I am trying to calculate the complex power in this circuit. I used nodal analysis to find Vc, and the voltage at the top of the 2H inductor (=3.13<177.8 V_RMS). I did the math for all elements in the circuit, my problem is with the voltage source. Voltage and Current are in phasor form, in RMS.

After calculating the complex power of the voltage source using the current direction as in I1, I don't get the correct answer (I summed up all the real and the reactive powers from the elements and the current source and they don't compare).

However, if I swap the direction of the current (I just added a minus sign) then the complex power turns out correct.

I understand that when using nodal analysis we can arbitrarily specify the current direction, and after doing the math we will find the 'actual' direction of the current - this was easy while doing DC calculations. But now that the current is in complex form (for example 6.48<-78.7 A_RMS) how do I know it's direction? This is critical in calculating the complex power correctly.

I asked in class if the current through a voltage-source will always be away from the positive end (as the voltage source pushes power into the circuit) yet my teacher answered that this is not always true, as a powerful source can force another source to accept current through it's positive end.

So how can I find the actual direction of current in this and other cases?


  • \$\begingroup\$ I'm not sure if this will help you understand (because I'm not taking the time to go through your work right now), but your statement about "changing the sign" brought back a post I did a while ago about why, when multiplying complex voltage notation by complex current notation that you must use the complex conjugate of the current. It's here. \$\endgroup\$ – jonk Feb 9 at 19:29
  • \$\begingroup\$ @jonk I have taken the complex conjugate of the current when calculating the complex power. The problem is with the direction of current which is wrong. It should be the other way round. Trying to figure out how to tell the direction correctly. \$\endgroup\$ – Tal J Feb 9 at 19:33
  • \$\begingroup\$ Okay, thanks for letting me know that. It merely crossed my mind, skimming. Probably someone else will help before I get a chance (stuff I need to do), but I'll come back when I get a moment. \$\endgroup\$ – jonk Feb 9 at 19:35

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