Question

Two capacitors of capacitance $C$ are connected in series. If one of them is filled with a substance of dielectric constant $K$, what is the effective capacitance?

• A. $\frac{KC}{(1+k)}$
• B. $C(K+1)$
• C. $\frac{2KC}{(1+k)}$
• D. None of these

Answer 1

The correct option is A $\frac{KC}{(1+k)}$

When a substance of dielectric constant $K$ is filled in the capacitor, its capacity
$C_m=\frac{K{\epsilon }_{0}A}{d}=K{C}_o$
Here, $C_o=C$
$\therefore C_m==KC$
Now two capacitors of capacities $KC$ and $C$ are connected in series, therefore their effective capacitance
$\frac{1}{C^{\prime }}=\frac{1}{KC}+\frac{1}{C}=\frac{1+K}{KC}\Rightarrow C^{\prime }=\frac{KC}{(1+K)}$