In an AC circuit, a resistance R is connected in series with an inductance L. If the phase angle between the voltage and the current is pi//4` then the value of ihe inductive reactance is

Options

A. `R//4`
B. `R//2`
C. R
D. `R//s`

Explanation

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 (φ) between the voltage and the current is given as π/4.

### Step-by-Step Solution:

1. **Understanding the Phase Angle**:
The phase angle (φ) in an R-L circuit is given by the formula:
\[ \tan(\phi) = \frac{X_L}{R} \]
where \(X_L\) is the inductive reactance.

2. **Substituting the Given Phase Angle**:
Since the phase angle is given as π/4, we can substitute this into the equation:
\[ \tan\left(\frac{\pi}{4}\right) = \frac{X_L}{R} \]

3. **Calculating the Tangent of π/4**:
We know that:
\[ \tan\left(\frac{\pi}{4}\right) = 1 \]
Therefore, we can rewrite the equation as:
\[ 1 = \frac{X_L}{R} \]

4. **Solving for Inductive Reactance (X_L)**:
Rearranging the equation gives us:
\[ X_L = R \]

5. **Conclusion**:
The value of the inductive reactance \(X_L\) is equal to the resistance \(R\).

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

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