A parallel plate air capacitor has a capacitance C . When it is half-filled with a dielectric constant 5 , the percentage increase in the capacitance will be

Question

A parallel plate air capacitor has a capacitance C . When it is half-filled with a dielectric constant 5 , the percentage increase in the capacitance will be, 400 %, 66.6 %, 33.3 %, 200 %

MARKS App · Accepted Answer

Initial capacitance C = ε 0 A d When it is half filled by a dielectric of dielectric constant K , then C 1 = K ε 0 A d / 2 = 2 K ε 0 A d and C 2 = ε 0 A d / 2 = 2 ε 0 A d ∴ 1 C ' ' = 1 C 1 + 1 C 2 = d 2 ε 0 A 1 K + 1 = d 2 ε 0 A 1 5 + 1 = 6 10 d ε 0 A ∴ C ' ' = 5 ε 0 A 3 d Hence, increase in capacitance = 5 3 ε 0 A d - ε 0 A d ε 0 A d = 5 3 - 1 = 2 3 = 66.6 %

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