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?