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Physics-

General

Easy

Question

A parallel plate capacitor has capacitance C. If it is equally filled with parallel layers of materials of dielectric constants K₁ and K₂ its capacity becomes C₁. The ratio of C₁ to C is

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

The correct answer is: $fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction$

$C subscript A end subscript equals fraction numerator K subscript 1 end subscript epsilon subscript 0 end subscript A over denominator d divided by 2 end fraction comma C subscript B end subscript equals fraction numerator K subscript 2 end subscript epsilon subscript 0 end subscript A over denominator d divided by 2 end fraction$
\ $C subscript e q end subscript equals fraction numerator C subscript 1 end subscript over denominator C subscript 2 end subscript end fraction equals fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction$
$equals fraction numerator C subscript A end subscript C subscript B end subscript over denominator C subscript A end subscript plus C subscript B end subscript end fraction equals open parentheses fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction close parentheses fraction numerator epsilon subscript 0 end subscript A over denominator d end fraction$
$open parentheses because c equals fraction numerator epsilon subscript 0 end subscript A over denominator d end fraction close parentheses$

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