Current and Voltage

• Current and Voltage

2.1 ATOMS AND THEIR STRUCTURE
A basic understanding of the fundamental concepts of current and voltage requires a degree of familiarity with the atom and its structure. The simplest of all atoms is the hydrogen atom, made up of two basic particles, the proton and the electron, in the relative positions shown in Fig. 2.1(a). The nucleus of the hydrogen atom is the proton, a positively charged particle. The orbiting electron carries a negative charge that is equal in magnitude to the positive charge of the proton. In all other ele
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Electron
Nucleus
Proton
–
+ +
–
–
Protons
Electrons
Nucleus
Neutrons
Electron
(b) Helium atom
(a) Hydrogen atom
FIG. 2.1 The hydrogen and helium atoms.
2
FIG. 2.2 Shells and subshells of the atomic structure.
2 electrons (2 e) 2 e 6 e 2 e 6 e 10 e 2 e 6 e 10 e 14 e
s s p s p d s p d f
4th shell3rd shell2nd shell1st shell
1 subshell 2 subshells 3 subshells 4 subshells
nl
Nucleus + k m
ments, the nucleus also contains neutrons, which are slightly heavier than protons and have no electrical charge. The helium atom, for example, has two neutrons in addition to two electrons and two protons, as shown in Fig. 2.1(b). In all neutral atoms the number of electrons is equal to the number of protons. The mass of the electron is 9.11 10 28 g, and that of the proton and neutron is 1.672 10 24 g. The mass of the proton (or neutron) is therefore approximately 1836 times that of the electron. The radii of the proton, neutron, and electron are all of the order of magnitude of 2 10 15 m. For the hydrogen atom, the radius of the smallest orbit followed by the electron is about 5 10 11 m. The radius of this orbit is approximately 25,000 times that of the radius of the electron, proton, or neutron. This is approximately equivalent to a sphere the size of a dime revolving about another sphere of the same size more than a quarter of a mile away. Different atoms will have various numbers of electrons in the concentric shells about the nucleus. The first shell, which is closest to the nucleus, can contain only two electrons. If an atom should have three electrons, the third must go to the next shell. The second shell can contain a maximum of eight electrons; the third, 18; and the fourth, 32; as determined by the equation 2n2, where n is the shell number. These shells are usually denoted by a number (n 1, 2, 3, . . .) or letter (n k, l, m, ...). Each shell is then broken down into subshells, where the first subshell can contain a maximum of two electrons; the second subshell, six electrons; the third, 10 electrons; and the fourth, 14; as shown in Fig. 2.2. The subshells are usually denoted by the letters s, p, d, and f, in that order, outward from the nucleus.
32  CURRENT AND VOLTAGE
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It has been determined by experimentation that unlike charges attract, and like charges repel. The force of attraction or repulsion between two charged bodies Q1 and Q2 can be determined by Coulomb’s law:
(newtons, N) (2.1)
where F is in newtons, k a constant 9.0 109 N⋅m2/C2, Q1 and Q2 are the charges in coulombs (to be introduced in Section 2.2), and r is
F (attraction or repulsion) kQ r 1 2 Q2
French (Angoulème, Paris) (1736–1806) Scientist and Inventor Military Engineer, West Indies
Courtesy of the Smithsonian Institution Photo No. 52,597
Attended the engineering school at Mezieres, the first such school of its kind. Formulated Coulomb’s law, which defines the force between two electrical charges and is, in fact, one of the principal forces in atomic reactions. Performed extensive research on the friction encountered in machinery and windmills and the elasticity of metal and silk fibers.
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f
Remaining subshells empty
nl
Nucleus + 3rd shell 4th shell 1st shell 2nd shell m
2 e 2 e 6 e 10 e 2 e 6 e
spddspsp
– 1 e (29th)
s
k
FIG. 2.4 The copper atom.
