What is the inductive reactance of a coil of inductance 10mH at a frequency (1) 50Hz (2)
1000Hz (3) 20kHz?

Answer

To find the inductive reactance (XL) of a coil with a given inductance at different frequencies, we can use the formula:

\[ X_L = 2 \pi f L \]

where:
- \( X_L \) is the inductive reactance in ohms (Ω),
- \( f \) is the frequency in hertz (Hz),
- \( L \) is the inductance in henries (H).

Given:
- Inductance \( L = 10 \, \text{mH} = 10 \times 10^{-3} \, \text{H} = 0.01 \, \text{H} \)

Now, we will calculate the inductive reactance for each frequency.

### Step 1: Calculate \( X_L \) at 50 Hz
1. Substitute \( f = 50 \, \text{Hz} \) and \( L = 0.01 \, \text{H} \) into the formula:
\[ X_L = 2 \pi (50) (0.01) \]
2. Calculate:
\[ X_L = 2 \times 3.14 \times 50 \times 0.01 = 3.14 \, \text{Ω} \]

### Step 2: Calculate \( X_L \) at 1000 Hz
1. Substitute \( f = 1000 \, \text{Hz} \) and \( L = 0.01 \, \text{H} \) into the formula:
\[ X_L = 2 \pi (1000) (0.01) \]
2. Calculate:
\[ X_L = 2 \times 3.14 \times 1000 \times 0.01 = 62.8 \, \text{Ω} \]

### Step 3: Calculate \( X_L \) at 20 kHz
1. Convert 20 kHz to Hz: \( 20 \, \text{kHz} = 20 \times 10^3 \, \text{Hz} = 20000 \, \text{Hz} \)
2. Substitute \( f = 20000 \, \text{Hz} \) and \( L = 0.01 \, \text{H} \) into the formula:
\[ X_L = 2 \pi (20000) (0.01) \]
3. Calculate:
\[ X_L = 2 \times 3.14 \times 20000 \times 0.01 = 1256 \, \text{Ω} \]

### Final Results:
1. At 50 Hz: \( X_L = 3.14 \, \text{Ω} \)
2. At 1000 Hz: \( X_L = 62.8 \, \text{Ω} \)
3. At 20 kHz: \( X_L = 1256 \, \text{Ω} \)