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Two Kirchhoff's circuit laws:

Law I: at each node the algebraic sum of the currents is zero

Law II: the sum of directed voltages across any loop is zero

When performing the nodal analysis, we use only the Law I and Ohm's law, the Law II is not used. Is there a proof that applying the Law I, the Law II is fulfilled automatically? Does it work only for circuits with passive elements e.g. resistors?

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1 Answer 1

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Law II in terms of node voltages is:

(V1-V2)+(V2-V3)+...+(Vn-V1)=0

But this is trivially true since the sum may be rearranged as:

(V1-V1)+(V2-V2)+...+(Vn-Vn)

which is, of course, equal to zero.

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