Why we are using single phase & three phase

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Three-phase systems are preferred over two-phase, four-phase, or five-phase systems due to their efficiency and cost-effectiveness. They require less conductor material for the same voltage, making them more economical for power transmission. A three-phase system can transmit approximately 73% more power than a single-phase system while only using 50% more wire. This efficiency in power transmission is a key reason for the widespread adoption of three-phase systems in electrical applications. Overall, three-phase power is favored for its superior performance and reduced material costs.
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Why we are using Three phase & single phase instead of using two phase , four phase, five phase.
 
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It's a trade-off between efficiency and cost.

A three-phase system is generally more economical than others because it uses less conductor material to transmit electric power than equivalent single-phase or two-phase systems at the same voltage.

http://en.wikipedia.org/wiki/Three-phase_power

The most obvious advantage of three-phase power transmission using three wires, as compared to single-phase power transmission over two wires, is that the power transmitted in the three-phase system is the voltage multiplied by the current in each wire times the square root of three (approximately 1.73). The power transmitted by the single-phase system is simply the voltage multiplied by the current. Thus the three-phase system transmits 73% more power but uses only 50% more wire.

http://en.wikipedia.org/wiki/Polyphase_system
 
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