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Physics-

General

Easy

Question

Separation between the plates of a parallel plate capacitor is $d$ and the area of each plate is $A$ . When a slab of material of dielectric constant $k$ and thickness $t left parenthesis t less than d right parenthesis$ is introduced between the plates, its capacitance becomes

$\frac{ε_{0} A}{d + t (1 - \frac{1}{k})}$
$\frac{ε_{0} A}{d + t (1 + \frac{1}{k})}$
$\frac{ε_{0} A}{d - t (1 - \frac{1}{k})}$
$\frac{ε_{0} A}{d - t (1 + \frac{1}{k})}$

The correct answer is: $fraction numerator epsilon subscript 0 end subscript A over denominator d minus t open parentheses 1 minus fraction numerator 1 over denominator k end fraction close parentheses end fraction$

Potential difference between the plates V = V_air + V_medium
$equals fraction numerator sigma over denominator epsilon subscript 0 end subscript end fraction cross times left parenthesis d minus t right parenthesis plus fraction numerator sigma over denominator K epsilon subscript 0 end subscript end fraction cross times t$
Þ $V equals fraction numerator sigma over denominator epsilon subscript 0 end subscript end fraction left parenthesis d minus t plus fraction numerator t over denominator K end fraction right parenthesis$
$equals fraction numerator Q over denominator A epsilon subscript 0 end subscript end fraction left parenthesis d minus t plus fraction numerator t over denominator K end fraction right parenthesis$
Hence capacitance $C equals fraction numerator Q over denominator V end fraction equals fraction numerator Q over denominator fraction numerator Q over denominator A epsilon subscript 0 end subscript end fraction left parenthesis d minus t plus fraction numerator t over denominator K end fraction right parenthesis end fraction$
$equals fraction numerator epsilon subscript 0 end subscript A over denominator left parenthesis d minus t plus fraction numerator t over denominator k end fraction right parenthesis end fraction equals fraction numerator epsilon subscript 0 end subscript A over denominator d minus t open parentheses 1 minus fraction numerator 1 over denominator k end fraction close parentheses end fraction$

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