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 remains the same, the self inductance increases by a factor of

• A. $4$
• B. $8$
• C. $12$
• D. $16$

Answer 1

The correct option is B $8$

We have, self inductance, $L=\frac{{\mu }_0{n}^{2}A}{I}$
Given, $n/I$ is constant, doubling the length would double $n$ also. Besides this, area would become four times on doubling linear dimensions.
So, $\frac{L_2}{L_1}=\frac{n_2^2}{n_1^2}\cdot \frac{A_2}{A_1}\times \frac{I_1}{I_2}$
Here, $\frac{L_2}{L_1}=4\times 4\times \frac{1}{2}=8$
$\Rightarrow L_2=8L_1$.