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First, consider single-phase 120/240 service like you would find in a house. the two hot wires are said to be 'in phase'.

Think of it this way. Imagine a ruler12 inches long. Put your finger on the six inch mark, the center. How far to each end? Six inches. Both ends are on the same line, just in opposite directions. So if you go six inches one way, and six inches the other way, the total distance is 12 inches.

120/240 volt systems are like that voltage-wise. The middle of the ruler is the neutral, and each end is a hot wire. When one hot leg is going positive, at the exact same time (that's the 'in phase' part) the other leg is going negative. Same line only opposite directions, like our ruler. So the two 120 volt legs just add up to 240.

Now, here's the important part. Since one leg goes positive while the other leg goes negative, they are said to be 180 degrees apart, 360 degrees making up one complete AC cycle (2 X 180 = 360). In three phase power, there are, not two, but THREE hot wires. Since there are three, they can no longer be 180 degrees apart. They are 120 degrees apart (3 X 120 = 360). So, when phase A peaks, phase B has not yet peaked. it is at some intermediate voltage between zero and maximum. The two phases cannot just be added up because of this fact.

Back to our ruler. Break the ruler in half. bend the two halves so the ruler is no longer straight (180 degrees) but bent at an angle of 120 degrees. Draw a line from end to end. See how we have formed a triangle? See also that the line we drew is not 12 inches long, but is shorter (the two ends are closer together)? That's why the voltages in a three phase system do not appear to add up.

Lets make our ruler 240 inches long. If we bend it into the 120 degree angle and measure end-to-end, we will find the length to be about 208 inches, not 240! In a 120/208 three-phase system, each hot leg (phase) measures 120 volts to ground, BUT phase-to-phase measures 208 volts. This is true whether you measure A to B, B to C, or C to A.

The math guys call this a vector sum. The vector is the angle at which the phases are in relation to each other (120 degrees) and the sum is the distance between the two bent ends (phases).

To figure the phase-to-phase voltage, multiply the phase-to-neutral voltage by 1.73 (the square root of 3). Thus: 120 X 1.73 = 208, 277 X 1.73 = 480, etc.

To figure the reverse, divide the phase-to-phase voltage by 1.73. Thus: 480 / 1.73 = 277, 208 / 1.73 = 120, etc.

You trig people see how this relates to our triangle example using the cosine rule.

It should be noted that the use of the term phase above, as in "phase to phase" is not strictly correct, although a common usage. Each hot conductor in a 3-phase system is correctly called a "line", so the correct terminology would be "line to line", "line to neutral", etc.

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11y ago
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12y ago
Three phase voltage will transfer higher power than single phaseP1-ph = Vp x Ip cosφ

P3-ph = _/3 x VL X IL x cosφ

= 3 x Vp x Ip cosφ

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13y ago

A three phase supply has a 120 degree AC voltage difference between phases.

For example: a 240VAC three phase circuit has three phase (hot) leads that measure 120VAC to neutral or ground. The voltage difference between two hot leads is 208VAC (120 * tangent of 120 degrees).

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Q: What is the phase difference between three phase supply?
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