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Many circuits combine series and parallel arrangements. One branch of a parallel circuit, for example, may have within it several objects in a series. The resistances of these objects must be combined according to the rules for a series circuit. On the other hand, a series circuit may at one point divide into two or more branches and then rejoin. The branches are parallel and must be treated by the rules for parallel circuits.

Complicated series-parallel circuits may be analyzed by means of two rules called Kirchhoff’s laws. These rules make it possible to find the amount of electric current flowing through each part of any circuit, as well as the voltage across it. 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 junction is equal to the sum of the currents flowing away from that point. The second law states that, starting at any point in a circuit and following any closed path back to the starting point, the net sum of the voltage encountered will be equal to the net sum of the products of the resistances encountered and the currents flowing through them. In other words, Ohm’s law applies not only to a circuit as a whole, but also to any given section of a circuit.

Many circuits combine series and parallel arrangements. One branch of a parallel circuit, for example, may have within it several objects in a series. The resistances of these objects must be combined according to the rules for a series circuit. On the other hand, a series circuit may at one point divide into two or more branches and then rejoin. The branches are parallel and must be treated by the rules for parallel circuits.

Complicated series-parallel circuits may be analyzed by means of two rules called Kirchhoff’s laws. These rules make it possible to find the amount of electric current flowing through each part of any circuit, as well as the voltage across it. 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 junction is equal to the sum of the currents flowing away from that point. The second law states that, starting at any point in a circuit and following any closed path back to the starting point, the net sum of the voltage encountered will be equal to the net sum of the products of the resistances encountered and the currents flowing through them. In other words, Ohm’s law applies not only to a circuit as a whole, but also to any given section of a circuit.