Question

Consider a parallel plate capacitator of capacity 10 $\mu F$ filled with air. When the gap between the plates is filled partly with a dielectric of dielectric constant $4$, as shown in figure, the new capacity of the capacitator is ($A$ is the area of plates):

• A. $20\mu F$
• B. $40\mu F$
• C. $2.5\mu F$
• D. $25\mu F$

Answer 1

The correct option is D $25\mu F$

Such a configuration can be thought of as a parallel combination of two capacitors- one with area A/2 and dielectric and another with same area and without dielectric.

$C_1=\frac{{ϵ}_{0}A}{2d}$; (for air in between)
In second case $k=4$

$C_2=\frac{4{ϵ}_{0}A}{2d}=\frac{2{ϵ}_{0}A}{d}$

Hence, effective capacitance is $C=C_1+C_2=2.5\frac{{ϵ}_{0}A}{d}=2.5C_0=25\mu F$