2.2 CURRENT
Consider a short length of copper wire cut with an imaginary perpendicular plane, producing the circular cross section shown in Fig. 2.5. At room temperature with no external forces applied, there exists within the copper wire the random motion of free electrons created by
the distance in meters between the two charges. In particular, note the squared r term in the denominator, resulting in rapidly decreasing levels of F for increasing values of r. (See Fig. 2.3.) In the atom, therefore, electrons will repel each other, and protons and electrons will attract each other. Since the nucleus consists of many positive charges (protons), a strong attractive force exists for the electrons in orbits close to the nucleus [note the effects of a large charge Q and a small distance r in Eq. (2.1)]. As the distance between the nucleus and the orbital electrons increases, the binding force diminishes until it reaches its lowest level at the outermost subshell (largest r). Due to the weaker binding forces, less energy must be expended to remove an electron from an outer subshell than from an inner subshell. Also, it is generally true that electrons are more readily removed from atoms having outer subshells that are incomplete and, in addition, possess few electrons. These properties of the atom that permit the removal of electrons under certain conditions are essential if motion of charge is to be created. Without this motion, this text could venture no further—our basic quantities rely on it. Copper is the most commonly used metal in the electrical/electronics industry. An examination of its atomic structure will help identify why it has such widespread applications. The copper atom (Fig. 2.4) has one more electron than needed to complete the first three shells. This incomplete outermost subshell, possessing only one electron, and the distance between this electron and the nucleus reveal that the twenty-ninth electron is loosely bound to the copper atom. If this twenty-ninth electron gains sufficient energy from the surrounding medium to leave its parent atom, it is called a free electron. In one cubic inch of copper at room temperature, there are approximately 1.4 10 24 free electrons. Other metals that exhibit the same properties as copper, but to a different degree, are silver, gold, aluminum, and tungsten. Additional discussion of conductors and their characteristics can be found in Section 3.2.
FIG. 2.3 Charles Augustin de Coulomb.
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the thermal energy that the electrons gain from the surrounding medium. When atoms lose their free electrons, they acquire a net positive charge and are referred to as positive ions. The free electrons are able to move within these positive ions and leave the general area of the parent atom, while the positive ions only oscillate in a mean fixed position. For this reason,
the free electron is the charge carrier in a copper wire or any other solid conductor of electricity.
An array of positive ions and free electrons is depicted in Fig. 2.6. Within this array, the free electrons find themselves continually gaining or losing energy by virtue of their changing direction and velocity. Some of the factors responsible for this random motion include (1) the collisions with positive ions and other electrons, (2) the attractive forces for the positive ions, and (3) the force of repulsion that exists between electrons. This random motion of free electrons is such that over a period of time, the number of electrons moving to the right across the circular cross section of Fig. 2.5 is exactly equal to the number passing over to the left.
With no external forces applied, the net flow of charge in a conductor in any one direction is zero.
Let us now connect copper wire between two battery terminals and a light bulb, as shown in Fig. 2.7, to create the simplest of electric circuits. The battery, at the expense of chemical energy, places a net positive charge at one terminal and a net negative charge on the other. The instant the final connection is made, the free electrons (of negative charge) will drift toward the positive terminal, while the positive ions left behind in the copper wire will simply oscillate in a mean fixed position. The negative terminal is a “supply” of electrons to be drawn from when the electrons of the copper wire drift toward the positive terminal.
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+ Ion
+ Ion
+ Ion
+ Ion
+ Ion
FIG. 2.6 Random motion of free electrons in an atomic structure.
Ielectron
Copper wire
Iconventional
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Chemical activity
Battery
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Imaginary plane
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FIG. 2.7 Basic electric circuit.
Imaginary plane
Copper wire
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FIG. 2.5 Random motion of electrons in a copper wire with no external “pressure” (voltage) applied.
French (Lyon, Paris) (1775–1836) Mathematician and Physicist Professor of Mathematics, École Polytechnique in Paris
Courtesy of the Smithsonian Institution Photo No. 76,524
On September 18, 1820, introduced a new field of study, electrodynamics, devoted to the effect of electricity in motion, including the interaction between currents in adjoining conductors and the interplay of the surrounding magnetic fields. Constructed the first solenoid and demonstrated how it could behave like a magnet (the first electromagnet). Suggested the name galvanometer for an instrument designed to measure current levels.
