Using a battery, a 100 pF capacitor is charged to 60 V and then the...

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)

Options

A $600$
B $200$
C $400$
D $100$

Correct answer

B. $200$

Step-by-step solution

New potential

=\frac{\mathrm{C}_0 \mathrm{~V}_0}{\mathrm{C}_0+\mathrm{C}}=\frac{\mathrm{V}_0}{3}

\begin{aligned} & 3 \mathrm{C}_0 \mathrm{~V}_0=\mathrm{C}_0 \mathrm{~V}_0+\mathrm{CV}_0 \\ & 2 \mathrm{C}_0 \mathrm{~V}_0=\mathrm{CV}_0 \\ & \mathrm{C} \Rightarrow 2 \mathrm{C}_0\end{aligned}

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