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.

Given-

Initially, the charge on the capacitor = 50 μC

Now, let the dielectric constant of the material inserted in the gap be k.

When this dielectric material is inserted, 100 μC of extra charge flows through the battery

Therefore , the net charge on the capacitor becomes

50 + 100 = 150 μC

Now, we know capacitance of a material is given by –

Where q is charge on the capacitance and v is the applied voltage

Also

Where A is the plate area and ∈₀ is the permittivity of the free space.

Initially, without dielectric material inserted, capacitance is given by

1)

Similarly, with the dielectric material place, capacitance is given by

2)

On dividing 1) by 2), we get

⇒

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