Question

If the potential of a capacitor having capacity $6\, \mu F$ is increased from $10$ volt to $20$ volt then increase in its energy is

• A. $ 12\times 10^{-6}J $
• B. $ 9\times 10^{-4}J $
• C. $ 4.5\times 10^{-6}J $
• D. $ 2.25\times 10^{-6}J $

Answer 1

Answer: (B)

Given : $C=6\, \mu F,\, V_{1}=10$ volt,
$V_{2}=20$ volt
Increase in energy
$E =\frac{1}{2} C V_{2^{2}}^{2}-\frac{1}{2} C V_{1}^{2}$
$=\frac{1}{2} C\left(V_{2}^{2}-V_{1}^{2}\right)$
$=\frac{1}{2} \times 6 \times 10^{-6}\left(20^{2}-10^{2}\right)$
$=3 \times 10^{-6}\left(20^{2}-10^{2}\right)$
$=3 \times 10^{-6} \times 300 =9 \times 10^{-4} J$