Question

The capacitance of a parallel plate capacitor is $2.5\mu F$. When it is half-filled with a dielectric shown in the figure Its capacitance becomes $5\mu F$, the dielectric constant of the dielectric is :

• A. $7.5$
• B. $3.0$
• C. $0.33$
• D. $4.0$

Answer 1

Answer: (B)

$3.0$

Let area of each plate be A and spacing between then be d.

Then capacitance of parallel plate capacitor, $C=\frac{{ϵ}_{0}A}{d}=2.5\mu F$

When it is half filled with dielectric, capacitance of capacitor filled with air, $C_1=\frac{{ϵ}_0\left(A/2\right)}{d}$

capacitance of capacitor filled with medium of dielectric constant $k$ is $C_2=\frac{k{ϵ}_0\left(A/2\right)}{d}$

Since $C_1$ and $C_2$ are in parallel, equivalent capacitance will be, $C^{\prime }=C_1+C_2=5\mu F$

$\frac{{ϵ}_{0}A}{2d}+\frac{k{ϵ}_0}{2d}=5$

$\frac{2.5}{2}+\frac{k\times 2.5}{2}=5$

$1+k=4$

$k=3$