Mutual inductance depends on:

Options

A. number of turns of coil 1 only
B. number of turns of coil 2 only
C. both (a) and (b)
D. neither (a) nor (b)

Explanation

To understand the factors that affect mutual inductance, let's break down the concept step by step.

### Step-by-Step Solution:

1. **Understanding Mutual Inductance**:
- Mutual inductance (M) is a measure of the ability of one coil to induce an electromotive force (emf) in another coil due to a change in current in the first coil.

2. **Formula for Mutual Inductance**:
- The mutual inductance between two coils can be expressed as:
\[ \Phi = M \cdot I_2 \]
where \( \Phi \) is the magnetic flux through the second coil, \( M \) is the mutual inductance, and \( I_2 \) is the current in the second coil.

3. **Dependence on Current**:
- The mutual inductance is directly proportional to the current flowing through the first coil. If the current in the first coil changes, it affects the magnetic field and thus the induced emf in the second coil.

4. **Dependence on Number of Turns**:
- The mutual inductance also depends on the number of turns in the second coil. More turns mean a greater area for the magnetic field lines to pass through, resulting in a higher induced emf.

5. **Dependence on Geometric Configuration**:
- The mutual inductance is influenced by the distance between the coils and their relative orientation. Closer coils or coils that are aligned properly will have a higher mutual inductance.

6. **Dependence on Magnetic Permeability**:
- The mutual inductance is also affected by the medium between the coils. If the coils are placed in a material with high magnetic permeability, the mutual inductance will increase.

### Summary of Factors Affecting Mutual Inductance:
- Current in the first coil (\(I_1\))
- Number of turns in the second coil (\(N_2\))
- Geometric configuration (distance and orientation of the coils)
- Magnetic permeability of the medium between the coils