Consider the following circuit :

enter image description here

When I'm writing the Kirchhkoff's second law on the outer loop, I can totally ignore the inner one, right? What I mean by this would be : Ui1 + Ui3 = I1R1 + I4R4 ( forgot to add I4 in the drawing ) while considering I1 = Is + I4 and I2 = I4 + I3.

My question is, when writing Kirchhoff's second law on outer loops that contain inner loops inside, is it correct to ignore the edges inside or are there cases in which I have to take them into consideration?

  • \$\begingroup\$ Another way to express Kirchoff's voltage law is to say that the voltage at a node is uniquely determined. Whatever path you take to get there from the reference node, you must traverse the same net voltage. You don't even have to follow circuit edges, you can jump between nodes that aren't even connected and KVL will still hold (but it will be less useful for solving the circuit because there's no equation you can write to find out the voltage between two nodes "connected" by an open circuit) \$\endgroup\$ – The Photon Jun 1 '16 at 21:29
  • \$\begingroup\$ @ThePhoton The way I understand it is that if I start from a point and end at the same point the voltage should be 0 no matter what way I choose to take. Is this right? \$\endgroup\$ – user1640736 Jun 1 '16 at 21:30
  • \$\begingroup\$ Yes, that's the more usual way to state KVL. But think about why the two rules are equivalent. \$\endgroup\$ – The Photon Jun 1 '16 at 21:32
  • \$\begingroup\$ @ThePhoton Therefore, the way I wrote the equations in the question is also correct. There's no problem that I completly ignored the n0-n2 edge ? \$\endgroup\$ – user1640736 Jun 1 '16 at 21:33

KVL is based upon the hypothesis that you are in a conservative field situation. A mathematical property of those fields is that the path you choose don't matter on the potential value. So the path doesn't matter so that why KVL stipulate that in a close potential loop, the sum of the voltages is equal to 0.

So to answer your question, you can write a loop equation in the outer part. However, KVL don't break algebra, most likely you will need more than 1 loop equation to find all the current and voltages.


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