In a Δ-connected (delta) generator, how do the three phase (line-to-line) voltages compare to each other?

Introduction / Context:
Recognizing the behavior of voltages in Δ-connected configurations is basic to three-phase power engineering. In a delta, each phase element is connected directly between a pair of line conductors, so each phase sees a line-to-line voltage. The symmetry guarantees consistent magnitude among phases in a balanced system.

Given Data / Assumptions:

• Balanced Δ connection.
• Sinusoidal steady-state.
• We compare phase voltages among phases a, b, and c.

Concept / Approach:
In a balanced Δ, each side of the delta is across a pair of lines, so each phase voltage is a line-to-line voltage. With system balance and symmetry, all three phase voltages are equal in magnitude and displaced by 120° in phase angle.

Step-by-Step Reasoning:

Verification / Alternative check:
If the system is perfectly symmetrical and the source is ideal, any measurement across each delta side yields the same rms value. Deviations indicate unbalance or faults, not normal operation.

Why Other Options Are Wrong:

• zero: A powered generator cannot have zero phase voltages unless faulted.
• one-third or one-sixth of total: These values do not describe delta relationships; they often stem from confusing Δ vs Y line/phase relations.

Common Pitfalls:

• Confusing Δ with Y. In Y, line voltage is √3 times the phase voltage; in Δ, line and phase voltages are the same in magnitude (line = phase).

Final Answer:
equal in magnitude