U_f-U_i+\Delta H$
$C{V}^2=\frac{1}{2}C{V}^2+\Delta H$
$\Delta H=\frac{1}{2}C{V}^2$