Question

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil :

• A. Decreases by a factor of $9 \sqrt{3}$
• B. Increases by a factor of 3
• C. Decreases by a factor of 9
• D. Increases by a factor of 27

Answer 1

Answer: (B)

Increases by a factor of 3

Answer 2

Total length L will remain constant

$L = (3a) N$ **(N = total, turns) **

and length of winding ($l$)= $(d) N$ (d = diameter of wire)

Self inductance = $\mu_o n^2 Al= \mu_o n^2(\frac{\sqrt3 }4 a^2)dN$

Self inductance (L) ∝ $a^2N$

As $N = \frac{l}{3a} \rightarrow N ∝\frac1{a}$

$\therefore L ∝a$

So, as a is increased to 3a the Self inductance will be 3 times.

Hence, the correct answer is option (B): Increases by a factor of 3