Question

A coil of wire of radius $r$ has $600$ turns and a self inductance of $108mH$. The self inductance of a coil with same radius and $500$ turns is:

• A. $80mH$
• B. $75mH$
• C. $108mH$
• D. $90mH$

Answer 1

The correct option is B $75mH$

Given : $N=600$ $L=108mH$ $N^{\prime }=500$

Self inductance of the coil $L=\frac{{\mu }_o{N}^{2}A}{l}$ where $A=\pi r^2$

$⟹$ $L\propto N^2$ $(\because A=constant)$

$⟹$ $\frac{L^{\prime }}{L}=\frac{N^{\prime 2}}{N^2}$

$\therefore$ $\frac{L^{\prime }}{108}=\frac{(500{)}^2}{(600{)}^2}$

OR $L^{\prime }=108\times \frac{25}{36}$ $⟹L^{\prime }=75mH$