When the number of turns in a coil is doubled | vedclass

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

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Four times

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(A) The self-inductance $L$ of a solenoid is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A$ is the cross-sectional area,and $l$ is the length of the coil.Since $A$ and $l$ remain constant,we have $L \propto N^2$.Given that the number of turns is doubled,$N_2 = 2N_1$.Therefore,the new self-inductance $L_2$ is given by $L_2 = L_1 \left( \frac{N_2}{N_1} \right)^2 = L_1 \left( \frac{2N_1}{N_1} \right)^2 = 4L_1$.Thus,the self-inductance becomes four times the original value.

When the number of turns in a coil is doubled without any change in the length of the coil,its self-inductance becomes

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