If 1-phase voltage is 220V, why is 3-phase 440V and not 660V ?
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we take in3-phase, L-L Voltage reading

and for 1-phase, L-N Voltage reading

we can't take reading L-L-L voltage reading so that 3-phase volt.. is 440v
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Come to the point, 

1/ In 3 phase line the phase voltage totally depends on line voltage, it’s √3 times lower than line voltage so if line voltage get high then phase voltage automatically comes higher. 

2/ why 440 not 660? Because insulation resistant need to increase with voltage accordingly. It is costly.
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1 phase there are one two wires Live and Neutral and voltage is the difference between these two which is 220V and due to the presence of neutral wire it is also called phase voltage. But in three phase there may be 3 wires or 4 wires system so if we suppose three wire system there is no neutral and all three wires are Live but 120° apart. So in this case the voltage difference between any two is 400V which is Line to line voltage...
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Phase voltage =220v /( phase to neutral)

Line voltage = 380 v ( phase to phase)

Phase angle difference 120°

So when two phases reach vmax +ve I.e. (+220v) + (+220v) = 440v that time due to phase angle difference one phase has reached -ve 220v and when two phases reached vmax-ve i.e. (-220v) + (-220v) =-440 v that time one phase has reached +ve 220v according to three phase sinewave diagram. due to 50 or 60 cycle per second i.e. 50 hz or 60 hz frequency these event happen very fast. Hence we have 440 v only in three phase motor. √3.phase voltage= 380 v.

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