When the number of turns in a coil is doubled without any change in the length of the coil, its…
When the number of turns in a coil is doubled without any change in the length of the coil, its self-inductance
becomes 4 times.
becomes 2 times.
gets halved.
remains unchanged.
Solution
Self-inductance of solenoid is,
$\frac{\mathrm{L}}{l}=\mu_0 \mathrm{~N}^2 \mathrm{~A}$
where N is the total number of turns.
As $\mathrm{L} \propto \mathrm{N}^2$
$\begin{array}{ll}
\therefore & \frac{\mathrm{L}_2}{\mathrm{~L}_1}=\left(\frac{\mathrm{N}_2}{\mathrm{~N}_1}\right)^2=(2)^2 \\
\therefore & \mathrm{~L}_2=4 \mathrm{~L}_1
\end{array}$