Reactance of an inductor of `1/(pi)` henry at `50Hz` frequency is

Options

A. `50/pi ohm`
B. `pi/50 ohm`
C. `100 ohm`
D. `50 ohm`

Explanation

To find the reactance of an inductor at a given frequency, we can use the formula for inductive reactance, which is given by:

\[ X_L = \omega L \]

where:
- \( X_L \) is the inductive reactance,
- \( \omega \) is the angular frequency in radians per second,
- \( L \) is the inductance in henries.

### Step-by-Step Solution:

1. **Identify the given values**:
- Inductance \( L = \frac{1}{\pi} \) henry
- Frequency \( f = 50 \) Hz

2. **Calculate the angular frequency \( \omega \)**:
The angular frequency is calculated using the formula:
\[ \omega = 2 \pi f \]
Substitute the value of \( f \):
\[ \omega = 2 \pi \times 50 \]
\[ \omega = 100 \pi \, \text{radians/second} \]

3. **Substitute \( \omega \) and \( L \) into the reactance formula**:
Now, we can calculate the inductive reactance \( X_L \):
\[ X_L = \omega L \]
Substitute the values of \( \omega \) and \( L \):
\[ X_L = (100 \pi) \left(\frac{1}{\pi}\right) \]

4. **Simplify the expression**:
The \( \pi \) in the numerator and denominator cancels out:
\[ X_L = 100 \, \text{ohms} \]

### Final Answer:
The reactance of the inductor at 50 Hz is \( 100 \, \text{ohms} \).

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