First slide

Redistribution of charges and concept of common potential

Question

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 :

Moderate

A

$\frac{25}{6} {CV}^{2}$
B

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

$z e r o$
D

$\frac{3}{2} {CV}^{2}$

Solution

$\begin{array}{l} Q_{f i n a l} = 4 C V - C V = 3 C V \\ C_{n e t} = C + 2 C = 3 C \\ \Rightarrow U_{final} = \frac{1}{2} \frac{{(Q_{final})}^{2}}{C_{net}} \\ \Rightarrow U_{final} = \frac{1}{2} \frac{{(3 CV)}^{2}}{3 C} \\ \Rightarrow U_{final} = \frac{3}{2} {CV}^{2} \end{array}$

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