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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?
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.
