Question

Two capacitors of capacitance $C$ and $2C$ are charged to potentials $2V$ and $V$ respectively and then these capacitors are disconnected from the charging batteries. Now capacitors are connected together such that their opposite polarity plates are connected together. The loss in potential energy of the system, is

• A. $\frac{3}{8}C{V}^2$
• B. $\frac{3}{2}C{V}^2$
• C. $\frac{3}{4}C{V}^2$
• D. $3C{V}^2$

Answer 1

The correct option is D $3C{V}^2$

$\Delta U=\frac{1}{2}\frac{C_1{C}_2}{C_1+C_2}(V_1-V_2{)}^2$

$=\frac{1}{2}\times \frac{2C}{3}\times 9V^2$

$=3C{V}^2$