Electrical Circuits

Type of physical science: Classical physics

Field of study: Electromagnetism

Electrical circuits are formed by the interconnection of elements through which electrical charges can be conducted, such as resistors, capacitors, inductors, and sources of electrical voltage or current. Such circuits can be made to produce and modify electrical signals in a wide variety of ways and have many practical applications in the fields of power generation, radio and television, computation, control systems, and medical and scientific instrumentation.

Overview

When an electrical force is applied to materials called "conductors," a flow of electrical charges, called an "electrical current," is produced. Electrical circuit theory studies the relations between such currents and the energy differences that produce them. In the international system of units used for electrical quantities, the current through an electrical device is measured in amperes. The "electrical potential," or energy per unit charge, is measured in volts, so potential differences between two points are commonly called voltages. Electrical networks consist of interconnected devices, or circuit elements, each of whose electrical behavior can be described by the relation between the current through the element and the voltage across it.

A common flashlight provides a simple example of an electrical network when its switch is closed, allowing current to flow from a battery through a thick metallic wire to a thinner wire lamp filament enclosed in glass bulb, and then back to the battery. The electrochemical reactions in the cells of the battery supply the electrical power to drive the current through the filament, where energy is converted to heat and light. A knowledge of the relation between the current and voltage of the filament is necessary to be able to specify the battery that will produce a bright enough light without burning out the lamp. The necessary complete two-way path for charges to flow out from and return to the power source justifies the alternative name of "electric circuit" for such a network.

There are many different useful types of electrical circuit elements--some of them being "active elements"--which are able to produce more electrical power than they absorb, such as voltage or current sources--and some being "passive elements--which cannot produce more electrical power than can be absorbed. It is possible to divide passive elements into three ideal types, which have different relations between the currents they conduct and the voltages that produce them. The current through ideal resistive elements, or "resistors," is dependent directly on the voltage across them. Many resistors exhibit a linear relation between the current (i) and the voltage (V) across them, expressed as V = iR, where R is a constant called the resistance. This expression is often called Ohm's law. Since many useful materials are nonlinear and have a resistance that depends on the current passing through them, Ohm's law is not universal; it is usually thought of as the definition of resistance. Common substances exhibit an astonishing range of resistances, with a poor conductor or "insulator" such as porcelain having a resistance a million times greater than an equal amount of a good conductor such as copper. Electrical engineers utilize this fact to guide currents from one element in a circuit to another through metallic wires.

The other two ideal types of devices do not dissipate energy like a resistor, but can store it temporarily through electric or magnetic forces; they are called "reactive elements." If opposite charges are stored on two conducting plates separated by an insulator, an electrical potential difference is created between these plates, even though charges do not move through the insulator. Such a storage device for electrical energy is called a capacitor, and its "capacitance" is merely the ratio between the stored charge and the voltage between the conductors. Charges moving through a wire also produce magnetic effects in the space surrounding the current path; these magnetic forces can, in turn, produce magnetic forces on the charges whenever there is a change in the current. Devices that exhibit only this behavior are called ideal inductors, and their "inductance" is merely the ratio between the voltage across them and the rate of change of the current through the inductors. Although all practical circuit elements exhibit resistance, inductance, and capacitance to some extent, in many cases it is possible to model their behavior by combinations of ideal resistors, inductors, and capacitors, simplifying the analysis of such circuits.

