How is the Square Root of Three Factor Derived in a Three Phase Generator?

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SUMMARY

The square root of three factor in a three-phase generator is derived from the geometric relationship of the voltage phases, which are arranged in an equilateral triangle formation. This configuration leads to a right triangle when one of the phases is bisected, resulting in a ratio of the sides that includes the square root of three. The derivation is essential for understanding phase relationships and voltage calculations in three-phase systems.

PREREQUISITES
  • Understanding of three-phase electrical systems
  • Familiarity with trigonometric ratios
  • Knowledge of equilateral triangles and their properties
  • Basic electrical engineering principles
NEXT STEPS
  • Study the derivation of the square root of three in three-phase systems
  • Learn about phasor diagrams in three-phase circuits
  • Explore the relationship between line and phase voltages in three-phase generators
  • Investigate the application of trigonometry in electrical engineering
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Electrical engineering students, professionals working with three-phase systems, and anyone interested in the mathematical foundations of generator design.

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Homework Statement



Can someone tell me how the (square root of three) factor is derived in a three phase generator?

Homework Equations


The Attempt at a Solution

 
Last edited:
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Can someone show me the derivation?
 
darkmagic said:

Homework Statement



Can someone tell me how the (square root of three) factor is derived in a three phase generator?

Homework Equations





The Attempt at a Solution


If you draw the three equally spaced voltage phases like in this diagram:

http://images.google.com/imgres?img...N&rlz=1T4GGLL_enUS301US302&ndsp=18&tbs=isch:1

You can see the they form equilateral triangles. What is the ratio of side lengths in a right triangle that bisects an equilateral triangle?
 

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