The coefficient of mutual induction between two circuits is equal to the, emf produced in one circuit when the current in the second circuit is

Options

A. kept steady at 1 A
B. cut-off ai 1 A level
C. changed at the rate of `1As^(-1)`
D. changed from `1 As^(-1)` to `2 As^(-1)`

Answer

To solve the problem regarding the coefficient of mutual induction between two circuits, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Mutual Induction**:
The coefficient of mutual induction (M) between two circuits is a measure of how much electromotive force (emf) is induced in one circuit due to a change in current in the other circuit.

2. **Using the Formula for Mutual Induction**:
The relationship between the emf (E) induced in one circuit and the rate of change of current (di/dt) in the second circuit can be expressed as:
\[ E = -M \frac{di_2}{dt} \]
where \( E \) is the induced emf in the first circuit, \( M \) is the mutual inductance, and \( \frac{di_2}{dt} \) is the rate of change of current in the second circuit.

3. **Rearranging the Formula**:
To find the coefficient of mutual induction, we can rearrange the formula:
\[ M = -\frac{E}{\frac{di_2}{dt}} \]

4. **Interpreting the Question**:
The question states that the coefficient of mutual induction is equal to the emf produced in one circuit when the current in the second circuit is changing. This implies:
\[ M = E \]
when \( \frac{di_2}{dt} = 1 \, \text{A/s} \).

5. **Conclusion**:
Therefore, if the rate of change of current in the second circuit is 1 ampere per second, then the coefficient of mutual induction \( M \) is numerically equal to the induced emf \( E \).

### Final Answer:
The coefficient of mutual induction between two circuits is equal to the emf produced in one circuit when the current in the second circuit is changing at the rate of 1 ampere per second.

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