The earliest types of electrical networks studied consisted only of resistors and constant power sources and were called "direct current," or DC circuits. One of the important properties of resistive circuit elements is that electrical energy is lost or "dissipated" when current passes through them because of the collisions between the moving electric charges and the molecules of the resistor. Although this energy is not lost being converted to heat or kinetic energy of the resistor molecules, power sources such as batteries or dynamos (short for dynamoelectric machine) that convert chemical or kinetic energy to electrical form are necessary to produce a flow of charge through the circuit. In order to analyze a network to predict a knowledge of the currents in each circuit element when the source voltages or currents are known, it is easiest if all network elements are linear. Aside from Ohm's law describing the relation between current and voltage in each resistive element, only one other physical principle is needed. Kirchhoff's current law states that at any junction or "node" connecting two or more circuit elements, the total current entering the junction is equal to the sum of the currents leaving it. This law is based both on the physical fact that electrical charge does not seem to be created spontaneously or destroyed and on the fact that most electrical circuits are surrounded by an insulating medium through which charges cannot leak off. An alternative method of circuit analysis is to use Kirchhoff's voltage law, which is based on the conservation of energy. The law predicts that when a complete circuit is traced through interconnected network elements and returned to the starting point, the sum of the voltages of the power sources encountered is equal to the voltage drops across the dissipative resistive elements that were passed. Writing either of these equations for the various nodes or circuit loops in the network furnishes a set of linear algebraic equations that can be solved simultaneously for the currents in each circuit element and the voltages across them. Another law, called the "superposition principle," applies to linear circuits and is very useful in simplifying the analysis. It states that when a circuit contains several power sources, the resulting voltages or currents can be found by solving for the voltages or currents produced by each power source alone and then merely adding them up.

Many electrical power sources employ coils rotating in a magnetic field and produce sinusoidally oscillating signals called "alternating currents," or AC circuits. The number of cycles or oscillations per second is called the "frequency" of the oscillation and is measured in hertz. In North America, electrical power is distributed as sinusoidal voltages oscillating at a frequency of 60 hertz. Alternating current signals are described both by their peak values or "amplitudes" and by the time delay or "phase" between the oscillations of the power source and the individual element currents or voltages. Alternating current circuits having only resistive elements exhibit no time delay, and all the currents or voltages are in step with the power source.

The addition of inductive and capacitive circuit elements introduces a time variation into the circuit equations, which is useful in producing a wide variety of desirable effects. Adding a resistor to a capacitor--a combination called an RC circuit--allows the charge stored on the capacitor to leak off gradually with time or produces a delay in the charging of the capacitor when a voltage is applied to the combination. Similarly, the combination of a resistor with an inductor, called an RL circuit, causes a gradual, rather than an immediate rise in the current through the inductor when a voltage is applied to the combination. Besides acting as delay elements, such circuits have immediate application as filters, which discriminate against certain frequency bands in radio or audio devices. The combination of all three passive circuit elements is an RLC circuit and can produce an oscillatory behavior in which energy is transferred periodically between the inductor and the capacitor, with the oscillations dying out gradually as power is dissipated in the circuit resistance. The variations of voltage and current in such "resonant" circuits act very much as changes in position and velocity in mechanical oscillators such as pendulums and, in fact, are described by exactly the same type of mathematical second-order differential equations. The RLC circuits with low dissipation (also called high "Q," or quality factor) can be used to generate or select AC signals of a particular frequency, a very useful property in radio or television circuits.

Analysis methods for AC networks are similar to those for DC circuits, but a considerable simplification can be made by using the mathematical trick of substituting complex exponentials for the sines or cosines describing the actual currents or voltages. The expressions relating the AC currents and voltages across inductive and capacitive elements can be reduced to a relation that resembles Ohm's law, V = iZ, where the complex "impedance"

Z describes both the relations between the amplitudes of the current and voltage and the phase delays between them. Kirchhoff's laws can then be applied as in the DC case to predict the resulting voltages and currents when the power sources are known. The principle of superposition can simplify situations involving sources of several different frequencies.

Alternating current analysis can even solve circuits with nonsinusoidal sources, using a mathematical principle called Fourier analysis, which allows periodic (but nonsinusoidal signals) oscillating at a frequency f to be analyzed as though they were produced by separate sinusoidal sources oscillating at the harmonically related frequencies f, 2f, 3f, and the like.

