Question

Two insulated metallic spheres of \(3 \mu F\) and \(5 \mu F\) capacitance are charged to \(300 V\) and \(500 V\) respectively. The energy loss, when they are connected by a wire is

Answer 1

Energy loss in charge redistribution
Loss of energy \(=\dfrac{1}{2}\dfrac{C_1C_2}{C_1+C_2} (V_1−V_2)^2\)
here, \(\dfrac{C_1C_2}{C_1+C_2}=\dfrac{3\times10^{−6}F\times5\times10^{−6}F}{(3+5) (10^{−6})F}\)
\(=\dfrac{15}{8}\times10^{−6}F\)
Loss of energy \(=\dfrac{1}{2}\times\dfrac{15}{8}\times10^{−6}F\times(500 V−300 V)^2\)
\(=\dfrac{15}{4}\times10^{−2}\)
\(= 0.0375 J\)
Thus, energy lost is \(0.0375 J\)