A parallel plate capacitor with air as a dielectric has capacitance $C$ . A slab of dielectric constant $K,$ having same thickness as the separation between the plates is introduced so as to fill one fourth of the capacitor as shown in the figure. The new capacitance will be

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A parallel plate capacitor with air as a dielectric has capacitance

C

. A slab of dielectric constant

K,

having same thickness as the separation between the plates is introduced so as to fill one fourth of the capacitor as shown in the figure. The new capacitance will be

A parallel plate capacitor with air as a dielectric has capacitance C . A slab of dielectric constant K, having same

A parallel plate capacitor with air as a dielectric has capacitance C . A slab of dielectric constant K, having same

Quantrex Academy · Accepted Answer

Correct answer: A. (K + 3)(C)/(4)

The two condensers with K and with air are in parallel. With air, C _ 1 = ε _ 0 d ((3A)/(4)) = 3 ε _ 0 A 4d With medium, C _ 2 = ε _ 0 K d ((A)/(4)) = ε _ 0 AK 4d ∴ C^ ′ = C _ 1 + C _ 2 or C^ ′ = 3 ε _ 0 A 4d + ε _ 0 AK 4d = ε _ 0 A d [(3)/(4) + (K)/(4)] or cases C^ ′ = (C)/(4)(K + 3) & [∵ C = A ε _ 0 d ] cases

A parallel plate capacitor with air as a dielectric has capacitance...

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