The development of the vacuum tube and active devices based on combinations of semiconducting materials such as the transistor introduced new active electrical elements that amplify electrical signals and provide a much wider variety of circuit behavior than that available from passive elements alone. Since the charges passing through these elements are associated with electronic charges that have been pulled away from individual atoms, networks employing such devices are called electronic circuits. Although most such devices have a linear behavior in a certain portion of their operating range and networks using them can be solved by using classical linear analysis methods, the complete description of such circuits must include their nonlinear behavior as well. Unlike analog circuit elements, which respond to a wide range of voltages with a continuously changing current, digital circuit elements are extremely nonlinear and have only two stable current-voltage states. Strangely enough, this factor makes them much more reliable and easier to design than analog circuitry, and modern computers are composed almost entirely of digital circuit elements.

Applications

One of the first applications of circuit analysis was in the design of power distribution networks. While the first power generation stations built by Edison employed DC dynamos, the later AC generators of competitors such as Westinghouse were somewhat more efficient.

Eventually, AC rather than DC came to be used for power distribution because of the invention of an inductive circuit element with two coils called a transformer, which, by using different numbers of turns on the coils, can step oscillating voltages up or down with very little loss of power. Alternating current power of 60 hertz from the generators is stepped up to potentials as high as a million volts while maintaining low currents, so that there is little heat loss along the transmission wires. When it reaches the consumer, another set of transformers steps the potential down to an AC voltage of standard size for use with electrical appliances. In North America, the standard amplitude is about 169 volts, but lamp bulbs and motors are usually labeled with an "effective voltage" of 120 volts AC because it has the same heating effect in a resistor as a DC voltage of that magnitude.

The worldwide telephone network with all of its interconnections is certainly the largest and most complex electrical circuit ever devised. Many developments in electrical circuit theory were stimulated by the desire to predict and correct factors causing degradation in telephone service. Many electronic devices had their first practical use in telephone circuitry, such as audio amplifiers to amplify signals degraded by the resistance of transmission lines, wave-shaping filters to correct for the capacitance and inductance of such lines, or testing instruments to measure the characteristics of a network element, which had their impetus in detecting faults in long wires or undersea cables.

If AC currents of frequencies between about 20 hertz and 20,000 hertz are passed through the coil surrounding the magnetic core of a loudspeaker, the resulting motion of its diaphragm converts the electrical energy into pressure waves in the air that are perceived by humans as sound of different pitches. In the early years of the twentieth century, long before the invention of high fidelity audio systems, phonograph records were made by mechanical means, although some entrepreneurs attempted to broadcast organlike music to city subscribers by using a cumbersome array of switches controlling AC generators spinning at different frequencies. The music industry received a tremendous boost by the development of electronic amplifier circuits, which could combine the signals picked up by many microphones, record it on a phonograph record or magnetic tape, and then play it back at any desired volume. A wide variety of electronic amplifiers, filters, and recording equipment are found universally in both the home and concert hall. The development of electrical musical instruments that create electrical signal waveforms directly, instead of using a microphone to convert an acoustic sound to an electrical current, is a continuation of this trend.

After it was discovered that electromagnetic waves did not need conducting wires but could be transmitted and detected by specially adapted electrical circuits, the development of applications to long-distance communication such as radio and television followed rapidly.

Communication of information is accomplished by varying or "modulating" the amplitude of a high-frequency "carrier" signal at an audio rate and then launching the composite signal by applying it to a length of wire called an antenna. The power level of the transmitted wave is weakened as it travels away from the transmitting antenna. When it is reconverted into an electrical voltage by a receiving antenna, it is ordinarily much weaker than noise from nearby electric power lines or motors. Nevertheless, these interfering signals generally have different frequencies, and resonant circuits can be used to select only the frequencies of interest and suppress the noise. Electronic amplifier circuits step up the received signals to the point where their information content can be recovered by a "demodulator" circuit, after which further amplification can drive a loudspeaker to recover audio information, or it can control an electron beam sweeping across the phosphor coating of a television tube to produce a visible picture.

