Question

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

The correct option is A $1.5$ and $1.33$

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