An inductor of 30 mH is connected to a 220 V, 100 Hz ac source. The inductive reactance is

Options

A. `10.58 Omega`
B. `12.64 Omega`
C. `18.85 Omega`
D. `22.67 Omega`

Explanation

To calculate the inductive reactance (XL) of an inductor connected to an AC source, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Inductance (L) = 30 mH = 30 × 10^(-3) H
- Frequency (f) = 100 Hz
- Voltage (V) = 220 V (not needed for this calculation)

2. **Recall the formula for inductive reactance:**
The formula for inductive reactance (XL) is given by:
\[ X_L = 2 \pi f L \]

3. **Substitute the known values into the formula:**
\[ X_L = 2 \pi (100 \, \text{Hz}) (30 \times 10^{-3} \, \text{H}) \]

4. **Calculate the value:**
- First, calculate \(2 \pi\):
\[ 2 \pi \approx 6.2832 \]
- Now substitute this value into the equation:
\[ X_L = 6.2832 \times 100 \times 30 \times 10^{-3} \]
- Simplifying further:
\[ X_L = 6.2832 \times 3 = 18.8496 \, \text{ohms} \]

5. **Round the answer:**
- Rounding to two decimal places gives:
\[ X_L \approx 18.84 \, \text{ohms} \]

### Final Answer:
The inductive reactance (XL) is approximately **18.84 ohms**.

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