When are the voltage and current in LCR-series AC circuit in phase? A- XL<XC B- XL> XC C. XL=XC D- Indeterminant

Voltage and Current in LCR-Series AC Circuit

In an LCR (Inductor-Capacitor-Resistor) series AC circuit, the relationship between the reactance of the inductor ($X_L$) and the reactance of the capacitor ($X_C$) determines the phase difference between the voltage across the circuit and the current flowing through it.

1. Understanding Reactance:

   • $X_L$ is the inductive reactance, given by the formula $X_L = \omega L$, where $L$ is the inductance and $\omega$ is the angular frequency.
   • $X_C$ is the capacitive reactance, given by the formula $X_C = \frac{1}{\omega C}$, where $C$ is the capacitance.

2. Phase Relationship:

   • When $X_L = X_C$, the circuit is said to be at resonance, and the voltage and current are in phase.
   • If $X_L < X_C$, the circuit behaves predominantly like a capacitive circuit, with current leading the voltage.
   • If $X_L > X_C$, the circuit behaves predominantly like an inductive circuit, with voltage leading the current.

3. Conclusion:

   • The voltage and current in an LCR-series AC circuit are in phase when $X_L = X_C$.

Final Answer

C. $X_L = X_C$