A capacitor is charged with a battery and energy stored is $U$. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is
AIPMT 2000, Medium
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Now charge will flow in such a way that total charge is $Q$ and potential diffrence across both capacitors remains same.
$V =\frac{ Q }{2 C }$
Energy in each capacitor $=\frac{1}{2} CV ^{2}=\frac{1}{2} C \left(\frac{ Q }{2 C }\right)^{2}=\frac{1}{4}\cdot \frac{1}{2} \left(\frac{ Q ^{2}}{2 C }\right) =\frac{ U }{4}$
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