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

Given:

Initial charge on the capacitor = 50 µC

Now, let the dielectric constant of the material inserted be k.
As 100 µC of extra charge flows through the battery,  the net charge on the capacitor becomes

50 + 100 = 150 µC

Now , 

`C_1 = q_1/V = (∈_0A)/d`               ............(i)

`C_2 = q_2/V = (∈_0Ak)/d`               ............(ii)

On dividing (i) by (ii), we get

`C_1/C_2 = q_1/q_2 = 1/k`

⇒ `50/150 = 1/k`

⇒ `k = 3`

Thus, the dielectric constant of the given material is 3.