Question

A capacitor is charged with a battery and the energy stored is $U$. After disconnecting battery another capacitor of the same capacity is connected in parallel with it. Then the energy stored in each capacitor is :

• A. $\frac{U}{2}$
• B. $\frac{U}{4}$
• C. $4U$
• D. $2U$

Answer 1

The correct option is B $\frac{U}{4}$

Energy stored $\left(U\right)=\frac{q^2}{2C}$ After connecting with another capacitor

$V_{common}=\frac{q_1+q_2}{C_1+C_2}=\frac{q+0}{C+C}=\frac{q}{2C}$

$\because$ Energy on each capacitor

$=\frac{1}{2}C{V}_{Common}^2=\frac{1}{2}{\left(\frac{q}{2C}\right)}^2=\frac{U}{4}.$