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The chemical activity of the battery will absorb the electrons at the positive terminal and will maintain a steady supply of electrons at the negative terminal. The flow of charge (electrons) through the bulb will heat up the filament of the bulb through friction to the point that it will glow red hot and emit the desired light. If 6.242 1018 electrons drift at uniform velocity through the imaginary circular cross section of Fig. 2.7 in 1 second, the flow of charge, or current, is said to be 1 ampere (A) in honor of André Marie Ampère (Fig. 2.8). The discussion of Chapter 1 clearly reveals that this is an enormous number of electrons passing through the surface in 1 second. The current associated with only a few electrons per second would be inconsequential and of little practical value. To establish numerical values that permit immediate comparisons between levels, a coulomb (C) of charge was defined as the total charge associated with 6.242 1018 electrons. The charge associated with one electron can then be determined from
Charge/electron Qe 1.6 10 19 C
The current in amperes can now be calculated using the following equation:
I amperes (A) Q coulombs (C) (2.2) t seconds (s)
The capital letter I was chosen from the French word for current: intensité. The SI abbreviation for each quantity in Eq. (2.2) is provided to the right of the equation. The equation clearly reveals that for equal time intervals, the more charge that flows through the wire, the heavier the current. Through algebraic manipulations, the other two quantities can be determined as follows:
(coulombs, C) (2.3)
and (seconds, s) (2.4)
EXAMPLE 2.1 The charge flowing through the imaginary surface of Fig. 2.7 is 0.16 C every 64 ms. Determine the current in amperes.
Solution: Eq. (2.2):
I 2.50 A
EXAMPLE 2.2 Determine the time required for 4 1016 electrons to pass through the imaginary surface of Fig. 2.7 if the current is 5 mA.
Solution: Determine Q: 4 1016 electrons 0.641 10 2 C 0.00641 C 6.41 mC 1 C 6.242 1018 electrons
160 10 3 C 64 10 3 s
0.16 C 64 10 3 s
Q t
t Q I
Q It
I Q t
1 C 6.242 1018
CURRENT  35
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FIG. 2.8 André Marie Ampère.
Calculate t [Eq. (2.4)]:
t 1.282 s
A second glance at Fig. 2.7 will reveal that two directions of charge flow have been indicated. One is called conventional flow, and the other is called electron flow. This text will deal only with conventional flow for a variety of reasons, including the fact that it is the most widely used at educational institutions and in industry, it is employed in the design of all electronic device symbols, and it is the popular choice for all major computer software packages. The flow controversy is a result of an assumption made at the time electricity was discovered that the positive charge was the moving particle in metallic conductors. Be assured that the choice of conventional flow will not create great difficulty and confusion in the chapters to follow. Once the direction of I is established, the issue is dropped and the analysis can continue without confusion.
Safety Considerations
It is important to realize that even small levels of current through the human body can cause serious, dangerous side effects. Experimental results reveal that the human body begins to react to currents of only a few milliamperes. Although most individuals can withstand currents up to perhaps 10 mA for very short periods of time without serious side effects, any current over 10 mA should be considered dangerous. In fact, currents of 50 mA can cause severe shock, and currents of over 100 mA can be fatal. In most cases the skin resistance of the body when dry is sufficiently high to limit the current through the body to relatively safe levels for voltage levels typically found in the home. However, be aware that when the skin is wet due to perspiration, bathing, etc., or when the skin barrier is broken due to an injury, the skin resistance drops dramatically, and current levels could rise to dangerous levels for the same voltage shock. In general, therefore, simply remember that water and electricity don’t mix. Granted, there are safety devices in the home today [such as the ground fault current interrupt (GFCI) breaker to be introduced in Chapter 4] that are designed specifically for use in wet areas such as the bathroom and kitchen, but accidents happen. Treat electricity with respect—not fear.
2.3 VOLTAGE
The flow of charge described in the previous section is established by an external “pressure” derived from the energy that a mass has by virtue of its position: potential energy. Energy, by definition, is the capacity to do work. If a mass (m) is raised to some height (h) above a reference plane, it has a measure of potential energy expressed in joules (J) that is determined by
(joules, J) (2.5)
where g is the gravitational acceleration (9.754 m/s2). This mass now has the “potential” to do work such as crush an object placed on the ref
W (potential energy) mgh
6.41 10 3 C 5 10 3 A
Q I
36  CURRENT AND VOLTAGE
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erence plane. If the weight is raised further, it has an increased measure of potential energy and can do additional work. There is an obvious difference in potential between the two heights above the reference plane. In the battery of Fig. 2.7, the internal chemical action will establish (through an expenditure of energy) an accumulation of negative charges (electrons) on one terminal (the negative terminal) and positive charges (positive ions) on the other (the positive terminal). A “positioning” of the charges has been established that will result in a potential difference between the terminals. If a conductor is connected between the terminals of the battery, the electrons at the negative terminal have sufficient potential energy to overcome collisions with other particles in the conductor and the repulsion from similar charges to reach the positive terminal to which they are attracted. Charge can be raised to a higher potential level through the expenditure of energy from an external source, or it can lose potential energy as it travels through an electrical system. In any case, by definition:
A potential difference of 1 volt (V) exists between two points if 1 joule (J) of energy is exchanged in moving 1 coulomb (C) of charge between the two points.
