A capacitor is half filled with dielectric $ (\mathrm{K}=2) $ as shown in diagram (1). If the same dielectric is to be filled in the same capacitor as shown in diagram (2), then what would be the thickness of dielectric so that capacitor still has same capacitance ?

Question

A capacitor is half filled with dielectric $ (\mathrm{K}=2) $ as shown in diagram (1). If the same dielectric is to be filled in the same capacitor as shown in diagram (2), then what would be the thickness of dielectric so that capacitor still has same capacitance ?, $ \frac{2 \mathrm{~d}}{3} $, $ \frac{3 \mathrm{~d}}{2} $, $ \frac{3 \mathrm{~d}}{4} $, $ \frac{4 \mathrm{~d}}{3} $

MARKS App · Accepted Answer

C ′ = ∈ 0 A 2 d C" = C 0 K 2 ∴ C 1 = C ′ + C ′ ′ ∴ C 1 = C 0 2 + C 0 K 2 = C 0 2 1 + K (Equivalent capacitance of 1 s t diagram) C 2 = ∈ 0 A d – t + t K (Equivalent capacitance of 2 n d diagram) Both are same hence : C 0 2 K + 1 = ∈ 0 A d – t + t K ∈ 0 A 2 d 2 + 1 = ∈ 0 A d – t + t 2 3 d – 3 t 2 = 2 d d = 3 t 2 o r t = 2 d 3

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