Resonance duplicate (clarified wording): For a series RLC circuit at its resonant frequency (where XL = XC), the total current from a fixed-voltage source reaches a maximum. Is this statement accurate?

Difficulty: Easy

Correct Answer: Accurate

Explanation:


Introduction / Context:
This item reaffirms the behavior of a series RLC at resonance, emphasizing the equality of reactances and the resulting purely resistive impedance that dictates the current peak for a given source voltage.


Given Data / Assumptions:

  • Series RLC network, sinusoidal steady state.
  • Source RMS voltage held constant.
  • Losses modeled by a series resistance R.


Concept / Approach:
At resonance, |Z| = R (minimum), so I = V/|Z| is largest. Although VL and VC can be large and cancel phasorially, they do not increase |Z| at resonance; instead, they produce internal voltage magnification characterized by Q, while the source sees a small resistive |Z|.


Step-by-Step Solution:

Impose XL = XC → Z = R.Compare current off-resonance: |Z| grows as |XL − XC| increases → current falls.Therefore, the maximum current occurs at the resonant frequency.


Verification / Alternative check:
Measure current while sweeping frequency; the plot yields a bell-shaped resonance curve with peak at f0 and −3 dB bandwidth linked to Q.


Why Other Options Are Wrong:

Requiring L = C numerically is irrelevant; resonance depends on ωL = 1/(ωC).Parallel resonance property is different (feed current minimum).Q affects sharpness of the peak, not whether a peak exists.


Common Pitfalls:
Confusing internal reactive voltages with source current; overlooking that the source only “sees” R at resonance.


Final Answer:
Accurate

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