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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The two condensers with K and with air are in parallel. With air, C 1 = ε 0 d 3 A 4 = 3 ε 0 A 4 d With medium, C 2 = ε 0 K d A 4 = ε 0 A K 4 d ∴ C ′ = C 1 + C 2 or C ′ = 3 ε 0 A 4 d + ε 0 A K 4 d = ε 0 A d 3 4 + K 4 or C ′ = C 4 K + 3 ∵ C = A ε 0 d

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