Question

A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is $U$.
Now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. If the work performed against the forces of electric field in pulling out the insulator is $4U$, then dielectric constant of the insulator is

Answer 1

Answer: 5

$U=\frac{1}{2}\frac{q^2}{C}$ ...(i)
$U+4U=\frac{1}{2}\frac{q^2}{C_0}$
$\Rightarrow 5U=\frac{1}{2}\frac{q^2}{C_0}$ ...(ii)
Dividing (ii) by (i), we get
$K=\frac{C}{C_0}=5$