Question

A capacitor stores $60\mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of $120\mu C$ flows through the battery. The dielectric constant of the material inserted is :

• A. $1$
• B. $2$
• C. $3$
• D. none

Answer 1

The correct option is C $3$

The capacitance before filled with dielectric is $C=\frac{A{ϵ}_0}{d}$
The capacitance after filled with dielectric is $C^{\prime }=\frac{Ak{ϵ}_0}{d}=kC$
Initial charge, $Q=60\mu C$ and total charge after filled with dielectric $Q^{\prime }=120+60=180\mu C$
Here, $Q=CV$ and $Q^{\prime }=C^{\prime }V=kCV$
$\frac{Q^{\prime }}{Q}=\frac{kCV}{CV}$
$k=\frac{Q^{\prime }}{Q}=\frac{180}{60}=3$