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(A) The self-inductance $L$ of a circular coil is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A$ is the area of

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$4$

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(A) The self-inductance $L$ of a circular coil is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A$ is the area of cross-section,and $l$ is the length of the coil.From this relation,we see that $L \propto N^2$.Given that the number of turns $N$ is doubled $(N' = 2N)$,the new inductance $L'$ will be $L' \propto (2N)^2 = 4N^2$.Therefore,$L' = 4L$.The resistance of the coil does not affect the self-inductance of the coil,as inductance depends only on the geometry and the number of turns of the coil.Thus,the inductance becomes $4$ times the initial value.

In a circular coil,when the number of turns is doubled and the resistance becomes $1/4$th of the initial value,then the inductance becomes ....... times.

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