The unit of inductance is

Options

A. `A( V-s )^(-1) `
B. `JA^(-1)`
C. `V-sA^(-1)`
D. `V-As^(-1)`

Explanation

To find the unit of inductance, we start with the formula for induced electromotive force (e.m.f.) in a circuit, which is given by:

\[ e = L \frac{di}{dt} \]

Where:
- \( e \) is the induced e.m.f. (in volts),
- \( L \) is the inductance (in henries),
- \( \frac{di}{dt} \) is the rate of change of current (in amperes per second).

### Step 1: Rearrange the formula to isolate \( L \)

From the formula, we can rearrange it to solve for \( L \):

\[ L = \frac{e}{\frac{di}{dt}} \]

### Step 2: Substitute the units

Now, we substitute the units for each component:
- The unit of e.m.f. (voltage) is volts (V).
- The unit of current (i) is amperes (A).
- The unit of time (t) is seconds (s).

Thus, we can express the units as:

\[ L = \frac{\text{volts}}{\text{amperes per second}} = \frac{V}{A/s} \]

### Step 3: Simplify the expression

This can be simplified further:

\[ L = \frac{V \cdot s}{A} \]

### Step 4: Identify the unit of inductance

The derived unit of inductance is therefore:

\[ L = \text{volt} \cdot \text{second} \cdot \text{per} \text{ampere} = \text{volt second per ampere} \]

### Conclusion

The unit of inductance is:

\[ \text{volt second per ampere} \]

### Answer

Thus, the correct option is **volt second per ampere**.

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