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  4. Two indentical capacitors each of capacitance 5 μ F are charged to potentials 2 kV and 1 kV respectively. The -ve ends are connected together. When the +ve ends are also connected together, the loss of energy of the system is

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Q. Two indentical capacitors each of capacitance $5 \mu F$ are charged to potentials $2 \,kV$ and $1\, kV$ respectively. The $-ve$ ends are connected together. When the $+ve$ ends are also connected together, the loss of energy of the system is

KCETKCET 2007Electrostatic Potential and Capacitance

Solution:

Loss of energy $ = \frac{1}{2} \frac{C_{1}C_{2}}{\left(C_{1} + C_{2}\right)} \left(V_{1} -V_{2}\right)^{2} $
$= \frac{1}{2} \frac{5\times10^{-6} \times5 \times 10^{-6}\left(2000-1000\right)^{2}}{\left(5+5\right)\times 10^{-6}} $
$ = \frac{5\times 5}{2\times 10} =1.25\, J$