A series LCR circuit, has equal resistance capacitive reactance. What is the phase angle between voltage across generator and resistor ?

Options

A. `0^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To solve the problem, we need to analyze the given series LCR circuit where the resistance (R) is equal to the capacitive reactance (X_C). We are required to find the phase angle between the voltage across the generator and the voltage across the resistor.

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
- In a series LCR circuit, the components are connected in series: an inductor (L), a capacitor (C), and a resistor (R).
- The total voltage (V) is supplied by the generator.

2. **Given Condition**:
- It is given that the resistance (R) is equal to the capacitive reactance (X_C). Therefore, we can write:
\[ R = X_C \]

3. **Impedance Calculation**:
- The total impedance (Z) of the circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
- Since \(X_L\) (inductive reactance) and \(X_C\) (capacitive reactance) are equal, we have:
\[ X_L = X_C \]
- Thus, the equation simplifies to:
\[ Z = \sqrt{R^2 + (X_L - R)^2} \]
- Since \(X_L = R\), we can substitute:
\[ Z = \sqrt{R^2 + (R - R)^2} = \sqrt{R^2} = R \]

4. **Current Calculation**:
- The current (I) in the circuit can be calculated using Ohm's law:
\[ I = \frac{V}{Z} = \frac{V}{R} \]

5. **Phase Angle Determination**:
- In a series LCR circuit, the phase angle (\(\phi\)) between the total voltage and the current can be determined using:
\[ \tan(\phi) = \frac{X_L - X_C}{R} \]
- Since \(X_L = X_C\), we have:
\[ \tan(\phi) = \frac{0}{R} = 0 \]
- Therefore, the phase angle \(\phi\) is:
\[ \phi = 0^\circ \]

6. **Conclusion**:
- The phase angle between the voltage across the generator and the voltage across the resistor is \(0^\circ\).

### Final Answer:
The phase angle between the voltage across the generator and the resistor is \(0^\circ\).