First slide

Inductance

Question

A coil is wound on a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor 2 and the number of turns per unit length of the coil remain the same, the self-inductance is increased by a factor of

Moderate

A

16
B

12
C

8
D

4

Solution

Self-inductance, $L = μ_{0} N^{2} A / l = μ_{0} n^{2} lA$
Where n is the number of turns per unit length and N is the total number of turns, i.e., N = nl
In the given question n is same. A is increased 4 times and l is increased 2 times and hence L will be increased 8 times.

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