In a series LCR circuit at resonance, the resistance alone is raised from a smaller value to a larger value. What happens to the circuit characteristics?

The bandwidth of the circuit increases.
The resonant frequency increases.
The quality factor increases.
Both the quality factor and resonant frequency stay unchanged.

Correct answer: The bandwidth of the circuit increases.

Solution

Resonant frequency depends only on L and C, so changing R leaves it fixed. Bandwidth equals R/L, so increasing R widens the band. The quality factor (1/R)*sqrt(L/C) falls as R rises. Hence only the bandwidth increases.

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