2. Electric Potential and Capacitance
medium

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

A

Zero

B

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

C

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

D

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

(IIT-1995)

Solution

(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}$

Standard 12
Physics

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