The unit of measurement volt was chosen to honor Alessandro Volta (Fig. 2.9). Pictorially, if one joule of energy (1 J) is required to move the one coulomb (1 C) of charge of Fig. 2.10 from position x to position y, the potential difference or voltage between the two points is one volt (1 V). If the energy required to move the 1 C of charge increases to 12 J due to additional opposing forces, then the potential difference will increase to 12 V. Voltage is therefore an indication of how much energy is involved in moving a charge between two points in an electrical system. Conversely, the higher the voltage rating of an energy source such as a battery, the more energy will be available to move charge through the system. Note in the above discussion that two points are always involved when talking about voltage or potential difference. In the future, therefore, it is very important to keep in mind that
a potential difference or voltage is always measured between two points in the system. Changing either point may change the potential difference between the two points under investigation.
In general, the potential difference between two points is determined by
(volts) (2.6)
Through algebraic manipulations, we have
(joules) (2.7)
and (coulombs) (2.8) Q W V
W QV
V W Q
VOLTAGE  37
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Vxy = 1 volt
1 C
W = 1 J
xy
FIG. 2.10 Defining the unit of measurement for voltage.
FIG. 2.9 Count Alessandro Volta.
Italian (Como, Pavia) (1745–1827) Physicist Professor of Physics, Pavia, Italy
Courtesy of the Smithsonian Institution Photo No. 55,393
Began electrical experiments at the age of 18 working with other European investigators. Major contribution was the development of an electrical energy source from chemical action in 1800. For the first time, electrical energy was available on a continuous basis and could be used for practical purposes. Developed the first condenser known today as the capacitor. Was invited to Paris to demonstrate the voltaic cell to Napoleon. The International Electrical Congress meeting in Paris in 1881 honored his efforts by choosing the volt as the unit of measure for electromotive force.
EXAMPLE 2.3 Find the potential difference between two points in an electrical system if 60 J of energy are expended by a charge of 20 C between these two points.
Solution: Eq. (2.6):
V 3 V
EXAMPLE 2.4 Determine the energy expended moving a charge of 50 mC through a potential difference of 6 V.
Solution: Eq. (2.7): W QV (50 10 6 C)(6 V) 300 10 6 J 300 mJ
Notation plays a very important role in the analysis of electrical and electronic systems. To distinguish between sources of voltage (batteries and the like) and losses in potential across dissipative elements, the following notation will be used:
E for voltage sources (volts) V for voltage drops (volts)
An occasional source of confusion is the terminology applied to this subject matter. Terms commonly encountered include potential, potential difference, voltage, voltage difference (drop or rise), and electromotive force. As noted in the description above, some are used interchangeably. The following definitions are provided as an aid in understanding the meaning of each term:
Potential: The voltage at a point with respect to another point in the electrical system. Typically the reference point is ground, which is at zero potential.
Potential difference: The algebraic difference in potential (or voltage) between two points of a network.
Voltage: When isolated, like potential, the voltage at a point with respect to some reference such as ground (0 V).
Voltage difference: The algebraic difference in voltage (or potential) between two points of the system. A voltage drop or rise is as the terminology would suggest.
Electromotive force (emf): The force that establishes the flow of charge (or current) in a system due to the application of a difference in potential. This term is not applied that often in today’s literature but is associated primarily with sources of energy.
In summary, the applied potential difference (in volts) of a voltage source in an electric circuit is the “pressure” to set the system in motion and “cause” the flow of charge or current through the electrical system. A mechanical analogy of the applied voltage is the pressure applied to the water in a main. The resulting flow of water through the system is likened to the flow of charge through an electric circuit. Without the applied pressure from the spigot, the water will simply sit in the hose, just as the electrons of a copper wire do not have a general direction without an applied voltage.
