Series RLC phasor convention: In a series RLC circuit, what quantity is most appropriately chosen as the universal phasor reference for analyzing voltages and angles across the elements?

Introduction:
Phasor analysis requires choosing a consistent reference phasor so that all other phasors can be measured in magnitude and angle. In series RLC circuits, the same current flows through R, L, and C, making current an ideal reference for comparing element voltages and determining impedance angles.

Given Data / Assumptions:

• Series RLC topology (single loop)
• Sinusoidal steady state
• Goal: choose a stable, universal reference for phasor diagrams

Concept / Approach:

Because series elements share the same current, setting the current phasor at 0 degrees (as the reference) simplifies analysis: VR is in phase with I, VL leads I by 90 degrees, and VC lags I by 90 degrees. Impedance angle then directly equals the angle of the voltage relative to the current, and power factor is cos(angle).

Step-by-Step Solution:

Verification / Alternative check:

Textbook convention universally sets current as the reference for series circuits, minimizing ambiguity and keeping sign conventions consistent across R, L, and C voltage drops.

Why Other Options Are Wrong:

• a leading vector / a lagging vector: Describe relative angles, not a universal reference choice.
• an angle: An angle is a measurement, not a phasor.
• a phasor of voltage: Possible, but it complicates series analysis; using I is standard and simpler.

Common Pitfalls:

• Picking different references mid-solution, causing sign mistakes.
• Confusing the power factor angle (between V and I) with individual element voltage angles.

Final Answer:

a reference