Final answer:
Phasors provide a graphical method to analyze the current and voltages in an RLC series circuit at resonance, where the circuit behaves as purely resistive, and both inductive and capacitive reactances cancel each other out. The resonant frequency occurs where this condition is met, leading to in-phase current and voltage across the resistor with a phase angle of zero.
Step-by-step explanation:
Understanding Phasors in a Resonant RLC Series Circuit
The question refers to a common topic in college-level physics, specifically within the subject of electricity and magnetism. Phasors are a graphical representation used to analyze the behavior of alternating currents (AC) and voltages in an RLC (Resistor, Inductor, Capacitor) series circuit at resonance. In an RLC series circuit at resonance, the inductive and capacitive reactances are equal in magnitude but opposite in phase, causing them to cancel out. As a result, the circuit's impedance is purely resistive, and the current, I, and voltage across the resistor, VRo, are in phase.
The voltage across the inductor, VLo, and the voltage across the capacitor, VCo, are 180 degrees out of phase at resonance. Consequently, the magnitude of these voltages can be much larger than the source voltage but they subtract to zero, effectively leaving only the resistive voltage drop in the circuit. The resonance frequency, fo, is the frequency at which this condition occurs, and it can be calculated using the resonant frequency formula for a series RLC circuit.
An important concept in this scenario is the quality factor, Q, which represents the sharpness of the resonance peak, and the bandwidth, which represents the frequency range over which the circuit effectively resonates. The phase angle in this circuit will be zero because the current and voltage across the resistor are in phase, while the power factor will be 1 because the circuit behaves as a pure resistor at resonance.