Question 120 of 153
Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:
Show answer and solution
Answer: (C) only
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.
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.
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.
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.
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 \(\mathrm{A}, \mathrm{C}, \mathrm{D}\), and E.
Thus, the correct answer is:
Option C
A, C, D, E only
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.
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.
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.
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.
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 \(\mathrm{A}, \mathrm{C}, \mathrm{D}\), and E.
Thus, the correct answer is:
Option C
A, C, D, E only