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"If the phase voltage of a three three-phase star-connected generator is 200 V, what will be the line voltages:

a) when the phases are correctly connected

b) when the connections to one of the phases are reversed?"

I understand that the line voltage is related to the phase voltage by

Line Voltage = √3*Phase Voltage

when all the phases are connected "correctly" however what will the line voltage be when the connection to one of the phases is reversed? Thanks!

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To answer the first part of your question, you are right. (Assuming everything is ballanced) $$ \left | V_{line} \right | = \sqrt{3}\left |V_{phase}\right | $$

However lets not forget the change in angle. Taking the phase voltage as reference the line voltages under normal operation will lead the phase by 30 degrees. (Vab leads Va by 30º).

Now for the second part of your question when we interchange the phases. The magnitude relationship will remain the same. However the angle will change. Now your line voltages will lag your phase voltage by 30º.

Essentially if you connected the output of your 3 phase generator to a 3phase motor, your motor would rotate in the opposite direction, than previously under normal operation. This is because there is a change in the direction of your rotating magnetic field.

Draw a phasor diagram and you will see why it leads under normal operation and lags when you interchange the phases.

Reference for further information:

http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_10.html

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