Phase angle definition in AC circuit analysis: What is meant by the phase angle in a series RL circuit driven by a sinusoidal source?

Introduction / Context:
Phase angle is a cornerstone of AC analysis, capturing the timing relationship between voltage and current in reactive networks. In a series RL circuit, the current lags the source voltage by an angle determined by the ratio of inductive reactance to resistance. Properly defining the phase angle avoids confusion in power factor and impedance calculations.

Given Data / Assumptions:

• Sinusoidal steady state.
• Series RL elements only.
• Standard phasor conventions (voltage reference unless stated otherwise).

Concept / Approach:
The phase angle theta in a series RL is defined by tan(theta) = XL / R with theta positive (current lags voltage). In words, it is the angular difference between the applied source voltage phasor and the circuit current phasor. This angle directly determines power factor: pf = cos(theta). The concept generalizes to any linear AC network but is especially transparent in first-order cases.

Step-by-Step Solution:

Verification / Alternative check:
Oscilloscope Lissajous plots or dual-channel measurements show current zero crossings delayed relative to voltage when an inductor is present, confirming the lag and the phase relation.

Why Other Options Are Wrong:
“Between any two node voltages” is ambiguous and not the standard definition. The magnetic-field/heat-flow comparison is not an electrical phase definition. DC has no meaningful phase angle between power vectors because frequency is zero and reactive effects vanish.

Common Pitfalls:
Swapping lead/lag sign; confusing the angle of impedance with the angle between two unrelated node voltages.

Final Answer:
The angular difference between the applied source voltage and the circuit current