Coil Q at resonance — effect of series resistance: Does increasing a coil’s series resistance increase its quality factor Q at resonance?

Introduction / Context:The quality factor Q expresses how under-damped or selective a resonant circuit is. For a series RLC at resonance, Q relates the reactive energy exchange to real power dissipation. Coil resistance is a major contributor to series loss, so its effect on Q is fundamental to RF design and filters.

Given Data / Assumptions:

• Series resonant circuit model with inductor series resistance R.
• Sinusoidal steady state at resonant frequency f0.
• Ideal L and C except for the noted resistance.

Concept / Approach:For series resonance, Q = X_L / R at f0 (equivalently Q = ω0L / R). Increasing R in the denominator reduces Q. Lower Q widens the bandwidth (BW ≈ f0/Q) and reduces peak voltage magnification across L and C at resonance.

Step-by-Step Solution:

Verification / Alternative check:Network analyzer measurements show increased 3 dB bandwidth and lower peak response as series resistance rises. Simulation likewise confirms Q ∝ 1/R for fixed L, C at f0.

Why Other Options Are Wrong:

Common Pitfalls:Mixing up series and parallel definitions of Q; overlooking that parallel-resonant “Rp” enters Q_p = Rp / X_L, a different configuration.

Final Answer:Incorrect — increasing resistance lowers Q