Series RLC at resonance — is the current minimum at resonance in a series circuit?

Introduction / Context:
Resonance in series and parallel circuits has opposite current characteristics. Recognizing which topology exhibits maximum current at resonance prevents design mistakes in filters and matching networks.

Given Data / Assumptions:

• Series RLC with source voltage V_rms.
• XL = omega * L, XC = 1 / (omega * C).
• Resonance at omega0 where XL = XC.

Concept / Approach:

At series resonance, the reactive terms cancel, yielding Z = R (minimum magnitude). With Z minimized, current is maximized for a given source voltage by Ohm’s law. Therefore the current is at its maximum, not minimum, at series resonance.

Step-by-Step Solution:

Verification / Alternative check:

Contrast with parallel resonance, where input current from the source can be minimum at resonance due to high input impedance, while large circulating currents can exist within the branches.

Why Other Options Are Wrong:

• High Q increases the current peak but does not change the fact that the peak occurs at resonance.
• The condition “only if XL equals XC” defines resonance; even then the current is maximum, not minimum.

Common Pitfalls:

Confusing series and parallel resonance properties. Remember: series resonance minimizes impedance and maximizes current; parallel resonance maximizes impedance and minimizes source current.

Final Answer:

False