Question

If N is the number of turns in a coil, the value of self inductance varies as

• A. $N^0$
• B. N
• C. $N^2$
• D. $N^{-2}$

Answer 1

The correct option is C $N^2$

The flux linked with a turn of the coil is given by:

$\varphi =LI$

Here, $\varphi \to$ flux per turn, $L$ is the self inductance and $I$ is the current.

For N-turns in the coil, flux will be given by:

$N\varphi =LI$ ___(1)

We know that flux linked with the coil is given by:

$\varphi =NBA$

Substitute the value of $\varphi$ in equation $\left(1\right)$.

$N.NBA=LI$

$N^{2}BA=LI$

$⟹L\propto N^2$

Option $\left(C\right)$ is correct.