In an LCR series ac circuit, the current is

Options

A. always in phase with the voltage
B. lags the generator voltage
C. leads the generator voltage
D. none of these

Answer

To solve the question regarding the behavior of current in an LCR series AC circuit, we can break it down into clear steps:

### Step-by-Step Solution

1. **Understanding the Circuit**:
- In an LCR series circuit, we have an inductor (L), a capacitor (C), and a resistor (R) connected in series. The current flowing through the circuit is the same through each component.

2. **Current in the Circuit**:
- The current in a series LCR circuit is constant. This means that the same current flows through the resistor, inductor, and capacitor at any given moment.

3. **Phasor Diagram**:
- To analyze the phase relationships, we can draw a phasor diagram. In this diagram, we take the current as the reference phasor (0 degrees).
- The voltage across the resistor (Vr) is in phase with the current.
- The voltage across the capacitor (Vc) leads the current by 90 degrees.
- The voltage across the inductor (Vl) lags the current by 90 degrees.

4. **Comparing Voltages**:
- We can analyze three cases based on the relationship between the voltages across the inductor and capacitor:
- **Case 1**: If \( V_L > V_C \) (inductive reactance is greater than capacitive reactance), the total voltage \( V_{total} \) leads the current.
- **Case 2**: If \( V_L < V_C \) (capacitive reactance is greater than inductive reactance), the total voltage \( V_{total} \) lags behind the current.
- **Case 3**: If \( V_L = V_C \) (the circuit is at resonance), the voltages cancel each other out, and the total voltage is equal to the voltage across the resistor \( V_R \), which is in phase with the current.

5. **Conclusion**:
- The behavior of the current in an LCR series circuit can be summarized as follows:
- The current is always in phase with the voltage across the resistor.
- The total voltage can either lead or lag the current depending on the relationship between \( V_L \) and \( V_C \).
- At resonance, the current and voltage are in phase.