The inductance of a resistance less coil is 0.5 henry. In the coil the value of A.C. is 0.2 Amp whose frequency is 50Hz. The reactance of circuit is -

Options

A. `15.7 Omega`
B. `157 Omega`
C. `1.57 Omega`
D. `757 Omega `

Answer

To find the reactance of the circuit, we can use the formula for inductive reactance, which is given by:

\[ X_L = 2 \pi f L \]

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Inductance \(L = 0.5 \, \text{H}\)
- Frequency \(f = 50 \, \text{Hz}\)

2. **Substitute the values into the formula**:
\[ X_L = 2 \pi (50) (0.5) \]

3. **Calculate the value**:
- First, calculate \(2 \pi\):
\[ 2 \pi \approx 6.2832 \]
- Now, multiply:
\[ X_L = 6.2832 \times 50 \times 0.5 \]
- Calculate \(50 \times 0.5 = 25\):
\[ X_L = 6.2832 \times 25 \]
- Finally, calculate \(6.2832 \times 25\):
\[ X_L \approx 157.08 \, \Omega \]

4. **Conclusion**:
The reactance of the circuit is approximately \(157.08 \, \Omega\).