Question

Between the plates of parallel plate capacitor of capacity $C$, two parallel plates of the same material and area same as the plate of the original capacitor, are placed. If the thickness of these plates is equal to $1/5th$ of the distance between the plates of the origin

• A. $\frac{5}{3}C$
• B. $\frac{3}{5}C$
• C. $\frac{3C}{10}C$
• D. $\frac{10C}{3}C$

Answer 1

Answer: (A)

Thickness of each plates $=\frac{1}{5}$ distance between plates
$=\frac{1}{5}\times d$
The capacitance of capacitor is given by
$C_1=\frac{{\epsilon }_{0}A}{d-t}...(i)$
Thickness of two conductor is given by
$t=2(\frac{d}{5})=\frac{2d}{5}$
Putting the values oft in Eq. (i)
$C_1=\frac{{\epsilon }_{0}A}{d-\frac{2d}{5}}=\frac{5}{3}\frac{{\epsilon }_{0}A}{d}$
$=\frac{5}{3}C$ (where $C=\frac{{\epsilon }_{0}A}{d}$