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

AI Thread Summary
In a 120/208 three-phase system, the voltage between two hot leads is calculated using the formula that incorporates the square root of three. Multiplying 120 volts by 1.73 (the square root of three) yields 208 volts, which represents the line-to-line voltage. The confusion arises from misunderstanding how voltages in a three-phase system interact; they do not simply add together. Instead, the voltage difference between two phases must be considered, not their sum. This clarification helps resolve the initial question about the relationship between the voltages in the system.
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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