A capacitor $4 \mu F$ charged to 50 V is connected to another capacitor of $2 \mu F$ charged to 100 V with plates of like charges connected together. The total energy before and after connection in multiples of $(10^{-2} J)$ is
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The total energy before connection
$=\frac{1}{2}\times 4\times 10^{-6}\times (50)^2 + \frac{1}{2}\times 2\times 10^{-6}\times (100)^2$
$= 1.5 \times 10^{-2} \, J$
When connected in parallel
$4 \times 50 + 2 \times 100 = 6 \times V$ ⇒ ⇒ $V = \frac{200}{3}$
Total energy after connection
$= \frac{1}{2} \times 6 \times 10^{-6} \times \left(\frac{200}{3}\right)^2 = 1.33 \times 10^{-2} J$
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