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Question

If in one case an asbestos sheet of thickness t(<d) is introduced between the plates of a parallel plate capacitor and in other case an aluminium slab of same thickness is introduced, then

A
Capacitance is more when the medium is asbestos as compared to aluminium.
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B
Capacitance is the same for both the media.
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C
Capacitance is more when the medium is aluminium as compared to asbestos.
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D
Insufficient information
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Solution

The correct option is C Capacitance is more when the medium is aluminium as compared to asbestos.
As we know that capacitance of partially filled dielectric slab of thickness t and dielectric constant K is given by

C=ϵ0Adt+tK

So, when the dielectric medium is asbestos (K>1)

C1=ϵ0Adt+tK

And, when the dielectric medium is aluminium (K=), since field inside the metal(aluminium) is zero.

C2=ϵ0Adt

Clearly, the denominator of C1 is greater than C2, which implicates that C2>C1

Hence, option (c) is correct.
Key concept-
1.) Capacitance with partial dielectric is given by
C=ϵ0Adt+tK
2.) Aluminium is a metal.

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