Physics - Capacitor Question with Solution | TestHub

The capacitance of a parallel plate air capacitor is given by $C=\frac{{\epsilon }_{0}A}{d}$.

When a conducting sheet of thickness $t$ is inserted between the plates, the new capacitance is $C_1=\frac{{\epsilon }_{0}A}{d-t}$.

Given $t=\frac{2d}{3}$, we have:

$C_1=\frac{{\epsilon }_{0}A}{d-\frac{2d}{3}}=\frac{{\epsilon }_{0}A}{\frac{d}{3}}=3\left(\frac{{\epsilon }_{0}A}{d}\right)$

$C_1=3C$

The ratio $\frac{C_1}{C}=\frac{3}{1}=3:1$.

Answer: $3:1$