A series combination of n₁ capacitors, each of value C₁ is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C₂, in terms of C₁ is then

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$\frac{16 C_{1}}{n_{1} n_{2}}$

$2 \frac{n_{2}}{n_{1}} C_{1}$

$\frac{2 C_{1}}{n_{1} n_{2}}$

$16 \frac{n_{2}}{n_{1}} C_{1}$

answer is D.

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Detailed Solution

$\begin{array}{rcl} \frac{1}{2} \frac{C_{1}}{n_{1}} 16 V^{2} & = & \frac{1}{2} n_{2} C_{2} V^{2} \\ \frac{16 C_{1}}{n_{1} n_{2}} & = & C_{2} \end{array}$

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