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:
(K+3)C4
(K+1)C4
(K+2)C4
KC4
A
(K+3)C4
B
(K+1)C4
C
(K+2)C4
D
KC4
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Solution
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The two condensers with K and with air are in parallel. With air, C1=ϵ0d(3A4)=3ϵ0A4d With medium, C2=ϵ0Kd(A4)=ϵ0AK4d ∴C′=C1+C2 or C′=3ϵ0A4d+ϵ0AK4d=ϵ0Ad[34+K4] or C′=C4(K+3)[∵C=Aϵ0d].
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