In an AC circuit, a resistance of `Rohm` is connected is series with an inductance `L`. If phase angle between volage and current be `45^(@)`, the value of inductive reactance will be

Options

A. `R//4`
B. `R//2`
C. `R`
D. cannot be found with the given data

Answer

To solve the problem, we need to find the value of the inductive reactance \( X_L \) in an AC circuit where a resistance \( R \) is connected in series with an inductance \( L \), and the phase angle \( \phi \) between the voltage and current is \( 45^\circ \).

### Step-by-Step Solution:

1. **Understand the relationship between phase angle and reactance**:
The phase angle \( \phi \) in an AC circuit is related to the resistance \( R \) and the inductive reactance \( X_L \) by the formula:
\[ \tan(\phi) = \frac{X_L}{R} \]

2. **Substitute the given phase angle**:
We know that the phase angle \( \phi \) is \( 45^\circ \). Therefore, we can substitute this value into the equation:
\[ \tan(45^\circ) = \frac{X_L}{R} \]

3. **Calculate \( \tan(45^\circ) \)**:
The value of \( \tan(45^\circ) \) is \( 1 \). So we can rewrite the equation as:
\[ 1 = \frac{X_L}{R} \]

4. **Solve for inductive reactance \( X_L \)**:
Rearranging the equation gives us:
\[ X_L = R \]

5. **Conclusion**:
Therefore, the value of the inductive reactance \( X_L \) is equal to the resistance \( R \):
\[ X_L = R \]

### Final Answer:
The value of inductive reactance \( X_L \) is equal to \( R \).

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