X and Y, two metallic coils are arranged in such a way that, when steady change in current flowing in X coil is 4 A, change in magnetic flux associated with coil Y is 0.4 Wb. Mutual inductance of the system of these coils is

Options

A. 0.2 H
B. 5 H
C. 0.8 H
D. 0.1 H

Answer

To find the mutual inductance of the system of coils X and Y, we can use the formula that relates the change in magnetic flux in one coil to the change in current in another coil. The formula for mutual inductance \( M \) is given by:

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

where:
- \( \Delta \Phi \) is the change in magnetic flux associated with coil Y,
- \( \Delta I \) is the change in current flowing through coil X.

### Step-by-Step Solution:

1. **Identify the given values**:
- Change in current flowing through coil X, \( \Delta I = 4 \, \text{A} \)
- Change in magnetic flux associated with coil Y, \( \Delta \Phi = 0.4 \, \text{Wb} \)

2. **Substitute the values into the mutual inductance formula**:
\[ M = \frac{\Delta \Phi}{\Delta I} = \frac{0.4 \, \text{Wb}}{4 \, \text{A}} \]

3. **Perform the calculation**:
\[ M = \frac{0.4}{4} = 0.1 \, \text{H} \]

4. **Conclusion**:
The mutual inductance of the system of coils X and Y is \( 0.1 \, \text{H} \).

### Final Answer:
The mutual inductance \( M \) is \( 0.1 \, \text{H} \).

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