Question

A dielectric slab of dielectric constant $k=5$ is placed between plates of parallel plate capacitor, thickness of slab is $30$% of plate spacing & its area is same as that of the plates, new capacitance is $C^{\prime }$ & old capacitance was $C$. The ratio $\frac{C^{\prime }}{C}$ is approximately equal to

• A. $\frac{5}{4}$
• B. $\frac{3}{5}$
• C. $\frac{7}{5}$
• D. $\frac{4}{3}$

Answer 1

The correct option is D $\frac{4}{3}$

If dielectric slab is placed in between the plates & slab plane is parallel to plane of plates then
$C^{\prime }=\frac{{\in }_{0}A}{\sum t/k}=\frac{{\in }_{0}A}{\frac{0.7d}{1}+\frac{0.3d}{5}}=\frac{{\in }_{0}A}{0.7d+0.06d}$
$=\frac{{\in }_{0}A}{0.76d}=\frac{4{\in }_{0}A}{3d}$
$=\frac{4C}{3}$