A parallel plate capacitor with air as the dielectric has capacitance $C$ . A slab of dielectric constant $K$ and 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

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A parallel plate capacitor with air as the dielectric has capacitance

C

. A slab of dielectric constant

K

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

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

Quantrex Academy · Accepted Answer

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

The condenser with air as the dielectric has capacitance C_1=( _0)/(d)((3 A)/(4))=(3 _0 A)/(4 d) Similarly, the condenser with K as the dielectric constant has capacitance C_2=( _0 K)/(d)((A)/(4))=( _0 A K)/(4 d) Since, C_1 and C_2 are in parallel C_ net =C_1+C_2 =(3 _0 A)/(4 d)+( _0 A K)/(4 d)=( _0 A)/(d)[(3)/(4)+(K)/(4)] =(C)/(4)(K+3)

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