Calculate the reactance of 10 m H inductor connected to an AC source with frequency of 100 Hz.

Answer

To calculate the reactance of a 10 mH inductor connected to an AC source with a frequency of 100 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Inductance (L) = 10 mH = 10 × 10^(-3) H = 0.01 H
- Frequency (f) = 100 Hz

2. **Calculate the angular frequency (ω)**:
The angular frequency (ω) is given by the formula:
\[ \omega = 2\pi f \]
Substituting the value of frequency:
\[ \omega = 2 \times \pi \times 100 \]
Using π ≈ 3.14:
\[ \omega = 2 \times 3.14 \times 100 = 628.0 \, \text{rad/s} \]

3. **Calculate the inductive reactance (X_L)**:
The inductive reactance (X_L) is calculated using the formula:
\[ X_L = \omega L \]
Substituting the values of ω and L:
\[ X_L = 628.0 \times 0.01 \]
\[ X_L = 6.28 \, \Omega \]

4. **Final Result**:
The inductive reactance of the inductor is:
\[ X_L = 6.28 \, \Omega \]