Question

If the distance between the plates of a parallel plate capacitor of capacity $ 10 \,\mu F $ is doubled, then new capacity will be

• A. $ 5 \,\mu F $
• B. $ 20 \,\mu F $
• C. $ 10 \,\mu F $
• D. $ 15 \,\mu F $

Answer 1

Answer: (A)

In parallel plate capacitor
$C=\varepsilon_{0} \frac{A}{d}\,\,\,\,\,...(i)$
Now $\,\,\,d'=2 d$
Hence, $\,\,\, C'=\frac{\varepsilon_{0} A}{d'}=\frac{\varepsilon_{0} A}{2 d}\,\,\,\,...(ii)$
From Eqs. (i) and (ii)
$\frac{C'}{C}=\frac{1}{2}$
$C'=\frac{C}{2}$
Putting $C =10\, \mu F $
$ C'=\frac{10}{2}=5\, \mu F $