Parallel resonance quality factor — is it correct that the Q of a parallel resonant circuit at resonance equals VC/VS or VL/VS (ratio of reactive branch voltage to source voltage)?

Introduction / Context:
Quality factor (Q) measures selectivity and energy storage relative to loss. Its definition and practical expressions differ between series and parallel resonant circuits. This item checks a common misconception about using a simple voltage ratio for Q in parallel resonance.

Given Data / Assumptions:

• Parallel RLC at resonance (admittance is purely real).
• Reactive branch voltages equal the applied source voltage in parallel topology.
• Realistic losses exist in R, L, and C.

Concept / Approach:
In a series resonant circuit, reactive element voltages can be much larger than the source voltage, and ratios like VL/VR can relate to Q (e.g., Q = XL/R). In a parallel resonant circuit, each branch is directly across the source, so VC ≈ VS and VL ≈ VS at resonance; the ratios VC/VS or VL/VS are about 1, not equal to Q. For parallel resonance, Q is more naturally expressed via currents (reactive branch current to source current) or via reactive/real power in the tank.

Step-by-Step Solution:

Verification / Alternative check:
Tank circuits exhibit large circulating reactive currents at resonance while source current is minimal; this current ratio aligns with Q, not a voltage ratio of ~1.

Why Other Options Are Wrong:

Common Pitfalls:
Transferring series-circuit voltage relationships directly to parallel tanks.

Final Answer:
False