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
Where A is the plate area and ∈0 is the permittivity of the free space.
Initially, without dielectric material inserted, capacitance is given by
Similarly, with the dielectric material place, capacitance is given by
On dividing 1) by 2), we get
Thus, the dielectric constant of the given material is 3.
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