A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
IIT 1995, Medium
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(c) Total charge $ = (2C)\,(2V) + (C)\,( - V) = 3CV$
Common potential $ = \frac{{3CV}}{{3C}} = V$
Energy $ = \frac{1}{2}(3C)\,{(V)^2} = \frac{3}{2}C{V^2}$
Common potential $ = \frac{{3CV}}{{3C}} = V$
Energy $ = \frac{1}{2}(3C)\,{(V)^2} = \frac{3}{2}C{V^2}$
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