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 question regarding the coefficient of mutual induction between two circuits, we can follow these steps:

### Step 1: Understand Mutual Inductance
Mutual inductance (M) is a measure of the ability of one circuit to induce an electromotive force (emf) in another circuit due to a change in current. When the current in one coil changes, it creates a changing magnetic field, which induces an emf in the second coil.

### Step 2: Use the Formula for Induced EMF
The induced emf (E) in one coil due to a change in current in the other coil can be expressed using the formula:
\[ E = -M \frac{di}{dt} \]
Where:
- \( E \) is the induced emf,
- \( M \) is the mutual inductance,
- \( \frac{di}{dt} \) is the rate of change of current in the first coil.

### Step 3: Analyze the Given Information
According to the question, we need to find the coefficient of mutual induction when the current in the second circuit changes at a rate of 1 ampere per second. This means:
- \( \frac{di}{dt} = 1 \, \text{A/s} \)

### Step 4: Relate Mutual Inductance to Induced EMF
From the formula:
\[ E = -M \frac{di}{dt} \]
We can rearrange it to express mutual inductance:
\[ M = -\frac{E}{\frac{di}{dt}} \]

### Step 5: Substitute the Values
Since we are looking for the coefficient of mutual induction when the current changes at a rate of 1 A/s, we can substitute:
- \( \frac{di}{dt} = 1 \, \text{A/s} \)

Thus, the equation simplifies to:
\[ M = -E \]

### Step 6: Conclusion
The coefficient of mutual induction (M) is equal to the induced emf (E) produced in one circuit when the current in the second circuit changes at a rate of 1 ampere per second.

### 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 changes at a rate of 1 ampere per second.

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