Which of the following is equivalent to unit of inductance ?

Options

A. `("volt"xx"ampere")/("second")`
B. `("second")/("volt"xx"ampere")`
C. `("volt")/("ampere" xx"second")`
D. `("volt" xx "second")/("ampere")`

Explanation

To find the equivalent unit of inductance, we need to start with the relationship that defines inductance in terms of voltage (V), current (I), and time (t).

### Step-by-Step Solution:

1. **Understanding Inductance**:
Inductance (L) is defined as the ratio of the induced electromotive force (emf) in a circuit to the rate of change of current through that circuit. Mathematically, this is expressed as:
\[ L = \frac{V}{\frac{dI}{dt}} \]
where:
- \( V \) is the voltage (in volts),
- \( \frac{dI}{dt} \) is the rate of change of current (in amperes per second).

2. **Rearranging the Formula**:
Rearranging the formula gives us:
\[ L = \frac{V \cdot dt}{dI} \]

3. **Identifying Units**:
- The unit of voltage (V) is volts (V).
- The unit of time (dt) is seconds (s).
- The unit of current (dI) is amperes (A).

4. **Substituting Units into the Formula**:
Substituting the units into the rearranged formula gives:
\[ [L] = \frac{[V] \cdot [s]}{[A]} = \frac{\text{volts} \cdot \text{seconds}}{\text{amperes}} \]

5. **Final Unit of Inductance**:
Therefore, the unit of inductance can be expressed as:
\[ [L] = \frac{\text{V} \cdot \text{s}}{\text{A}} = \text{henry (H)} \]
Hence, the equivalent unit of inductance is the henry (H).

### Conclusion:
Among the given options, the correct answer that represents the unit of inductance is the henry (H).