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.

Difficulty: Easy

Correct Answer: 3,464 V

Explanation:


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:

Use the relation V_line = √3 * V_phase.Compute: √3 * 2,000 ≈ 1.732 * 2000 = 3,464 V.


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

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