Question

A coil is wound as 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 increased by a factor of

Answer 1

Step 1: Formula used:

Self inductance:$L={\mu }_0{N}^{2}A/I={\mu }_0{n}^{2}IA$

here, n = number of turns per unit length

N=total number of turns

Step2: linear dimensions are increased by factor of 2 ,that is = I is increased by 2 times

number of turns per unit length = n(same)

A is increased 4 times as $\mathrm{L}\propto \mathrm{A}$

Applying self inductance formula,

we have,

L= 8 times ,hence L will be increased 8 times.