A radar device works somewhat like a two-way radio. Its internal circuits transmit a short pulse of electromagnetic radiation from a direction antenna, which bounces off any object in its path. A tiny portion of this signal will be reflected back to the antenna, where sensitive circuits amplify it and determine the distance of the object from the out-and-back travel time of the wave. At the high frequencies used for radar, electronic circuit analysis is complicated because the inductance, capacitance, and resistance of a circuit can no longer be considered to be lumped into ideal circuit elements. Because of their tendency to radiate, high-frequency signals called microwaves are often transmitted along the interiors of hollow waveguides instead of being sent along wires. Resonant circuits resemble plumbing fixtures more than coils of wire or capacitor plates. Since higher frequencies can be modulated at faster rates, the microwave transmitters of relay stations or satellites can carry millions of telephone conversations that can be separated out at the receiver by the proper electrical filter circuits.

Electronic circuits are also responsible for the rapid increase in the capabilities of measuring and control instruments used in science, medicine, and industry. By proper amplification and filtering, important signals often can be extracted from a much larger background of noise. By combining sensor signals electronically and presenting summary information on the proper kind of display, a surgeon can continuously monitor the vital signs of his patient, or one person can control a complex manufacturing process. Since electrical currents and voltages follow laws similar to those of the variables in mechanical, fluid dynamic, or other physical systems, a properly chosen electrical network can model and predict the behavior of other types of systems--a property used in simulators that train pilots or nuclear power plant operators.

Since the 1950's, a trend has been accelerating to use digital circuits in many types of applications previously handled by linear circuits. Many useful digital and analog circuit elements such as transistors, resistors, and capacitors have been miniaturized into standard integrated circuit chips to make amplifiers, switching circuits, and logic elements that are used as modular building blocks with known characteristics and are combined easily to form more complex circuits. Digital computers are often built from hundreds of thousands of such standardized circuits. The resulting reduction in cost and size has revolutionized industrial design, and miniature integrated electric circuits are now used to control such diverse products as kitchen appliances, automobile ignition systems, elevators, and even children's toys.

Context

Although the ancient Greeks were familiar with electrostatic forces (the word "electron" comes from the Greek word for an insulating amber, which could be used to hold electric charges), electricity was not studied scientifically until the experiments of Benjamin Franklin and Alessandro Volta in the last decades of the eighteenth century. The effects of electric currents were brought out by the work of Michael Faraday, Andre-Marie Ampere, Joseph Henry, Georg Simon Ohm, Lord Kelvin, and many others in the first half of the nineteenth century. The theoretical background of electromagnetic forces was essentially completed in 1865, with the laws of James Clerk Maxwell. The development of electric circuit analysis began about 1845, with the inventions of Sir Charles Wheatstone and the circuit laws of Gustav Robert Kirchhoff. Yet, many of the early practical applications came from nonscientists without much knowledge of theory, such as Samuel Finley Breese Morse--whose name is associated with the development of telegraphy about 1837--and Alexander Graham Bell, who is usually given the credit for invention of the telephone in 1876. Thomas Alva Edison produced an astounding range of electric inventions in the last half of the nineteenth century in what was essentially the world's first industrial research laboratory, ranging from the incandescent lamp to electric power distribution stations.

In about 1887, Heinrich Rudolf Hertz had discovered the propagation of electromagnetic waves through space. Guglielmo Marconi was able to demonstrate a practical though clumsy radio transmitter and receiver of transatlantic range at the beginning of the twentieth century. Radio broadcasting began about 1906, and electronic television followed as early as 1908; vacuum tubes were developed at about the same time. World War I stimulated the development of telephone and radio circuitry, much as the explosive development in radar and microwave circuitry came about in government laboratories in England and the United States in response to World War II needs. Between the wars, however, the development of amateur radio created a large expansion in the number of scientists interested in electronic circuitry. Transistors were developed, largely at the Bell Telephone Laboratories in the late 1930's, and were responsible for the miniaturization of electronic circuits, which took place in the 1950's, culminating in the invention of the integrated circuit about 1960 and the single-chip microcomputer about 1972. Modern trends in the continual quest for smaller and faster electronic devices are moving toward the use of optical-electronic devices and components that use quantum-mechanical phenomena.

