In a three-wire Y-connected generator with phase (line-to-neutral) voltages of 2 kV, determine the magnitude of each line-to-line voltage.

Introduction / Context:Calculating line-to-line voltage from a known phase voltage in a Y connection is a frequent task in power distribution and equipment specification. The √3 factor is a direct consequence of 120° phasor geometry in balanced three-phase systems.

Given Data / Assumptions:

• Y-connected generator (balanced).
• Phase voltage V_phase = 2 kV (rms, line-to-neutral).
• Find V_line (rms, line-to-line).

Concept / Approach:For Y: V_line = √3 * V_phase. The line-to-line voltage is the phasor difference of two line-to-neutral voltages separated by 120°, yielding a magnitude √3 times larger than a single phase voltage.

Step-by-Step Solution:

Verification / Alternative check:Common standards (e.g., 230/400 V) follow the same ratio. This consistency reinforces the calculation method and result here.

Why Other Options Are Wrong:

• 2,000 V: This would be true for Δ (line = phase), not for Y.
• 6,000 V: Assumes a factor of 3 rather than √3.
• 666 V: An inverse-type confusion (phase vs line) and off by a large factor.

Common Pitfalls:

• Mixing Δ and Y relationships or forgetting the 120° vector geometry.

Final Answer:3,464 V