Which statement about the Q factor is true for a resonant circuit?

• A. Higher Q broadens bandwidth
• B. Higher Q gives narrower bandwidth and sharper resonance.
• C. Q is independent of frequency
• D. Higher Q reduces peak current at resonance

Answer: (B)

The key idea here is that the Q factor measures how selective a resonant circuit is. It compares how much energy the circuit stores to how much it loses each cycle. That balance shows up as how wide or narrow the resonance is in frequency.

In a resonant circuit, the center frequency is f0 and the bandwidth around that frequency where the response stays strong is Δf. The higher the Q, the smaller that bandwidth, roughly Δf ≈ f0 / Q. So increasing Q makes the resonance peak thinner and the circuit more selective to frequencies very close to f0.

You can think of it in practical terms: a high-Q circuit stores energy efficiently (low losses) and releases it primarily near its resonant frequency, so the response falls off more quickly as you move away from resonance. For common topologies, a series circuit shows Q ≈ ω0L/R or 1/(ω0CR); reducing losses (lower R or appropriate L/C values) raises Q and narrows the resonance. In parallel forms, Q has a related dependence but with the same overall effect: a higher Q yields a sharper, more narrowly confined peak.

The other statements don’t hold as general truths. Increasing Q does not broaden the bandwidth; Q is directly related to narrowing it. Q is defined with respect to the operating frequency and losses, so it is not independent of frequency. And whether peak current at resonance goes up or down with Q depends on the circuit topology; in a series circuit higher Q (lower loss) typically means a larger peak current for a fixed input, not a reduction.