The unit of inductance is

Options

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

Explanation

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

### Step 1: Understand the relationship involving inductance
Inductance (L) is defined in terms of the potential difference (V) across an inductor and the rate of change of current (dI/dt) through it. The relationship is given by the formula:
\[ V = L \frac{dI}{dt} \]

### Step 2: Rearrange the formula to solve for inductance
From the equation above, we can rearrange it to express inductance:
\[ L = \frac{V}{\frac{dI}{dt}} \]

### Step 3: Identify the units of voltage and current
- The unit of voltage (V) is volts (V).
- The unit of current (I) is amperes (A).
- The rate of change of current (dI/dt) has units of amperes per second (A/s).

### Step 4: Substitute the units into the formula
Now, substituting the units into the equation for inductance:
\[ L = \frac{\text{Volts}}{\text{Amperes/second}} \]

### Step 5: Simplify the units
This can be simplified as follows:
\[ L = \frac{V \cdot s}{A} \]
Where 's' represents seconds.

### Step 6: Final expression for the unit of inductance
Thus, the unit of inductance can be expressed as:
\[ L = \text{Volt} \cdot \text{second} \cdot \text{per} \text{Ampere} \]
Or more commonly written as:
\[ L = \text{Henry} \, (H) \]

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

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