Fundamental spacing in three-phase systems: By how many electrical degrees are the three phase voltages separated?

Introduction / Context:
Three-phase AC systems are defined by three sinusoidal voltages of equal magnitude and frequency, spaced evenly in time (phase). The phase separation determines torque smoothness in motors, power constancy, and conductor economy. Identifying the canonical spacing is a core concept in power engineering.

Given Data / Assumptions:

• Balanced three-phase sinusoidal sources.
• Equal magnitude and frequency across phases.
• Ideal conditions with no distortion.

Concept / Approach:

Even spacing of three sinusoids over 360° requires a separation of 360° / 3 = 120°. This results in constant total instantaneous power for balanced resistive loads and smooth electromagnetic torque in three-phase motors.

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagrams place the three voltage vectors at 0°, −120°, and +120°, forming a symmetric equilateral triangle on the complex plane. This symmetry underlies the power and torque characteristics of three-phase systems.

Why Other Options Are Wrong:

90° corresponds to two-phase systems; 180° is single-phase with reversed polarity; 45° is used in some modulation schemes but not as fundamental three-phase spacing.

Common Pitfalls:

Confusing electrical degrees with mechanical degrees in machines; mixing two-phase with three-phase conventions.

Final Answer:

120°