Series RLC resonance definition: Resonance occurs when the inductive and capacitive reactances are equal in magnitude (XL = XC), causing the net reactance to be zero. True or false?

Introduction / Context:Resonance in a series RLC circuit is a cornerstone concept in AC analysis, filters, and tuned amplifiers. At resonance, reactive effects cancel, leaving purely resistive behavior that maximizes current for a given source voltage.

Given Data / Assumptions:

• Series R, L, C circuit driven by a sinusoidal source.
• XL = 2 * pi * f * L and XC = 1 / (2 * pi * f * C).
• Resonant frequency often denoted by f0.

Concept / Approach:

In series RLC, the net reactance is Xnet = XL − XC. Resonance is defined by Xnet = 0, which requires XL = XC. Solving XL = XC yields f0 = 1 / (2 * pi * sqrt(L * C)). At f0, impedance is purely resistive (equal to R), current is in phase with voltage, and reactive power exchange between L and C is internal and equal.

Step-by-Step Solution:

Verification / Alternative check:

Measure phase angle between source voltage and current. At resonance, phase angle is zero and the power factor is unity, confirming XL = XC and Xnet = 0.

Why Other Options Are Wrong:

• “False” would deny the established definition of series resonance (XL equals XC), which is fundamental in circuit theory.

Common Pitfalls:

Mixing series and parallel resonance definitions. In parallel resonance, the condition is different when expressed in terms of susceptances and involves R, but the equality XL = XC in magnitude still indicates reactive cancellation.

Final Answer:

True