The space between two plates of a parallel plate condenser is filled longitudinally with two dielectric materials each of thickness $d / 2$ . The dielectric constant of each material is $K_{1}$ and $K_{2}$ . The resultant dielectric constant is :

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

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\frac{K_{1} K_{2}}{2 (K_{1} + K_{2})}

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\frac{2 (K_{1} + K_{2})}{K_{1} K_{2}}

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\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

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Solution

The correct option is A $\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}$
This combination can be assumed to be a combination of two parallel plates capacitors connected in series with capacity $\frac{2 K_{1} ϵ_{0} A}{d}$ and $\frac{2 K_{2} ϵ_{0} A}{d}$ .
In series, the resultant capacitance is $\frac{2 K_{1} K_{2} ϵ_{0} A}{(K_{1} + K_{2}) d}$ .

Thus resulatant dielectric constant is $\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}$ .

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