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Question:

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

(K+1)C/4

(K+2)C/4

(K+3)C/4

KC/4

Solution:

The two condensers with K and with air are in parallel. With air, C1 = ε₀(3A/4d) = 3ε₀A/4d. With medium, C2 = ε₀K(A/4d) = ε₀AK/4d. ∴C' = C1 + C2 or C' = 3ε₀A/4d + ε₀AK/4d = ε₀Ad[3/4 + K/4] or C' = C/4(K+3) [∵C = Aε₀/d].