Question

Two capacitors of capacitances 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 potentialenergy 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 $3C{V}^2$

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

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

$=3C{V}^2$