Question

A parallel plate condenser with oil between the plates (dielectric constant of oil $K=2$) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes :

• A. $\sqrt{2}C$
• B. 2C
• C. $\frac{C}{\sqrt{2}}$
• D. $\frac{C}{2}$

Answer 1

Answer: (D)

$\frac{C}{2}$

The dielectric constant is directly proportional to value of capacitance.
Since in the earlier case,K=2, so the final case answer is half of the previous one.
Mathematically, when oil is placed between space of plates.
$C=\frac{2A\epsilon 0}{d}....\left(1\right)[\because C=\frac{KA{\epsilon }_0}{d},ifK=2]$
When oil is removed, $C^{\prime }=\frac{A{\epsilon }_0}{d}......\left(2\right)$
On comparing both equations, we get $C^{\prime }=\frac{C}{2}$