The unit of mutual inductance is-

Options

A. volt
B. weber
C. tesla
D. henry

Answer

To determine the unit of mutual inductance, we can follow these steps:

### Step 1: Understand the Concept of Mutual Inductance
Mutual inductance is the property of a coil (or inductor) that quantifies the induced electromotive force (emf) in one coil due to a change in current in another coil. It is represented by the symbol \( M \).

### Step 2: Recall the Definition of Inductance
Inductance (L) is defined as the ratio of the induced emf in a coil to the rate of change of current through it. The formula for inductance is given by:
\[ L = -\frac{d\Phi}{dt} \cdot \frac{1}{\frac{di}{dt}} \]
where \( \Phi \) is the magnetic flux.

### Step 3: Relate Mutual Inductance to Induced EMF
For mutual inductance, the induced emf (\( \mathcal{E} \)) in one coil due to a change in current in another coil can be expressed as:
\[ \mathcal{E} = -M \frac{di}{dt} \]
where \( M \) is the mutual inductance.

### Step 4: Determine the Unit of Mutual Inductance
From the equation \( \mathcal{E} = -M \frac{di}{dt} \), we can rearrange it to find the unit of mutual inductance:
\[ M = -\frac{\mathcal{E}}{\frac{di}{dt}} \]
The unit of emf (\( \mathcal{E} \)) is volts (V), and the unit of current (\( i \)) is amperes (A). Therefore, the unit of \( \frac{di}{dt} \) is A/s (amperes per second).

Thus, the unit of mutual inductance can be expressed as:
\[ \text{Unit of } M = \frac{\text{Volts}}{\text{Amperes/second}} = \frac{V \cdot s}{A} \]

### Step 5: Simplify the Units
Using the relation \( 1 \, \text{Henry} = 1 \, \frac{V \cdot s}{A} \), we find that the unit of mutual inductance is indeed Henry (H).

### Conclusion
The unit of mutual inductance is Henry (H).

### Final Answer
The correct option is D: Henry (H).

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