A coil having 50 turns has self-inductance of 10 mH. On increasing the number of turns to 150, the self-inductance is

Given,

Total turns $N_1$ = 50 turns 

self-inductance $L_1$= 10 mH. 

New number of turns $N_2$=150, 

Suppose new self-inductance = $L_2$

Now we know that,

$$\begin{gathered} \frac{L_1}{L_2}=\frac{N_1^2}{N_2^2} \\ \frac{10}{L_2}=\frac{{50}^2}{{150}^2} \\ {L}_2=\frac{22500\times 10}{2500} \\ {L}_2=90 mH \end{gathered}$$