Resonance in a series RLC — total current behavior: If the given circuit operates exactly at series resonance, is the total current drawn from the source at its maximum value (for a fixed source voltage)?

Introduction / Context:Series resonance is a cornerstone concept in AC circuit theory and filter/tank design. It occurs when the inductive reactance equals the capacitive reactance in magnitude (X_L = X_C), causing reactances to cancel so the impedance is purely resistive and minimal.

Given Data / Assumptions:

• Series RLC circuit driven by a fixed RMS voltage.
• Ideal L and C, with a finite series resistance R.
• Frequency is adjustable and can be set to the resonant frequency.

Concept / Approach:Impedance of a series RLC is Z = R + j(X_L − X_C). At resonance, X_L = X_C → Z = R (minimum magnitude). Ohm’s law shows I = V/Z is largest when |Z| is smallest (for fixed V), hence current peaks at resonance. Large reactive voltages may appear across L and C individually, but the net reactive effect in the loop is zero at resonance.

Step-by-Step Solution:

Verification / Alternative check:Plot I versus frequency (a resonance curve). The peak occurs at f_0. Bandwidth relates to quality factor Q = X_L/R at resonance.

Why Other Options Are Wrong:

Common Pitfalls:Confusing series and parallel resonance characteristics; focusing on large VL or VC and missing that total impedance is minimized, not maximized.

Final Answer:Correct