we use 3 phase supply for induction motor why not use two
phase supply .

Answer Posted / kj

A 3 phase supply is the lowest number of phases where a
rotating field is produced. No extra starting controls are
needed (e.g. capacitor start or start windings)
Two phase systems have been used and can produce a rotating
field but it has to use a setup with separate neutrals for
each of the 2 phase. It therefore requires 4 wires to each
motor instead of 3 and it is also not as efficient.
Three phases also has the advantage of the currents in the
nuetral not being the sum of the 3 phase currents. In that
way only a single neutral can be used as the return for any
single phase load on all the 3 phases.

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