A sinusoidal voltage of peak value 210 V and angular frequency 300/s is applied to a series LCR circuit. Given that `R-5Omega, L-25` mH and `C - 1000 muF`.
Calculate the inductive reactance.

Options

A. `7 Omega`
B. `7.5 Omega`
C. `5 Omega`
D. `10 Omega`

Explanation

To calculate the inductive reactance (XL) in a series LCR circuit, we can use the formula:

\[ X_L = \omega L \]

Where:
- \( X_L \) is the inductive reactance,
- \( \omega \) is the angular frequency,
- \( L \) is the inductance.

### Step 1: Identify the given values
From the problem statement, we have:
- Angular frequency (\( \omega \)) = 300 rad/s
- Inductance (\( L \)) = 25 mH = \( 25 \times 10^{-3} \) H

### Step 2: Substitute the values into the formula
Now we can substitute the values into the formula for inductive reactance:

\[ X_L = \omega L = 300 \, \text{rad/s} \times 25 \times 10^{-3} \, \text{H} \]

### Step 3: Perform the multiplication
Calculating the multiplication:

\[ X_L = 300 \times 25 \times 10^{-3} = 7500 \times 10^{-3} = 7.5 \, \Omega \]

### Step 4: State the final answer
Thus, the inductive reactance \( X_L \) is:

\[ X_L = 7.5 \, \Omega \]