A parallel palte condenser is filled with two dielectrics as shown in figure. Area of each pate is A m² and the separation is d metre. The dielectric constants are K₁ and K₂ respectively. Its capacitance in farad will be

$\frac{2 ε_{o} A}{d} (\frac{K_{1} + K_{2}}{K_{1} K_{2}})$

$\frac{2 ε_{o} A}{d} (\frac{K_{1} K_{2}}{K_{1} + K_{2}})$

$\frac{ε_{o} A}{d} (\frac{K_{1} + K_{2}}{2 K_{1} K_{2}})$

$\frac{ε_{o} A K_{1} K_{2}}{2 (d_{2} K_{1} + d_{1} K_{2})}$

Solution

$\frac{2 ε_{o} A}{d} (\frac{K_{1} K_{2}}{K_{1} + K_{2}})$

From the formula

C = $\frac{ε_{o} A}{\frac{1}{K_{1}} + \frac{1}{K_{2}}}$

C = $\frac{ε_{o} A}{t} (\frac{K_{1} K_{2}}{K_{1} + K_{2}})$

C = $\frac{2 ε_{o} A}{d} (\frac{K_{1} K_{2}}{K_{1} + K_{2}})$

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