Question
A parallel$-$plate capacitor having plate area $25\ cm^2$ and separation $1.00\ mm$ is connected to a battery of $6.0V.$ Calculate the charge flown through the battery. How much work has been done by the battery during the process?
✓
Answer
$\text{A}=25\text{ cm}^2=2.5\times10^{-3}\text{ cm}^2$
$\text{d}=1\text{ mm}=0.01\text{m}$
$\text{V}=\text{6V},\ \text{Q}=1$
$\text{C}=\frac{\epsilon_0\text{A}}{\text{d}}=\frac{8.854\times10^{-12}\times2.5\times10^{-3}}{0.01}$
$\text{Q}=\text{CV}=\frac{8.854\times10^{-12}\times2.5\times10^{-3}}{0.01}\times6$
$=1.32810\times10^{-10}\text{C}$
$\text{W}=\text{Q}\times\text{V}=1.32810\times10^{-10}\text{C}\times6$
$=8\times10^{-10}\text{J}.$
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