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2. Electric Potential and Capacitance
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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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