60 J 20 C
W Q
38  CURRENT AND VOLTAGE
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2.4 FIXED (dc) SUPPLIES
The terminology dc employed in the heading of this section is an abbreviation for direct current, which encompasses the various electrical systems in which there is a unidirectional (“one direction”) flow of charge. A great deal more will be said about this terminology in the chapters to follow. For now, we will consider only those supplies that provide a fixed voltage or current.
dc Voltage Sources
Since the dc voltage source is the more familiar of the two types of supplies, it will be examined first. The symbol used for all dc voltage supplies in this text appears in Fig. 2.11. The relative lengths of the bars indicate the terminals they represent. Dc voltage sources can be divided into three broad categories: (1) batteries (chemical action), (2) generators (electromechanical), and (3) power supplies (rectification).
Batteries
General Information For the layperson, the battery is the most common of the dc sources. By definition, a battery (derived from the expression “battery of cells”) consists of a combination of two or more similar cells, a cell being the fundamental source of electrical energy developed through the conversion of chemical or solar energy. All cells can be divided into the primary or secondary types. The secondary is rechargeable, whereas the primary is not. That is, the chemical reaction of the secondary cell can be reversed to restore its capacity. The two most common rechargeable batteries are the lead-acid unit (used primarily in automobiles) and the nickel-cadmium battery (used in calculators, tools, photoflash units, shavers, and so on). The obvious advantage of the rechargeable unit is the reduced costs associated with not having to continually replace discharged primary cells. All the cells appearing in this chapter except the solar cell, which absorbs energy from incident light in the form of photons, establish a potential difference at the expense of chemical energy. In addition, each has a positive and a negative electrode and an electrolyte to complete the circuit between electrodes within the battery. The electrolyte is the contact element and the source of ions for conduction between the terminals.
Alkaline and Lithium-Iodine Primary Cells The popular alkaline primary battery employs a powdered zinc anode ( ); a potassium (alkali metal) hydroxide electrolyte; and a manganese dioxide, carbon cathode ( ) as shown in Fig. 2.12(a). In particular, note in Fig. 2.12(b) that the larger the cylindrical unit, the higher the current capacity. The lantern is designed primarily for long-term use. Figure 2.13 shows two lithium-iodine primary units with an area of application and a rating to be introduced later in this section.
Lead-Acid Secondary Cell For the secondary lead-acid unit appearing in Fig. 2.14, the electrolyte is sulfuric acid, and the electrodes are spongy lead (Pb) and lead peroxide (PbO2). When a load is applied to the battery terminals, there is a transfer of electrons from the spongy lead electrode to the lead peroxide electrode through the load. This
FIXED (dc) SUPPLIES  39
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E
FIG. 2.11 Symbol for a dc voltage source.
transfer of electrons will continue until the battery is completely discharged. The discharge time is determined by how diluted the acid has become and how heavy the coating of lead sulfate is on each plate. The state of discharge of a lead storage cell can be determined by measuring the specific gravity of the electrolyte with a hydrometer. The specific gravity of a substance is defined to be the ratio of the weight of a given volume of the substance to the weight of an equal volume of water at 4°C. For fully charged batteries, the specific gravity should be somewhere between 1.28 and 1.30. When the specific gravity drops to about 1.1, the battery should be recharged. Since the lead storage cell is a secondary cell, it can be recharged at any point during the discharge phase simply by applying an external dc current source across the cell that will pass current through the cell in a direction opposite to that in which the cell supplied current to the
40  CURRENT AND VOLTAGE
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(b)
1.5 V “C” cell
1.5 V “D” cell
1.5 V “AAA” cell
1.5 V “AA” cell
9 V transistor
6 V lantern
[7.2 Ah] (0–1 A)
[16.0 Ah] (0–1 A)
Capacity Continuous Current
[1.1 Ah] (0–300 mA)
[2.5 Ah] (0–500 mA)
[520 mAh] (0–250 mA)
[22.0 Ah] (0–1.5 A)
Capacity Continuous Current
(a)
Metal spur Rivet — brass
Negative cover — plated steel
Can — steel
Metallized plastic film label
Anode — powdered zinc
Current collector — brass
Seal — nylon
Inner cell cover — steel
Positive cover — plated steel
Electrolyte — potassium hydroxide
Cathode — manganese dioxide, carbon
Separator — non-woven fabric
Metal washer
FIG. 2.12 (a) Cutaway of cylindrical Energizer® alkaline cell; (b) Eveready® Energizer primary cells. (Courtesy of Eveready Battery Company, Inc.)
FIG. 2.13 Lithium-iodine primary cells. (Courtesy of Catalyst Research Corp.)
