Electric Circuit

I

Introduction

Electric Circuit, path of an electric current. The term is usually taken to mean a continuous path composed of conductors and conducting devices and including a source of electromotive force (emf) that drives the current around the circuit. A circuit of this type is termed a closed circuit, and a circuit in which the current path is not continuous is called an open circuit. A short circuit is a closed circuit in which a direct connection is made, with no appreciable resistance, inductance, or capacitance, between the terminals of the source of electromotive force.

II

Ohm's Law

Current flows in an electric circuit in accordance with several definite laws. The basic law of current flow is Ohm's law, named after its discoverer, the German physicist Georg Ohm. Ohm's law states that, over a wide range of circumstances and materials, the amount of current flowing through a conductor is directly proportional to the electromotive force applied between the ends of the conductor. If resistance is defined as the ratio of electromotive force to current, then V = IR, where I is the current in amperes, V is the electromotive force in volts (see Electrical Units), then Ohm's law is equivalent to saying that R (which is measured in ohms) is a constant in the specified circumstances. A material for which this holds true is described as ohmic. Ohm's law can apply to electric circuits for both direct current (DC) and alternating current (AC), but additional principles must be invoked for the analysis of complex circuits and for AC circuits involving inductances and capacitances.

A series circuit is one in which the devices or elements of the circuit are arranged in such a way that the entire current passes through each element without division or branching into parallel circuits.

When two or more resistances are in series in a circuit, the total resistance may be calculated by adding the values of such resistances. If the resistances are in parallel, the total value of the resistance in the circuit is given by the formula

In a parallel circuit, electrical devices, such as incandescent lamps or the cells of a battery, are arranged to allow all positive (+) poles, electrodes, and terminals to be joined to one conductor, and all negative (-) ones to another conductor, so that each unit is, in effect, on a parallel branch. The value of two equal resistances in parallel is equal to half the value of the component resistances, and in every case the value of resistances in parallel is less than the value of the smallest of the individual resistances involved. In AC circuits, or circuits with varying currents, circuit components other than resistance must be considered.

III

Kirchhoff's Laws

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.

IV

Impedance

The application of Ohm's law to circuits in which there is an alternating current is complicated by the fact that capacitance 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 I is current, E is electromotive force, R is resistance, 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.