In an RLC circuit that behaves net inductively (current lags the applied voltage), what is the corresponding power-factor angle and qualitative power factor?

Introduction:
Power factor describes how effectively alternating current power is converted to useful work. In reactive circuits, voltage and current are not in phase, leading or lagging by an angle φ. Inductive behavior means current lags the voltage (negative phase angle with the usual reference), impacting both the angle and the numerical power factor cos(φ).

Given Data / Assumptions:

• Sinusoidal steady-state operation.
• RLC circuit with net inductive reactance (X_L > X_C).
• Idealized discussion of limiting behaviors (purely reactive vs. mixed R–X).

Concept / Approach:
For a purely inductive circuit, the current lags the voltage by 90 degrees. The power factor is cos(−90°) = 0, meaning no average real power is consumed (only reactive exchange). In a general inductive R–L–C with resistance, the lag angle would be between 0 and −90 degrees, and the power factor between 0 and 1 lagging. Among the offered choices, the statement that best represents an inductive power-factor condition is '−90 degrees lagging' (the purely inductive limit).

Step-by-Step Solution:
Identify inductive behavior: X_L > X_C ⇒ current lags voltage.Limit case for pure inductor: φ = −90°.Power factor PF = cos(φ) ⇒ PF = cos(−90°) = 0.Therefore, the representative angle/power-factor description is '−90 degrees lagging' (PF approaching zero).

Verification / Alternative check:
Phasor analysis: Z = R + j(X_L − X_C). If R → 0 and X_L > X_C, arg(Z) → +90°, so arg(I) = −90° relative to V. This confirms the lagging current and purely reactive behavior at the limit.

Why Other Options Are Wrong:

• +90 degrees leading / about +45 degrees leading: These indicate capacitive behavior (current leads), not inductive.
• one: PF = 1 only for purely resistive circuits (φ = 0°), not inductive.
• zero: While the numeric PF is zero in the pure inductor limit, the option lacks the crucial lagging/angle qualifier; the more accurate descriptive choice is '−90 degrees lagging'.

Common Pitfalls:

• Equating inductive behavior with a specific numeric PF without stating lagging angle.
• Assuming PF = 1 can occur in reactive circuits; it requires zero reactance.
• Confusing sign convention for leading vs. lagging angles.

Final Answer:
−90 degrees lagging