Suppose we have a 3 phase load connected to a 3 phase voltage source and connect a capacitor parallel to one of the phase loads like in the image below.


simulate this circuit – Schematic created using CircuitLab

How do we solve this kind of circuit?The current flowing through the neutral is not 0 right?How do we find the voltage across the resistor R4?

  • \$\begingroup\$ If you want a purely numerical answer I'd use a simulator. \$\endgroup\$
    – Andy aka
    Commented Jun 30, 2021 at 11:56
  • \$\begingroup\$ I want to know how to solve this circuit.\ \$\endgroup\$
    – user290044
    Commented Jun 30, 2021 at 11:59

1 Answer 1


Three voltage sources connected via three independent series impedances to a star point where, the star-point has an impedance to ground is crying out for Millman's theorem to be used: -

enter image description here

Picture taken from this slideshow.

Regarding the equations, it's this from this tutorial: -

enter image description here

If one of the sources is zero volts (as per the voltage in series with R4 in the question) then, it makes no difference; it becomes 0 volts and one of the terms in the numerator of the equation above disappears.

Make sure you use the correct phasor or complex number notation in solving the answer.

  • \$\begingroup\$ Does it apply to voltage sources which are out of phase? \$\endgroup\$
    – user290044
    Commented Jun 30, 2021 at 12:15
  • \$\begingroup\$ @RobSmith of course. \$\endgroup\$
    – Andy aka
    Commented Jun 30, 2021 at 12:16
  • \$\begingroup\$ so for each voltage I replace it with the polar form of the voltage correct? \$\endgroup\$
    – user290044
    Commented Jun 30, 2021 at 12:17
  • \$\begingroup\$ @RobSmith correct, polar or rectangular, whichever is your preference. \$\endgroup\$
    – Andy aka
    Commented Jun 30, 2021 at 12:24

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