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

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 (L/√2) henry

Tardigrade Admin · Accepted Answer

The self-inductance (L) of a coil having N number of turns is given by L=(μ0 N2 A/l) ⇒ (L1/L2)=(N12/N22) Given, L1=L, N1=N, N2=2 N ∴ L2=4 L

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

remains same

becomes $2 L$ henry

becomes $4 L$ henry

becomes $\frac{L}{2}$ henry

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

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

remains same

becomes 2L henry

becomes 4L henry

becomes 2​L​ henry

The self-inductance (L) of a coil having N number of turns is given by L=lμ0​N2A​ ⇒L2​L1​​=N22​N12​​ Given, L1​=L,N1​=N,N2​=2N ∴L2​=4L

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

becomes $2 L$ henry

becomes $4 L$ henry

becomes $\frac{L}{2}$ henry

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