Why does multiplying 120 by 1.73 give me 208 volts in a 3 phase system?

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SUMMARY

The discussion clarifies the calculation of voltage in a 120/208 three-phase system. Multiplying 120 volts by the square root of three (1.73) results in 208 volts, which represents the line-to-line voltage in this system. The confusion arises from the misunderstanding that voltage can be summed directly rather than calculated based on phase differences. The correct approach involves recognizing that the voltage between two points is determined by the vector difference of their respective voltages.

PREREQUISITES
  • Understanding of three-phase electrical systems
  • Knowledge of voltage phase relationships
  • Familiarity with vector addition in electrical engineering
  • Basic mathematics involving square roots and trigonometry
NEXT STEPS
  • Study the principles of three-phase power systems
  • Learn about vector representation of AC voltages
  • Research the concept of line-to-line and line-to-neutral voltages
  • Explore the use of phasors in electrical engineering calculations
USEFUL FOR

Electrical engineers, technicians working with three-phase systems, and students studying electrical power systems will benefit from this discussion.

Evil Bunny
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Ok... This is a simple question that I'm having a hard time with. I'm forgetting something that I learned and I want to clear it up...

I know that a 120/208 3 phase system has 3 hot leads that are 120 degrees out of phase with each other with respect to the neutral.

If you multiply 120 X 1.73 (square root of three), you get 208 volts. I'm not sure why...

If I add 120 + 120@120 degrees, my calculator tells me the answer is 120@60 degrees.

I expected it to say 208.

Why? What am I getting confused here?
 
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Hi Evil Bunny. The voltage between two points is equal to the difference in their voltages, not their sum.

Try calculating 120 - 120@120 degrees. :smile:
 
Thank you!
 

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