Reactances in RLC circuits — do inductive reactance (XL) and capacitive reactance (XC) act in opposition to each other?

Introduction / Context:
RLC behavior depends on how reactive components combine in the impedance domain. Inductive and capacitive effects oppose each other in phase, which determines net reactance and the condition for resonance.

Given Data / Assumptions:

• Sinusoidal steady-state operation.
• Inductor reactance XL = omega * L (positive imaginary).
• Capacitor reactance XC = 1 / (omega * C) and impedance is negative imaginary.

Concept / Approach:

In phasor form, inductive reactance contributes +jXL, while capacitive reactance contributes −jXC. The net reactive term is j(XL − XC) in series, or the difference of susceptances in parallel. This sign opposition is the mathematical expression of their opposing effects.

Step-by-Step Solution:

Verification / Alternative check:

Bode plots of a series RLC show phase crossing zero at the frequency where XL equals XC, confirming the cancellation between the opposing reactances.

Why Other Options Are Wrong:

• They do not always add; their signs are opposite in the imaginary axis.
• The opposition exists at all frequencies, not only at resonance.
• Presence of resistance does not change the sign opposition, only the damping.

Common Pitfalls:

Using magnitudes only (XL and XC) without considering sign in phasor arithmetic. Always keep the j sign to avoid mistakes.

Final Answer:

True