In an AC circuit, a resistance of `Rohm` is connected in 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 given data

Answer

To solve the problem step by step, we will analyze the given information and apply relevant formulas from AC circuit theory.

### Step 1: Understand the given information
We have an AC circuit with:
- Resistance \( R \) (in ohms)
- Inductance \( L \)
- Phase angle \( \phi = 45^\circ \)

### Step 2: Relate phase angle to power factor
The phase angle \( \phi \) is related to the power factor \( \cos \phi \). For \( \phi = 45^\circ \):
\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]
This is the power factor of the circuit.

### Step 3: Use the relationship in an RL circuit
In a series RL circuit, the relationship between the inductive reactance \( X_L \), resistance \( R \), and phase angle \( \phi \) can be expressed using the tangent function:
\[ \tan \phi = \frac{X_L}{R} \]
Since \( \phi = 45^\circ \):
\[ \tan 45^\circ = 1 \]
Thus, we have:
\[ 1 = \frac{X_L}{R} \]

### Step 4: Solve for inductive reactance \( X_L \)
From the equation above, we can rearrange it to find \( X_L \):
\[ X_L = R \]

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

### Final Answer
\[ X_L = R \]

---