Power factor limits in AC circuits: Identify the maximum and minimum possible values of the power factor for practical AC circuits.

Introduction / Context:
Power factor (PF) is the cosine of the phase angle between voltage and current in sinusoidal steady state, or more generally the ratio of real power to apparent power. It is a cornerstone metric for efficiency and power quality in AC systems. This question asks for the extreme limits of power factor for typical passive or general AC loads as used in engineering practice.

Given Data / Assumptions:

• Standard definition PF = P / S for sinusoidal systems with P ≥ 0 for passive loads.
• We consider the magnitude behavior in typical utility contexts; sign (leading/lagging) indicates reactive direction but not the limit on magnitude.
• No active power reversal (generation) unless explicitly noted.

Concept / Approach:

For passive loads absorbing power, real power P is nonnegative and bounded by apparent power S. Hence 0 ≤ PF ≤ 1, with PF = 1 for purely resistive loads (no reactive component) and PF = 0 for purely reactive loads (inductor or capacitor only). Some texts allow negative PF when current leads or lags by more than 90° or when power flow reverses, but in standard distribution contexts we report magnitude between 0 and 1 and then state “leading” or “lagging.” Therefore, the correct pair of maximum and minimum values is 1 and 0.

Step-by-Step Solution:

Verification / Alternative check:

In power system measurements, utilities target PF close to 1 via capacitor banks or filters. Measurements on unloaded induction motors (highly inductive) show PF near 0, approaching the lower limit in practice.

Why Other Options Are Wrong:

• 2 and 0: PF cannot exceed 1 by definition (P ≤ S).
• 0 and −1 or 1 and −1: these mix sign conventions; the magnitude still does not exceed 1.
• 0.95 and 0: 0.95 is a common target but not the maximum theoretical limit.

Common Pitfalls:

• Confusing sign (leading/lagging) with magnitude; magnitude is capped at 1.
• Assuming non-sinusoidal definitions change the upper bound; with suitable generalization, the magnitude remains ≤ 1.

Final Answer:

1 and 0