QJEEM25Ph9bcb: JEE Main 2025 Physics - Class 12 JEEM25Ph9bcb Solution: Regarding self-inductance: A. The self-inductance of the coil…

Let's analyze each statement:

$\textbf{A. The self-inductance of the coil depends on its geometry.}$

This is true because the self-inductance of a coil is given by formulas that include its geometrical parameters (number of turns, cross-sectional area, length, etc.). For example, for a solenoid,

$L = \mu_0 \mu_r \frac{N^2 A}{l},$

where $N$ is the number of turns, $A$ is the cross-sectional area, and $l$ is the length.

$\textbf{B. Self-inductance does not depend on the permeability of the medium.}$

This is false. The permeability of the medium (represented by $\mu = \mu_0 \mu_r$ ) directly influences the inductance, as seen in the formula above. So, any change in the medium’s permeability will affect the inductance.

$\textbf{C. Self-induced e.m.f. opposes any change in the current in a circuit.}$

This is true, and it is a direct consequence of Lenz's law. The induced electromotive force (e.m.f.) always acts in a direction such that it opposes the change in current that produced it.

$\textbf{D. Self-inductance is the electromagnetic analogue of mass in mechanics.}$

This is true. Just as mass resists changes in velocity (inertia), inductance resists changes in current, which is why it is often compared to the inertial mass in mechanical systems.

$\textbf{E. Work needs to be done against self-induced e.m.f. in establishing the current.}$

This is true because, when you try to change the current, you must do work to overcome the opposing self-induced e.m.f., storing energy in the magnetic field of the inductor.

Based on the above reasoning, the true statements are A, C, D, and E.

Thus, the correct answer is:

Option C

A, C, D, E only