Question

The two parallel plates of a condenser have been connected to a battery of $300V$ and the charge collected at each plates is $1\mu C$. The energy supplied by the battery is :

• A. $6\times {10}^{-4}J$
• B. $3\times {10}^{-4}J$
• C. $1.5\times {10}^{-4}J$
• D. $4.5\times {10}^{-4}J$

Answer 1

Answer: (C)

$1.5\times {10}^{-4}J$

Given,

$Q=1\mu C$

$V=300V$

Charge-capacitance relationship is given by,

$Q=CV$

$C=\frac{Q}{V}=\frac{1\times {10}^{-6}}{300}=\frac{1}{300}\times {10}^{-6}F$

The energy supplied by the battery,

$E=\frac{1}{2}C{V}^2$

$E=\frac{1}{2}\frac{1}{300}\times {10}^{-6}\times 300\times 300$

$E=\frac{3}{2}\times {10}^{-4}$

$E=1.5\times {10}^{-4}J$

The correct option is A.