Question

A coil made of Copper wire having radius $r$, self inductance $L$ is bent in two concentric turns each having radius $\frac{r}{2}$ . The new self inductance is

• A. $2L$
• B. $L$
• C. $4L$
• D. $\frac{L}{2}$

Answer 1

The correct option is A $2L$

$\because L\propto N^{2}r;\frac{L}{L_2}={\left(\frac{N_1}{N_2}\right)}^2\times \frac{r_1}{r_2}$

$\Rightarrow \frac{L}{L_2}={\left(\frac{1}{2}\right)}^2\times \left(\frac{r}{\frac{r}{2}}\right)=\frac{1}{2};L_2=2L$