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 of the coils X and Y, we can use the formula for mutual inductance (M):

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

where:
- \( \Delta \Phi \) is the change in magnetic flux in coil Y (in Webers),
- \( \Delta I \) is the change in current in coil X (in Amperes).

### 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 mutual inductance 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. **Conclusion:**
The mutual inductance of the coils X and Y is \( 0.2 \, \text{H} \).

### Final Answer:
The value of mutual inductance of the coils is \( 0.2 \, \text{H} \).

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