Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\, V$ and $500\, V$ respectively. The energy loss, when they are connected by a wire is
Medium
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$ \Delta \mathrm{U} =\frac{1}{2} \frac{\mathrm{C}_{1} \mathrm{C}_{2}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)^{2}}{\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right)} $
$=\frac{1}{2} \times \frac{(3 \times 5) \times 10^{-12} \times(500-300)^{2}}{(3+5) \times 10^{-6}} $
$=\frac{15 \times 10^{-12} \times 4 \times 10^{4}}{2 \times 8 \times 10^{-6}}=0.0375 \mathrm{\,J} $
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