Physics - Capacitor Question with Solution | TestHub

Initial effective capacity of two capacitors in series is $C_1=\frac{C\times C}{C+C}=\frac{C}{2}$.

When one capacitor is filled with a dielectric of constant $K$, its new capacity becomes $KC$.

The new effective capacity of the series combination is $C_2=\frac{C\times KC}{C+KC}=\frac{KC}{K+1}$.

The change in effective capacity is $\Delta C=C_2-C_1=\frac{KC}{K+1}-\frac{C}{2}$.

$\Delta C=C\left[\frac{K}{K+1}-\frac{1}{2}\right]=C\left[\frac{2K-(K+1)}{2(K+1)}\right]=\frac{C}{2}\left[\frac{K-1}{K+1}\right]$.

Answer: $\frac{\mathrm{C}}{2}\left[\frac{\mathrm{K}-1}{\mathrm{K}+1}\right]$