In a circuit, the reactance of a coil is 20`Omega`. If the inductance of the coil is 50mH then angular frequency of the current will be –

Options

A. 400 rad/sec.
B. 1 rad/sec
C. 2.5 rad/sec
D. 0.2 rad/sec

Answer

To find the angular frequency of the current in the circuit, we can follow these steps:

### Step 1: Understand the given values
We are given:
- Reactance of the coil, \( X_L = 20 \, \Omega \)
- Inductance of the coil, \( L = 50 \, \text{mH} = 50 \times 10^{-3} \, \text{H} \)

### Step 2: Use the formula for inductive reactance
The inductive reactance \( X_L \) is related to the angular frequency \( \omega \) and the inductance \( L \) by the formula:
\[ X_L = \omega L \]

### Step 3: Rearrange the formula to solve for angular frequency
We can rearrange the formula to solve for \( \omega \):
\[ \omega = \frac{X_L}{L} \]

### Step 4: Substitute the known values into the formula
Now, substitute the known values into the equation:
\[ \omega = \frac{20 \, \Omega}{50 \times 10^{-3} \, \text{H}} \]

### Step 5: Calculate the angular frequency
Calculating the right-hand side:
\[ \omega = \frac{20}{0.05} = 400 \, \text{rad/s} \]

### Conclusion
Thus, the angular frequency of the current is:
\[ \omega = 400 \, \text{rad/s} \]