First slide

Inductance

Question

The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be

Moderate

A

$\frac{1}{4} L$
B

L
C

4L
D

16L

Solution

$L = \frac{μ_{0} N^{2} A}{l} \frac{L_{1}}{L_{2}} = {(\frac{N_{1}}{N_{2}})}^{2} \frac{L}{L_{2}} = {(\frac{N_{1}}{4 N_{1}})}^{2} = \frac{1}{16} L_{2} = 16 L_{1}$ $L \propto N^{2}$

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