Question

Two capacitors are completely charged by a battery as shown in figure. Then battery is taken out and capacitor are connected together such that plates of opposite polarity are connected together. Select the correct statement :-

• A. No charge distribution will take place.
• B. Final potential on each capacitor is $\frac{V}{2}$
• C. Energy loss in charge distribution process is $\frac{4C{V}^2}{3}$
• D. Final charge on each capacitor will be equal.

Answer 1

Answer: (C)

Now, polarity change

$V_{common}=\frac{-CV+2CV}{3C}=\frac{V}{3}$
Charge flow $\Rightarrow 2CV-\frac{2CV}{3}\Rightarrow \frac{4CV}{3}$
Energy loss
$=\frac{1}{2}C{V}^2+\frac{1}{2}2C{V}^2-\frac{1}{2}C{\left(\frac{V}{3}\right)}^2-\frac{1}{2}2C{\left(\frac{V}{3}\right)}^2$
$=\frac{4}{3}C{V}^2$