Filter identification in a series R–L–C network: If the output voltage is taken across the series resistor (and the input drives the same series R–L–C loop from a voltage source), does the circuit behave as a band-stop (notch) filter or not?

Introduction / Context:
Series R–L–C circuits are used to build simple frequency-selective filters. Whether the network is band-pass or band-stop depends on where the output is measured. This item asks you to judge the claim that taking the output across the series resistor makes the circuit a band-stop (notch) filter.

Given Data / Assumptions:

• Single loop driven by an ideal voltage source.
• Elements R, L, and C in series; output measured across R only.
• Linear, time-invariant components; standard small-signal operation.

Concept / Approach:
In a series R–L–C, the current peaks at resonance because the net reactance cancels (XL = XC), leaving the loop impedance approximately R. The resistor's voltage is v_R = i * R, so when current peaks at resonance, the resistor's voltage also peaks. A response that peaks at a center frequency and falls off on both sides is the hallmark of a band-pass, not a band-stop. By contrast, taking the output across L or across C in the same series loop yields a deep minimum at resonance (because the reactive element's voltage tends toward zero there), which is a notch or band-stop behavior.

Step-by-Step Solution:

Verification / Alternative check:
Plotting |v_R/V_in| vs frequency shows a peak near f_0; plotting |v_L/V_in| or |v_C/V_in| shows a dip at f_0. This matches standard lab measurements and textbook Bode plots.

Why Other Options Are Wrong:
Correct: contradicts series-R output behavior (band-pass).
Applies only with an ideal current source: the statement concerns a voltage source; with a current source the mapping of outputs changes but does not make the R output a notch under a voltage-source assumption.
Cannot be determined: with the stated series topology and output node, it is determinable.

Common Pitfalls:
Confusing the R output (band-pass) with L or C outputs (notch). Mixing up series vs parallel tuned circuits.

Final Answer:
Incorrect