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(D) The formula for the self-inductance $L$ of a long solenoid is given by $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A$ is the cro

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(D) The formula for the self-inductance $L$ of a long solenoid is given by $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A$ is the cross-sectional area,and $l$ is the length of the coil.From this formula,we can see that $L \propto N^2$ when the length $l$ and area $A$ remain constant.Given that the number of turns $N$ is made $3$ times $(N' = 3N)$,the new self-inductance $L'$ will be:$L' \propto (N')^2 = (3N)^2 = 9N^2$.Therefore,$L' = 9L$.Thus,the self-inductance becomes $9$ times the original value.

When the number of turns in a coil is made $3$ times without any change in the length of the coil,its self-inductance becomes

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