In an LCR series circuit the current is

Options

A. in phase with applied emf
B. lags the applied voltage
C. lead the applied voltage
D. may lead or lag behind the applied voltage

Answer

To solve the problem regarding the current in an LCR series circuit, we need to understand the relationships between the voltage across the inductor (L), capacitor (C), and resistor (R), as well as how they relate to the total current in the circuit.

### 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 to an AC voltage source. The same current (I) flows through all components.

2. **Voltage Relationships**:
- The voltage across the resistor (Vr) is in phase with the current (I).
- The voltage across the inductor (VL) leads the current by 90 degrees (or π/2 radians).
- The voltage across the capacitor (VC) lags behind the current by 90 degrees (or π/2 radians).

3. **Phase Diagram**:
- We can represent these voltages as vectors (phasors) in a phase diagram.
- The voltage across the inductor (VL) is represented as a vector pointing upwards (leading).
- The voltage across the capacitor (VC) is represented as a vector pointing downwards (lagging).
- The voltage across the resistor (Vr) is represented as a vector along the horizontal axis (in phase).

4. **Resultant Voltage**:
- The total voltage (V) in the circuit can be found by vector addition of these voltages.
- If VL > VC, the resultant voltage vector will lead the current, indicating that the circuit is inductive.
- If VC > VL, the resultant voltage vector will lag behind the current, indicating that the circuit is capacitive.
- If VL = VC, the circuit is at resonance, and the total voltage is in phase with the current.

5. **Resonance Condition**:
- The resonance condition occurs when the inductive reactance (XL) equals the capacitive reactance (XC), i.e., \( XL = XC \).
- At resonance, the circuit behaves purely resistively, and the current is in phase with the total voltage.

6. **Conclusion**:
- In an LCR series circuit, the current can either lead or lag depending on the relationship between VL and VC.
- At resonance, the current is in phase with the voltage.

### Final Answer:
The current in an LCR series circuit can lead, lag, or be in phase with the total voltage depending on the values of the inductor and capacitor. The current is in phase when the inductive reactance equals the capacitive reactance (resonance condition).