Reactive voltage cancellation — at resonance, do the inductor and capacitor voltage drops (VL and VC) cancel each other?

Introduction / Context:
At resonance, reactive effects in RLC circuits balance. The concept of reactive voltage cancellation explains why the net reactive component of impedance disappears at the resonant frequency.

Given Data / Assumptions:

• Series RLC circuit under sinusoidal steady state (the explanation also extends to reactive power in parallel resonance).
• Inductive and capacitive reactances are equal in magnitude at resonance.
• Finite resistance is present, so current is finite.

Concept / Approach:

In a series RLC at resonance, XL = XC. The inductor drop is VL = I * XL, and the capacitor drop is VC = I * (−XC) in phasor form. These two phasors are equal in magnitude and 180 degrees apart, so their sum is zero. The source therefore only supplies the resistive drop across R.

Step-by-Step Solution:

Verification / Alternative check:

Applying Kirchhoff’s Voltage Law around the loop at resonance yields V_source = V_R, with the vector sum of VL and VC equal to zero. Oscilloscope measurements with current sensing show opposing inductor and capacitor waveforms that cancel vectorially.

Why Other Options Are Wrong:

• Cancellation does not require zero resistance; it requires equality of reactances.
• It is not restricted to parallel RLC; in parallel circuits, reactive powers cancel at resonance as well.
• Infinite Q is unnecessary; finite Q simply limits peak magnitudes.

Common Pitfalls:

Interpreting “cancel” as “each voltage is zero.” VL and VC can be large individually at high Q, yet their phasor sum is zero at resonance.

Final Answer:

True