A parallel plate condenser has a plate area $A$ and space in between plates is filled with layered dielectric parallel to plates consisting of $n$ layers of materials of dielectric constant $k_{1}$ and $n$ layers of material of dielectric constant $K_{2}$ . The layers are alternate and each has a thickness $t$ , capacity of such a condenser is :

\frac{\in_{0} A (K_{1} + K_{2})}{n t K_{1} K_{2}}

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\frac{\in_{0} A}{n t (K_{1} + K_{2})}

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\frac{\in_{0} A K_{1} K_{2}}{n t (K_{1} + K_{2})}

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\frac{\in_{0} A (K_{1} + K_{2})}{n t}

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Solution

The correct option is C $\frac{\in_{0} A K_{1} K_{2}}{n t (K_{1} + K_{2})}$
Here two capacitors are in series.
$C_{1} = \frac{A K_{1} ϵ_{0}}{n t}$
$C_{2} = \frac{A K_{2} ϵ_{0}}{n t}$
Net capacitance $C_{e q} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{\frac{A K_{1} ϵ_{0}}{n t} . \frac{A K_{2} ϵ_{0}}{n t}}{\frac{A K_{1} ϵ_{0}}{n t} + \frac{A K_{2} ϵ_{0}}{n t}} = \frac{A K_{1} K_{2} ϵ_{0}}{n t (K_{1} + K_{2})}$

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