Question

A capacitor of capacitance $2\mu F$ is charged to $40V$ and another capacitor of capacitance $4\mu F$ is charged to $20V$. If the capacitors are connected together in same polarity, then the energy lost in reorganisation of charge will be

• A. $316.2\mu J$
• B. $266.67\mu J$
• C. $402\mu J$
• D. $191.6\mu J$

Answer 1

The correct option is B $266.67\mu J$

Given
$V_1=40V$
$V_2=20V$
$C_1=2\mu F$
$C_2=4\mu F$
Energy loss is,
$\Delta E=\frac{1}{2}\times \frac{C_1{C}_2}{C_1+C_2}{(V_1-V_2)}^2$
$=\frac{1}{2}\times \frac{2\times 4\times {10}^{-12}}{(2+4)\times {10}^{-6}}(40-20{)}^2$
$=\frac{800}{3}\mu J.$