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Q.

Two capacitors of capacitance $C$ and $2 C$ are charged to potential differences $V$ and $2 V$ , respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :

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a

$\frac{25}{6} C V^{2}$

b

$\frac{3}{2} C V^{2}$

c

Zero

d

$\frac{9}{2} C V^{2}$

answer is B.

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Detailed Solution

When capacitors C and 2C capacitance are charged to V and 2V respectively.
Question Image
$Q_{1} = C V; Q_{2} = 2 C \times 2 V = 4 C V$
When connected in parallel
By conservation of charge
$\begin{array}{l} 4 C V - C V = (C + 2 C) V_{common} \\ \Rightarrow V_{com} = \frac{3 C V}{3 C} = V \\ U_{F} = [\frac{1}{2} C V^{2} + \frac{1}{2} 2 C V^{2}] \\ = \frac{3}{2} C V^{2} \end{array}$

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Two capacitors of capacitance C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :