# The solving of electric circuits by means of general equations

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By the solving of an electric circuit is usually meant the determining of the various unknown currents in terms of the known impedances and electromotive forces; however, this phrase sometimes refers to the determining of certain other quantities such as electromotive force drops, potential differences between various points of the circuit, and impedances between various points of the circuit. The solving of electric circuits is made possible by Kirchhoff's two laws which the currents and electromotive forces of every circuit obey at every instant. By representing the currents, electromotive forces, and impedances by complex numbers, Steinmetz has established Kirchhoff's laws, in their original forms, for steady state conditions in alternating current circuits. These laws may be written: (1) The algebraic sum of the currents at any point in the circuit is zero. (2) The algebraic sum of the electromotive force drops around any closed circuit is equal to the algebraic sum of the applied electromotive forces around this circuit. These laws make it possible to set up two sets of equations from the diagram of the circuit. The equations obtained by applying the first law to every point where three or more conductors branch are called current equations; these equations relate the currents one to another but do not determine any of them. The equations obtained by applying the second law to every closed circuit are called electromotive equations; this latter set of equations connects the unknown currents with the known impedances and electromotive forces but in general is not sufficient to determine any of the currents. However, if the coefficients of the currents in the electromotive force equations are independent of the currents flowing through them, a set of equations, part current and part electromotive force, can be obtained whose simultaneous solution will give the unknown currents in terms of the known impedances and electromotive forces. The necessary and sufficient conditions which such a set of equations must satisfy are that the number of equations equal the number of unknown currents and that the equations be independent