Question

A solenoid of length $ l $ metre has self-inductance $L$ henry. If number of turns are doubled, its self inductance:

• A. remains same
• B. becomes $2L$ henry
• C. becomes $4L$ henry
• D. becomes $ \frac{L}{\sqrt{2}} $ henry

Answer 1

Answer: (C)

The self-inductance $(L)$ of a coil having $N$ number of turns is given by
$L=\frac{\mu_{0} N^{2} A}{l} $
$\Rightarrow \frac{L_{1}}{L_{2}}=\frac{N_{1}^{2}}{N_{2}^{2}}$
Given, $L_{1}=L, N_{1}=N, N_{2}=2 \,N$
$\therefore L_{2}=4 \,L$