Question

In a solenoid, if number of turns is doubled, then self-inductance will become:

• A. half
• B. double
• C. 1/4 times
• D. quadruple

Answer 1

Answer: (D)

For a solenoid of length $l$, area of cross-section $A$, having $N$ closely wound turns, the self inductance of the solenoid is
$L=\frac{{\mu }_0{N}^{2}A}{l}$
When $N^{\prime }=2N$
$L^{\prime }=\frac{{\mu }_0(2N{)}^{2}A}{l}$
$=\frac{4{\mu }_0{N}^{2}A}{l}=4L$
Hence, when number of turns is doubled then self inductance becomes quadruple.