In a series RLC circuit operating exactly at its resonant frequency, what is the measured net voltage across the two reactive components considered together (inductor in series with capacitor)?

Introduction:
Series resonance is a cornerstone concept in AC circuit theory. At resonance, inductive and capacitive reactances are equal in magnitude and opposite in sign. This question examines what happens to the combined voltage across the series inductor and capacitor when the circuit is exactly at resonance.

Given Data / Assumptions:

• Series RLC topology.
• Operating frequency equals the resonant frequency f0.
• Ideal components; steady-state sinusoidal excitation.

Concept / Approach:
At resonance, XL = 2 * pi * f0 * L and XC = 1 / (2 * pi * f0 * C) satisfy XL = XC. Their phasor voltages are equal in magnitude but 180 degrees out of phase. Therefore, the phasor sum across L and C is zero even though each element may have a large individual voltage.

Step-by-Step Solution:
1) Recognize resonance condition: XL = XC.2) Phasor voltages: VL leads current by 90 degrees; VC lags current by 90 degrees.3) Since |VL| = |VC| and their phases are opposite, VL + VC = 0 in phasor terms.4) Hence, the net measured voltage across L and C together is zero.

Verification / Alternative check:
Impedance perspective: ZLC = jXL + (−jXC) = j(XL − XC) = 0 at resonance. A zero reactive impedance means zero net reactive drop across the pair.

Why Other Options Are Wrong:
applied: The applied source voltage appears across the series combination of R, L, and C; the net across L and C alone is zero at resonance.reactive: Not a magnitude; the correct magnitude of the net is zero.inductive and capacitive: Descriptive words, not the value; they cancel at resonance.

Common Pitfalls:
Confusing individual element voltages (which can be high with large Q) with their vector sum, which cancels at true resonance.

Final Answer:
zero