Calculate the frequency at which the inductive reactance of 0.7 H inductor is `220 Omega`.

Answer

To solve the problem of calculating the frequency at which the inductive reactance of a 0.7 H inductor is 220 Ω, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Inductive Reactance**:
The inductive reactance (XL) is given by the formula:
\[ X_L = \omega L \]
where \( \omega \) is the angular frequency in radians per second, and \( L \) is the inductance in henries.

2. **Relate Angular Frequency to Frequency**:
The angular frequency \( \omega \) can be expressed in terms of frequency \( F \) (in hertz) as:
\[ \omega = 2 \pi F \]
Therefore, we can rewrite the inductive reactance formula as:
\[ X_L = 2 \pi F L \]

3. **Rearranging the Formula to Solve for Frequency**:
We can rearrange the equation to solve for frequency \( F \):
\[ F = \frac{X_L}{2 \pi L} \]

4. **Substituting the Given Values**:
We know that:
- \( X_L = 220 \, \Omega \)
- \( L = 0.7 \, H \)

Substituting these values into the formula gives:
\[ F = \frac{220}{2 \pi \times 0.7} \]

5. **Calculating the Denominator**:
First, calculate \( 2 \pi \times 0.7 \):
\[ 2 \pi \approx 6.28 \quad \text{(using } \pi \approx 3.14\text{)} \]
Therefore:
\[ 2 \pi \times 0.7 \approx 4.396 \]

6. **Final Calculation for Frequency**:
Now substitute this back into the frequency equation:
\[ F = \frac{220}{4.396} \approx 50 \, \text{Hz} \]

### Conclusion:
The frequency at which the inductive reactance of a 0.7 H inductor is 220 Ω is approximately **50 Hz**.