Which of the following factors does NOT affect the value of self indu…

The correct answer is Option (4) → Current flowing through the inductor.

The self inductance of a long solenoid depends only on its geometry and its core:

    \( \displaystyle L = \mu_r \mu_0\, n^{2} A\, l = \frac{\mu_r \mu_0 N^{2} A}{l} \)

Here \( N \) is the number of turns, \( n = N/l \) the turns per unit length, \( A \) the area of cross-section, \( l \) the length and \( \mu_r \) the relative permeability of the core. The current does not appear: doubling the current doubles the flux, so the ratio \( L = N\Phi/I \) stays the same.

Option (1) Number of turns — Affects the inductance. \( L \propto N^{2} \).

Option (2) Area of cross-section of the solenoid — Affects the inductance. \( L \propto A \).

Option (3) Permeability of the core material — Affects the inductance. \( L \propto \mu_r \); an iron core raises \( L \) greatly.

Option (4) Current flowing through the inductor. — Does not affect the inductance. The flux linkage is proportional to the current, so their ratio is independent of the current.

NCERT (2026-27):
Self-Inductance – “… If we fill the inside of the solenoid with a material of relative permeability μ_r (for example soft iron, which has a high value of relative permeability), then,

    \( \displaystyle L = \mu_r \mu_0 n^2 A l \qquad (6.16) \)

The self-inductance of the coil depends on its geometry and on the permeability of the medium.”