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Two identical capacitors each of capacitance $5 \mu \mathrm{F}$ are charged to potentials $2 \mathrm{kV}$ and $1 \mathrm{kV}$ respectively, Their -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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1.25 J
$\begin{array}\\ \text { Loss of energy } & =\frac{1}{2} \frac{C_{1} C_{2}}{\left(C_{1}+C_{2}\right)}\left(V_{1}-V_{2}\right)^{2} \\ = & \frac{1}{2} \frac{5 \times 10^{-6} \times 5 \times 10^{-6}(2000-1000)^{2}}{(5+5) \times 10^{-6}} \\ = & \frac{5 \times 5}{2 \times 10}=1.25 \mathrm{~J}\end{array}$
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