At what frequency will a `0.5 H` inductor have a reactance of `1000 Omega `?

Options

A. `320 Hz `
B. `318 . 5 Hz `
C. `319 Hz `
D. `319 . 5 Hz`

Answer

To find the frequency at which a 0.5 H inductor has a reactance of 1000 Ω, we can use the formula for inductive reactance:

### Step-by-Step Solution:

1. **Understand the formula for inductive reactance (X_L)**:
The inductive reactance \( X_L \) is given by 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).

2. **Substitute the known values into the formula**:
We know that:
- \( X_L = 1000 \, \Omega \)
- \( L = 0.5 \, H \)

Substituting these values into the formula gives:
\[ 1000 = 2 \pi f (0.5) \]

3. **Simplify the equation**:
Rearranging the equation to solve for frequency \( f \):
\[ 1000 = \pi f \]
\[ f = \frac{1000}{\pi} \]

4. **Calculate the frequency**:
Using the approximate value of \( \pi \approx \frac{22}{7} \):
\[ f = \frac{1000 \times 7}{22} \approx \frac{7000}{22} \approx 318.18 \, Hz \]

5. **Round the answer**:
Rounding the answer gives:
\[ f \approx 318.5 \, Hz \]

### Final Answer:
The frequency at which the 0.5 H inductor has a reactance of 1000 Ω is approximately **318.5 Hz**.

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