Question

A capacitor $4\mu F$ charged to $50,V$ is connected to another capacitor of $2\mu F$ charged to $100V$ 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
$=\frac{1}{2}\times 6\times 10^{-6}\times {\left(\frac{200}{3}\right)}^2$
$=1.33\times 10^{-2}J$