Question

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

• A. A, B, C, D only
• B. A, C, D, E only
• C. A, B, C, E only
• D. B, C, D, E only

Hint:

Self-inductance depends on factors such as the coil's geometry, the medium's permeability, and the number of turns in the coil. Remember that it is directly related to the opposition of current change.

Answer 1

The Correct Option is B

To determine the correct statements regarding self-inductance, we need to analyze each given statement:

1. Statement A: The self-inductance of the coil depends on its geometry. 
   Self-inductance actually depends on several factors including the number of turns of the coil, the area of the coil, and the length of the coil. These are all geometrical parameters, meaning the self-inductance is influenced by the coil's geometry. Thus, this statement is correct.
2. Statement B: Self-inductance does not depend on the permeability of the medium.
   This statement is incorrect. Self-inductance is directly proportional to the permeability of the medium in which the coil is placed. Higher permeability increases the magnetic flux for a given current, increasing self-inductance.
3. Statement C: Self-induced e.m.f. opposes any change in the current in a circuit.
   According to Lenz's Law, the self-induced e.m.f. in a coil opposes the change in current that created it. This is known as the back e.m.f. of the coil. Therefore, this statement is correct.
4. Statement D: Self-inductance is the electromagnetic analogue of mass in mechanics.
   In mechanics, mass resists changes in velocity due to inertia. In an electrical circuit, self-inductance resists changes in current. Therefore, self-inductance can be considered analogous to mass in mechanics. This statement is correct.
5. Statement E: Work needs to be done against self-induced e.m.f. in establishing the current.
   When the current in a coil is changing, work must be done to overcome the back e.m.f. produced by the self-inductance. Therefore, this statement is also correct.

From the analysis above, statements A, C, D, and E are correct. Therefore, the correct answer is:

A, C, D, E only

Answer 2

Explanation:

To determine the correct statements regarding self-inductance, let's analyze each:

1. A: The self-inductance of the coil depends on its geometry.
   This statement is true. The self-inductance (\(L\)) of a coil is a function of its geometry, such as the number of turns, the cross-sectional area, and its length.
2. B: Self-inductance does not depend on the permeability of the medium.
   This statement is false. Self-inductance does depend on the permeability (\(\mu\)) of the medium in which the coil is placed. The inductance is generally given by \(L = \mu \cdot N^2 \cdot A / l\), where \(N\) is the number of turns, \(A\) is the cross-sectional area, and \(l\) is the length of the coil.
3. C: Self-induced e.m.f. opposes any change in the current in a circuit.
   This statement is true. According to Lenz's Law, the electromotive force (e.m.f.) induced by a changing current will oppose the change in current, adhering to the principle of conservation of energy.
4. D: Self-inductance is the electromagnetic analogue of mass in mechanics.
   This statement is true. Just as mass resists changes in motion (inertia) in mechanics, self-inductance resists changes in current in an electrical circuit.
5. E: Work needs to be done against self-induced e.m.f. in establishing the current.
   This statement is true. When the current changes, work must be done against the self-induced e.m.f. to establish or change the current flow in the circuit.

The correct option is A, C, D, E only because these statements accurately describe the characteristics and effects of self-inductance.