If a circuit has a number of interconnected branches, two other laws are applied in order to find the current flowing in the various branches. These laws, discovered by the German physicist Gustav Robert Kirchhoff, are known as Kirchhoff's laws of networks. The first of Kirchhoff's laws states that at any junction in a circuit through which a steady current is flowing, the sum of the currents flowing to the point is equal to the sum of the currents flowing away from that point. The second law states that, starting at any point in a network and following any closed path back to the starting point, the net sum of the electromotive forces encountered will be equal to the net sum of the products of the resistances encountered and the currents flowing through them. This second law is simply an extension of Ohm's law.
The application of Ohm's law to circuits in which there is an alternating current is complicated by the fact that capacity and inductance are always present. Inductance makes the peak value of an alternating current lag behind the peak value of voltage; capacitance makes the peak value of voltage lag behind the peak value of the current. Capacitance and inductance inhibit the flow of alternating current and must be taken into account in calculating current flow. The current in AC circuits can be determined graphically by means of vectors or by means of the algebraic equation
in which L is inductance, C is capacitance, and f is the frequency of the current. The quantity in the denominator of the fraction is called the impedance of the circuit to alternating current and is sometimes represented by the letter Z; then Ohm's law for AC circuits is expressed by the simple equation I = E/Z.