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=( _0)/(d)((3 A)/(4))=(3 _0 A)/(4 d) With medium, C_2=( _0 K)/(d)((A)/(4))=( _0 A K)/(4 d) C^ =C_1+C_2 or C^ =(3 _0 A)/(4 d)+( _0 A K)/(4 d)=( _0 A)/(d)[(3)/(4)+(K)/(4)] or C^ =(C)/(4)(K+3) [ C=(A _0)/(d)]

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