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

Answer: (B)

We have, self inductance,
$L=\frac{{\mu }_0{n}^{2}A}{l}$
Given, $n/l$ is constant, doubling the length would double n also. Besides this, area would become four times on doubling linear dimensions.
So, $\frac{L_2}{L_1}=\frac{n_2^2}{n_1^2}.\frac{A_2}{A_1}\times \frac{l_1}{l_2}$
Here, $\frac{L_2}{L_1}=4\times 4\times \frac{1}{2}=8$
$\Rightarrow$ $L_2=8L_1$