I had to find total impedance of the following three phase circuit with symmetric line voltages: enter image description here

I've been told that nodes 1 and 2 can be connected because their potentials are equal (zero).After connecting these two nodes, resistor R and inductor L are connected in parallel.Why can we connect these two nodes (/ why are their potentials equal to zero)?I know that in symmetric systems with one generator per phase (three generators in total) and one star receiver, node analysis shows that node potential of the receiving star's node is zero, but what happens in this case?


1 Answer 1


Assuming that the three feed voltages are balanced and are sine waves i.e. line voltages are identical with exactly 120 degrees between them, any star connected load of equal values will produce 0 volts at the star point. This means that three identical resistors will yield 0 volts AND three identical inductors (or capacitors) will also yield 0 volts.

With zero volts between a star network of resistors and a star network of (say) inductors, connecting those nodes will not cause a current to flow hence, they can be connected.

  • \$\begingroup\$ When we say that some node has potential of zero volts, what is the reference point?Why exactly do these star points have potential of zero volts? \$\endgroup\$ Jul 15, 2019 at 12:18
  • 1
    \$\begingroup\$ The reference point is the star point of the generator, so if the star point is at (say) 4.321 volts, then the star node voltage of 3 equal value resistors, capacitors or inductors is also 4.321 volts. But it's simpler (and with no incurred error), just to assume that the generator's star point is at 0 volts @user3711671 \$\endgroup\$
    – Andy aka
    Jul 15, 2019 at 12:54

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