The coefficient of self inductance and the coefficient of mutual inductance have

Options

A. me units but different dimensions
B. different units but same dimensions
C. different units and different dimensions
D. same units and same dimensions

Answer

To solve the question regarding the coefficient of self-inductance and the coefficient of mutual inductance, we will analyze the definitions and units of both concepts step by step.

### Step 1: Understanding Self-Inductance
- Self-inductance (L) is defined as the property of a coil (or inductor) that allows it to induce an electromotive force (emf) in itself due to a change in current flowing through it.
- The relationship can be expressed as:
\[ \Phi = L \cdot I \]
where \(\Phi\) is the magnetic flux linked with the coil, \(L\) is the self-inductance, and \(I\) is the current.

### Step 2: Deriving the Unit of Self-Inductance
- Rearranging the equation gives:
\[ L = \frac{\Phi}{I} \]
- The unit of magnetic flux (\(\Phi\)) is Weber (Wb), and the unit of current (I) is Ampere (A).
- Therefore, the unit of self-inductance (L) is:
\[ \text{Unit of } L = \frac{\text{Weber}}{\text{Ampere}} = \text{Wb/A} \]

### Step 3: Understanding Mutual Inductance
- Mutual inductance (M) is defined as the property of two coils whereby a change in current in one coil induces an emf in the other coil.
- The relationship can be expressed as:
\[ \Phi = M \cdot I_2 \]
where \(\Phi\) is the magnetic flux linked with one coil due to the current \(I_2\) in the other coil.

### Step 4: Deriving the Unit of Mutual Inductance
- Rearranging the equation gives:
\[ M = \frac{\Phi}{I_2} \]
- Again, the unit of magnetic flux (\(\Phi\)) is Weber (Wb), and the unit of current (\(I_2\)) is Ampere (A).
- Therefore, the unit of mutual inductance (M) is:
\[ \text{Unit of } M = \frac{\text{Weber}}{\text{Ampere}} = \text{Wb/A} \]

### Step 5: Comparing Self-Inductance and Mutual Inductance
- From the above steps, we find that both self-inductance (L) and mutual inductance (M) have the same unit, which is Weber per Ampere (Wb/A).
- Since both quantities are defined in terms of magnetic flux and current, their dimensions are also the same.

### Conclusion
- Therefore, the coefficient of self-inductance and the coefficient of mutual inductance have the same unit and the same dimension.

The correct option is **D: same unit and same dimension**.