A $2 μ F$ capacitor $C_{1}$ is charged to a voltage 100 V and a 4 $μ F$ capacitor $C_{2}$ is charged to a voltage 50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel connection?

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$1.7 \times 10^{- 3} J$

0.17 J

$1.7 \times 10^{- 2} J$

1.7 J

answer is C.

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Detailed Solution

Common potential in parallel grouping,

$V = \frac{Total charg e}{Total capacity}$

$= \frac{(2 \times 100) + (4 \times 50)}{2 + 4}$

$= \frac{200}{3} V$

Loss $= U_{i} - U_{f}$

$= 10^{- 6} [(\frac{1}{2} \times 2 \times 100 \times 100 + \frac{1}{2} + 4 \times 50 \times 50) - (\frac{1}{2} \times 6 \times \frac{200}{3} \times \frac{200}{3})$

$= 1.7 \times 10^{- 3} J$

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