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 total number of turns,$A$ is the cross-s

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becomes $4$ 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 total 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 $A$ and $l$ remain constant.Given that the number of turns is doubled,i.e.,$N_2 = 2N_1$.Therefore,the new self-inductance $L_2$ is:$L_2 = L_1 	imes \left(\frac{N_2}{N_1}ight)^2$$L_2 = L_1 	imes (2)^2$$L_2 = 4 L_1$Thus,the self-inductance becomes $4$ 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

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