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  • Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :
Option: 1 \frac{V}{K+2}      
Option: 2 \frac{V}{K}
Option: 3 \frac{3V}{K+2}
Option: 4 \frac{3V}{K}

Answers (1)

best_answer

Initial :

\begin{aligned} &q_{1}=(2 c) v \\ &q_{2}=c V \end{aligned}

Final :

For selected node, by charge conservation.

\begin{aligned} q_{1}+q_{2} &=q_{1 f}+q_{2 f} \\ 2 c V+c V &=2 cV^{\prime}+(c k) V^{\prime} \end{aligned}

V^{\prime}=\frac{3 C V}{(2 c+c k)}=\frac{3 V}{(2+k)}

V^{\prime} \rightarrow the common potential of both the capacitors.

The correct option is (3).

Posted by

vishal kumar

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