Series R–L–C notch output: In a series-tuned notch configuration where the output is taken across the series L–C branch, what is the ideal output voltage at exact resonance (assume a stiff voltage source and negligible component loss)?

Introduction / Context:
A common way to realize a band-stop (notch) response is to use a series R–L–C path and take the output across the reactive branch (L–C). At the notch (resonant) frequency, the inductive and capacitive reactances cancel in magnitude, dramatically changing the voltage division. This question asks for the ideal output at that frequency.

Given Data / Assumptions:

• Series R–L–C driven by an ideal voltage source.
• Output measured across the L–C series sub-branch.
• Ideal components (no resistance in L or leakage in C) to illustrate the principle.

Concept / Approach:
In a series R–L–C, the total impedance is Z = R + j(XL − XC). At resonance, XL = XC so the net reactive term is zero and Z ≈ R. Importantly, the inductor and capacitor voltages are equal and opposite at resonance, so the net voltage across the L–C series pair is ideally zero, even though the individual element voltages can be large and opposite in sign. Therefore, a detector connected across the L–C pair reads a deep minimum (the notch).

Step-by-Step Solution:

Verification / Alternative check:
Phasor diagram shows v_L and v_C 180 degrees apart with equal magnitude at f0, summing to zero. Practical parts have finite Q, so a small but nonzero residual appears; the ideal target remains 0 V.

Why Other Options Are Wrong:
557 mV, 6.08 V, 6.5 V: these imply a nonzero residual inconsistent with the ideal cancellation at resonance in a pure series L–C branch.

Common Pitfalls:
Forgetting that while the L and C each can have large voltages at f0, their sum across the series pair is zero. Confusing this notch with the band-pass response seen when measuring across the resistor.

Final Answer:
0 V