Principal terms

ACTIVE ELEMENT: an electrical circuit element in which a source of electrical power can be controlled by an electrical signal; transistors and vacuum tubes are common examples

CAPACITANCE: the property of an electrical circuit element that allows it to store an electrical charge when a voltage is placed across it

CURRENT: the rate of electrical charge movement through a circuit element; usually measured in coulombs per second or amperes

INDUCTANCE: the property of an electrical circuit element that produces a voltage across that element when the current through the element is changing

KIRCHHOFF'S LAWS: two laws governing the behavior of current and voltage in electrical circuits; equivalent to the physical principles of conservation of energy and charge

LINEAR RESPONSE: the region of operation in which the current or voltage associated with an electrical circuit element is proportional to the cause producing it; most devices are nonlinear if the current through them varies over too wide a range

OHM'S LAW: considered to be the definition of electrical resistance

RESISTANCE: the property of an electrical circuit element that produces an electrical current through the element when a voltage is placed across it

VOLTAGE: a measure of electrical potential (potential energy per unit charge) across a circuit element that is usually measured in volts; associated with the electrical forces that drive currents through an electrical circuit

Bibliography

Boylestad, Robert, and Louis Nashelsky. ELECTRONICS: A SURVEY. 3d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1989. Representative of the many books on modern circuit theory at the junior college or technical school level, this volume covers DC and AC circuits and analog and digital electronics. Contains many illustrations and examples.

Dummer, G. W. A. ELECTRONIC INVENTIONS AND DISCOVERIES. 2d ed. Oxford, England: Pergamon Press, 1978. A fascinating list of hundreds of electrical inventions with short descriptions of their historical context and references to original publications, not neglecting such mundane affairs as circuit "breadboards" and wire wrap techniques.

Harten, James H., and Paul Y. Lin. ESSENTIALS OF ELECTRIC CIRCUITS. 2d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1986. A junior college or technical-level text suitable for self-study. Mathematics is introduced only as necessary.

Horowitz, Paul, and Winfield Hill. THE ART OF ELECTRONICS. 2d ed. New York: Cambridge University Press, 1989. An introductory textbook in electronic circuit design beginning at a level suitable for readers with no previous knowledge of elec- tronics. Covers both analog and digital circuitry and stresses practical uses. Widely adopted for college and junior college laboratory courses.

Huelsman, Lawrence P. BASIC CIRCUIT THEORY. 2d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1984. This thorough volume is representative of the more advanced treatments of circuit theory, covering both passive and active analog circuits. Appendices are included on the use of matrix methods, complex algebra, and computer programs in the analysis of electric circuits. Readers should have some knowledge of simpler electric circuits before attempting this volume. Geared for second- or third-year college students.

Scott, Donald E. AN INTRODUCTION TO CIRCUIT ANALYSIS. New York: McGraw-Hill, 1987. Discusses modern circuit theory. Includes an appendix on the SPICE electronic circuit analysis program.

Sinclair, Ian R. UNDERSTANDING ELECTRONIC CIRCUITS. London: Fountain Press, 1973. Adequate for the beginner who wants to know how both analog and digital circuits work. Contains few formulas and little mathematics, therefore, the explanations are easily understandable to the casual reader.

Smith, Ralph J. CIRCUITS, DEVICES AND SYSTEMS. 4th ed. New York: Wiley, 1984. Furnishes an introduction to circuit theory for electrical engineers at the college level. Interesting reading.

Young, John D. PORTABLE ELECTRONICS DATA BOOK. Englewood Cliffs, N.J.: Prentice-Hall, 1989. Much information useful to electric circuit designers is included in this handy reference volume. Contains formulas, electronic symbols, tables, descriptions of electric circuit elements, and computer programs to help solve design problems.

Charges and Currents

Conductors and Resistors

Radio and Television