Question

A capacitor stores 50 µC charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 100 µC flows through the battery. Find the dielectric constant of the material inserted.

Answer 1

The dielectric constant of the material inserted = K = 3

Explanation:

Initially, charge stored in the capacitor = 50 µC

Consider the dielectric constant = K

As given, when the charge flown in the battery is 100

Charge stored in the capacitor = 100 µC

As $100 \mu C$ of extra charge flows through the battery, the net charge on the capacitor becomes,

$50+100=150 \mu C$

$C_{1}=\frac{q_{1}}{V}=\frac{\epsilon_{0} A}{d}$                     (1)

$C_{2}=\frac{q_{2}}{V}=\frac{\epsilon_{0} A k}{d}$                    (2)

On dividing (1) by (2), we get

$\frac{C_{1}}{C_{2}}=\frac{q_{1}}{q_{2}}=\frac{1}{k}$

$\frac{50}{150}=\frac{1}{k}$

k = 3

Thus, the dielectric constant of the given material is 3