Physics - Capacitor Question with Solution | TestHub

Initial effective capacity of two identical capacitors of capacity $C$ connected in series is given by:

$C_i=\frac{C\times C}{C+C}=\frac{C}{2}$

When one of the capacitors is completely filled with a dielectric material of constant $K$, its new capacity becomes $KC$. The other capacitor remains unchanged with capacity $C$.

Final effective capacity of the series combination is:

$C_f=\frac{KC\times C}{KC+C}=\frac{KC}{K+1}$

The change in the effective capacity of the series combination is:

$\Delta C=C_f-C_i$

$\Delta C=\frac{KC}{K+1}-\frac{C}{2}$

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

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

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

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