Question

Three concentric spherical conductors are shown, Find equivalent capacitance b/w A and B

Answer 1

The innermost conductor is at zero potential (same as infinity)
Equivalent diagram can be drawn as :

C1=4π∈0abb−a
C2=4π∈0c
C3=4π∈0bcc−b
Ceq=C3+C1C2C1+C2
=> 4π∈0bcc−b+4π∈0abcab+c(b−a)
Hence it is the correct answer

Answer 2

Concept:

The potential of the innermost shell will be zero and it is the same potential which we assume for infinity.

Given:

The radius of smallest shell is a.

The radius of biggest shell is c.

The radius of the rest shell is b.

Find:

Equivalent capacitance between A and B

Solution:

As, the innermost shell's potential is 0, which is the same potential we anticipate for infinity.

The conductors with radius a and b form one capacitor between b and c, while the other conductor and c form another capacitor with its other plate at infinity.

As a result, an analogous diagram can be created as

C1 = (4πε₀ab)/(b-c)

C2 = 4πε₀c

C3 = (4πε₀bc)/(c-b)

As, C1 and C2 are connected in the series and C3 is in parallel with them.

Ceq = C3 + (C1C2)/(C1+C2)

Ceq = 4πε₀( (bc/c-b) + (abc/(ab+cb-ca) )

Hence the equivalent capacitance between A and B is 4πε₀( (bc/c-b) + (abc/(ab+cb-ca) ).

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