Two coils X and Y are placed in a circuit such that when the current changes by 2 A in coil X. The magnetic flux changes by 0.4 Wb in Y. The value of mutual inductance of the coils is

Options

A. 0.2 H
B. 5 H
C. 0.8 H
D. 4 H

Explanation

To find the mutual inductance (M) between two coils X and Y, we can use the formula that relates the change in magnetic flux (Φ) in coil Y to the change in current (I) in coil X:

\[ M = \frac{\Delta \Phi}{\Delta I} \]

Where:
- \( M \) is the mutual inductance,
- \( \Delta \Phi \) is the change in magnetic flux in coil Y,
- \( \Delta I \) is the change in current in coil X.

### Step-by-step Solution:

1. **Identify the given values**:
- Change in current in coil X, \( \Delta I = 2 \, \text{A} \)
- Change in magnetic flux in coil Y, \( \Delta \Phi = 0.4 \, \text{Wb} \)

2. **Substitute the values into the formula**:
\[ M = \frac{\Delta \Phi}{\Delta I} = \frac{0.4 \, \text{Wb}}{2 \, \text{A}} \]

3. **Calculate the mutual inductance**:
\[ M = \frac{0.4}{2} = 0.2 \, \text{H} \]

4. **Final answer**:
The mutual inductance of the coils is \( 0.2 \, \text{H} \) (Henry).