Question

A capacitor $4\, \mu F$ charged to $50, V$ is connected to another capacitor of $2\, \mu F$ charged to $100\, V$ with plates of like charges connected together. The total energy before and after connection in multiples of $\left(10^{-2} J \right)$ is

• A. 1.5 and 1.33
• B. 1.33 and 1.5
• C. 3.0 and 2.67
• D. 2.67 and 3.0

Answer 1

Answer: (A)

The total energy before connection
$=\frac{1}{2} \times 4 \times 10^{-6} \times(50)^{2}+\frac{1}{2} \times 2 \times 10^{-6} \times(100)^{2}$
$=1.5 \times 10^{-2} J$
When connected in parallel,
$4 \times 50+2 \times 100=6 \times V$
$\Rightarrow V=\frac{200}{3}$
Total energy after connection
$=\frac{1}{2} \times 6 \times 10^{-6} \times\left(\frac{200}{3}\right)^{2}$
$=1.33 \times 10^{-2} J$