Mutual inductance of two coils can be increased by

Options

A. decreasing the number of turns in the coils
B. increasing the number of turns in the coils
C. winding the coils on wooden cores
D. none of these

Explanation

To solve the question regarding how to increase the mutual inductance of two coils, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mutual Inductance**:
Mutual inductance (M) between two coils is given by the formula:
\[ M = \frac{\mu_0 \mu_r N_1 N_2 A}{l} \]
where:
- \( \mu_0 \) = permeability of free space
- \( \mu_r \) = relative permeability of the core material
- \( N_1 \) = number of turns in the first coil
- \( N_2 \) = number of turns in the second coil
- \( A \) = cross-sectional area of the coils
- \( l \) = length of the coils

2. **Analyzing the Options**:
- **Option A**: Decreasing the number of turns.
- If \( N_1 \) or \( N_2 \) decreases, \( M \) will decrease. **Incorrect**.
- **Option B**: Increasing the number of turns.
- If \( N_1 \) or \( N_2 \) increases, \( M \) will increase. **Correct**.
- **Option C**: Winding the coil with a wooden core.
- Wood has low relative permeability (\( \mu_r \)), which would decrease \( M \). **Incorrect**.
- **Option D**: None of the above.
- Since Option B is correct, this option is also **Incorrect**.

3. **Conclusion**:
The mutual inductance of two coils can be increased by **increasing the number of turns in the coils**.