Question

A coil is wound on a frame of rectangular cross-section. If all the linear dimensions of the frame are increased by a factor 2 and the number of turns per unit length of the coil remains the same, self-inductance of the coil increases by a factor of(a) 4(b) 8(c) 12(d) 16

Answer 1

answer : option (b) 8

explanation : self inductance, $L=\mu_0 N^2A/l$

where N is number of turns , $\mu_0$ is permeability of medium ,A is cross sectional area and l is length of coil.

it can be written as $L=\mu_0 n^2V$

where V is volume of coil and n is number of turns per unit length.

it is clear that, self inductance is directly proportional to volume .

volume of rectangular coil, V = lbh

a/c to question,

all the linear dimensions of the frame are increased by a factor 2.

so, volume of rectangular coil are increased by a factor 2 × 2 × 2 = 8

hence, self inductance of the coil increases by a factor of 8

hence, option (b) is correct

Answer 2

Option B is correct.

8