In a three-phase Y-connected (wye) AC generator, each phase (line-to-neutral) voltage is 90 V(rms). What is the magnitude of each line-to-line voltage?

Introduction / Context:This problem tests the foundational relationship between phase voltage and line voltage in a balanced three-phase Y (wye) connection. Understanding this conversion is essential for sizing insulation, selecting meters, and ensuring the correct ratings for equipment in power systems and three-phase electronics.

Given Data / Assumptions:

• Connection: three-phase Y-connected generator (balanced).
• Phase (line-to-neutral) voltage magnitude: V_phase = 90 V(rms).
• We seek the line-to-line voltage magnitude V_line.
• Sinusoidal steady-state; ideal, symmetrical system.

Concept / Approach:For a balanced Y connection, the line-to-line voltage magnitude is related to the phase voltage by V_line = √3 * V_phase. The factor √3 arises from the 120° vector separation between phase voltages and the phasor difference defining line voltages.

Step-by-Step Solution:

Verification / Alternative check:In a Y system, if V_phase = 230 V, V_line commonly equals about 400 V (230 * 1.732), which is a well-known standard (400/230 V systems). This sanity check supports the use of the √3 factor here as well.

Why Other Options Are Wrong:

• 0 V: Not possible; the generator is energized.
• 90 V: That is the phase voltage, not the line-to-line voltage in a Y system.
• 180 V: No standard factor yields exactly double the phase voltage in Y; the correct multiplier is √3, not 2.

Common Pitfalls:

• Confusing Y and Δ relationships. In Δ, line voltage equals phase voltage, but in Y, line voltage is √3 times phase voltage.
• Forgetting that the values are rms and phasor-based (120° separation).

Final Answer:156 V