Parallel resonance (tank circuit): The statement “In a parallel resonant circuit, the total line current at resonance is maximum” is evaluated as true or false. Choose the correct judgement with reasoning.

Introduction / Context:
Parallel resonance, also called anti-resonance, occurs when an inductor and capacitor are connected in parallel (often with losses), forming a tank circuit. At the resonant frequency, the reactive currents in the inductor and in the capacitor circulate between the branches. Understanding whether the source (line) current is maximized or minimized at resonance is crucial for filters and reactive power control.

Given Data / Assumptions:

• Standard parallel RLC circuit where R models losses.
• Steady-state sinusoidal operation at or near resonance.
• Normal quality factor (finite Q), not an ideal lossless case.

Concept / Approach:

At parallel resonance, the net susceptance of the inductor and capacitor cancels (B_L + B_C = 0). As a result, the input admittance is minimized and the input impedance is maximized. While very large branch currents may circulate between L and C (because each branch sees near-resonant conditions), the vector sum at the source terminal is small because the reactive currents largely cancel. Therefore, the line current drawn from the source is minimized, not maximized, at resonance. This is the opposite of a series resonant circuit, where impedance is minimized and current is maximized at resonance.

Step-by-Step Solution:

Verification / Alternative check:

Measure current in a lab tank circuit: ammeter in the line shows a dip at resonance, while branch meters show peaks—directly confirming the theoretical claim of minimum line current at resonance.

Why Other Options Are Wrong:

• “True” and conditional versions mistake the high circulating branch currents for line current; the source sees maximum impedance at resonance, not minimum.
• “False if resistance is zero” is misleading; in the ideal lossless limit, the line current goes to zero (not maximum) because net susceptance cancels exactly.

Common Pitfalls:

• Confusing series vs. parallel resonance; they exhibit opposite input-current behaviors.
• Equating circulating reactive current with source current—these are not the same at resonance in a parallel network.

Final Answer:

False