Two capacitors of capacitance C are connected in series. If one of...

When plates of capacitor are separated by a dielectric medium of dielectric constant $K$, its capacity

${C}_{m} = \dfrac{K{ε}_{0}A}{d} = K{C}_{0}$

$ie, {C}_{m} = K{C}_{0}$

Here,${C}_{0} = C$

$∴ {C}_{m} = KC$

Now, two capacitors of capacities $KC$ and $C$ are in series, their effective capacitance

$\dfrac{1}{C^{′}} = \dfrac{1}{KC} + \dfrac{1}{C}$

or $\dfrac{1}{C^{′}} = \dfrac{1 + K}{KC}$

$∴ C^{′} = \dfrac{KC}{K + 1}$