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(C) When two conductors are connected by a conducting wire,they reach the same electric potential.Since the inner sphere $A$ is connected to the outer

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$4\pi {\varepsilon _0}b$

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(C) When two conductors are connected by a conducting wire,they reach the same electric potential.Since the inner sphere $A$ is connected to the outer sphere $B$ by a copper wire,all the charge given to the system will reside on the outer surface of the outer sphere $B$ because the inner sphere is at a higher potential than the outer sphere if they were isolated,but the wire forces them to be at the same potential.Effectively,the entire system acts as a single isolated spherical conductor of radius $b$.The capacitance of an isolated spherical conductor of radius $R$ is given by $C = 4\pi \varepsilon_0 R$.Therefore,the equivalent capacitance of this system is $C = 4\pi \varepsilon_0 b$.

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed concentrically in air. The two are connected by a copper wire as shown in the figure. Then the equivalent capacitance of the system is

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