Question

Two capacitors of capacitances $C$ and $2 C$ are charged to potential differences $V$ and $2 V$ respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

• A. $\frac{9}{2} CV ^{2}$
• B. $\frac{25}{6} CV ^{2}$
• C. zero
• D. $\frac{3}{2} C V^{2}$

Answer 1

Answer: (D)

$Q _{1}= CV$ $\quad$ $Q _{2}=2 C \times 2 V =4 CV$

$\Rightarrow $ By conservation of charge
$q _{ i }= q _{ f }$
$Q _{1}+ Q _{2}= q _{1}+ q _{2}$
$4 C V-C V=(C+2 C) V_{C}$
$V _{ C }=\frac{3 CV }{3 C } \Rightarrow V$

$\Rightarrow \frac{1}{2} \times(3 C ) \times V _{ c }^{2}$
$=\frac{1}{2} \times 3 C \times V ^{2}=\frac{3}{2} CV ^{2}$