Series resonance condition — at series resonance, are the inductive and capacitive reactances never equal?

Introduction / Context:Resonance in a series RLC circuit is defined by the balance between inductive and capacitive reactances. This balance governs impedance magnitude and phase, and it sets the peak current condition for a given source voltage.

Given Data / Assumptions:

• Series RLC under sinusoidal steady state.
• XL = omega * L, XC = 1 / (omega * C).
• Resonant frequency denoted as omega0.

Concept / Approach:

By definition of series resonance, XL equals XC in magnitude at omega0. The imaginary parts cancel, leaving net impedance Z = R (minimum magnitude). This is the basis for current maximization and purely resistive phase at resonance.

Step-by-Step Solution:

Verification / Alternative check:

Measured current peaks at resonance and the phase angle between source voltage and current is zero, both confirming that reactive terms are equal and opposite.

Why Other Options Are Wrong:

• Claims that equality never occurs contradict the definition of series resonance.
• Parallel resonance is a different topology; the equality condition discussed here is for series resonance.
• Non-ideal losses do not alter the equality condition; they only broaden the resonance and reduce current magnitude.

Common Pitfalls:

Confusing equality of reactances with equality of impedances. The magnitudes of reactances are equal at resonance; the net impedance is resistive, not zero.

Final Answer:

False