At resonant frequency in a series RLC circuit, what is the net voltage across the two reactive components (inductor and capacitor) when measured together?

Introduction:
Understanding voltage distribution at resonance helps in filter design and impedance matching. This question reinforces the vector cancellation of reactive drops in a resonant series RLC circuit.

Given Data / Assumptions:

• Series RLC circuit operating at resonance.
• Ideal sinusoidal steady-state behavior.
• Phasor analysis applies.

Concept / Approach:
At resonance, XL = XC. The inductor voltage phasor leads the current by 90 degrees; the capacitor voltage phasor lags by 90 degrees. Equal magnitudes and opposite phases yield a phasor sum of zero across L and C together.

Step-by-Step Solution:
1) Write XL = 2 * pi * f0 * L and XC = 1 / (2 * pi * f0 * C).2) At resonance: XL − XC = 0.3) Phasor addition: VL + VC = 0 (equal magnitude, 180-degree phase difference).4) Therefore, the net voltage across the combined series reactances is zero.

Verification / Alternative check:
Impedance view: ZLC = jXL + (−jXC) = j(XL − XC) = 0 at f0, so there is no reactive drop across L + C as a pair.

Why Other Options Are Wrong:
Applied voltage: At resonance most of the source voltage appears across R, not across L + C together.Reactive voltage: Not a numeric value; net reactive drop is zero.VL + VC voltage: The algebraic (phasor) sum equals zero, not a finite nonzero amount.

Common Pitfalls:
Assuming large circulating voltages imply a large net drop; in reality, large but opposite voltages cancel in phasor sum.

Final Answer:
Zero voltage