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load. This will remove the lead sulfate from the plates and restore the concentration of sulfuric acid. The output of a lead storage cell over most of the discharge phase is about 2.1 V. In the commercial lead storage batteries used in the automobile, 12.6 V can be produced by six cells in series, as shown in Fig. 2.14. In general, lead-acid storage batteries are used in situations where a high current is required for relatively short periods of time. At one time all lead-acid batteries were vented. Gases created during the discharge cycle could escape, and the vent plugs provided access to replace the water or electrolyte and to check the acid level with a hydrometer. The use of a grid made from a wrought lead–calcium alloy strip rather than the lead-antimony cast grid commonly used has resulted in maintenance-free batteries such as that appearing in Fig. 2.14. The lead-antimony structure was susceptible to corrosion, overcharge, gasing, water usage, and self-discharge. Improved design with the lead-calcium grid has either eliminated or substantially reduced most of these problems. It would seem that with all the years of technology surrounding batteries, smaller, more powerful units would now be available. However, when it comes to the electric car, which is slowly gaining interest and popularity throughout the world, the lead-acid battery is still the primary source of power. A “station car,” manufactured in Norway and used on a test basis in San Francisco for typical commuter runs, has a total weight of 1650 pounds, with 550 pounds (a third of its weight) for the lead-acid rechargeable batteries. Although the station car will travel at speeds of 55 mph, its range is limited to 65 miles on a charge. It would appear that long-distance travel with significantly reduced weight factors for the batteries will depend on a new, innovative approach to battery design.
Nickel-Cadmium Secondary-Cell The nickel-cadmium battery is a rechargeable battery that has been receiving enormous interest and
FIXED (dc) SUPPLIES  41
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−
12.6 V
FIG. 2.14 Maintenance-free 12-V (actually 12.6-V) lead-acid battery. (Courtesy of DelcoRemy, a division of General Motors Corp.)
development in recent years. For applications such as flashlights, shavers, portable televisions, power drills, and so on, the nickelcadmium (Ni-Cad) battery of Fig. 2.15 is the secondary battery of choice because the current levels are lower and the period of continuous drain is usually longer. A typical nickel-cadmium battery can survive over 1000 charge/discharge cycles over a period of time that can last for years. It is important to recognize that when an appliance or a system calls for a Ni-Cad battery, a primary cell should not be used. The appliance or system may have an internal charging network that would be dysfunctional with a primary cell. In addition, be aware that all Ni-Cad batteries are about 1.2 V per cell, while the most common primary cells are typically 1.5 V per cell. There is some ambiguity about how often a secondary cell should be recharged. For the vast majority of situations, the battery can be used until there is some indication that the energy level is low, such as a dimming light from a flashlight, less power from a drill, or a blinking light if one is provided with the equipment. Keep in mind that secondary cells do have some “memory.” If they are recharged continuously after being used for a short period of time, they may begin to believe they are short-term units and actually fail to hold the charge for the rated period of time. In any event, always try to avoid a “hard” discharge, which results when every bit of energy is drained from a cell. Too many hard discharge cycles will reduce the cycle life of the battery. Finally, be aware that the charging mechanism for nickel-cadmium cells is quite different from that for lead-acid batteries. The nickel-cadmium battery is charged by a constant current source, with the terminal voltage staying pretty steady through the entire charging cycle. The lead-acid battery is charged by a constant voltage source, permitting the current to vary as determined by the state of the battery. The capacity of the Ni-Cad battery increases almost linearly throughout most of the charging cycle. One may find that Ni-Cad
42  CURRENT AND VOLTAGE
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1.2 V 4 Ah
1.2 V 1.2
7.2 V 100 mAh
1.2 V 500 mAh
1.2 V 180 mAh
Eveready BH 500 cell 1.2 V, 500 mAh App: Where vertical height is severe limitation
(a)
(b)
FIG. 2.15 Rechargeable nickel-cadmium batteries. (Courtesy of Eveready Batteries.)
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batteries are relatively warm when charging. The lower the capacity level of the battery when charging, the higher the temperature of the cell. As the battery approaches rated capacity, the temperature of the cell approaches room temperature.
Nickel-Hydrogen and Nickel–Metal Hydride Secondary Cells Two other types of secondary cell include the nickel-hydrogen and nickel–metal hydride cells. The nickel-hydrogen cell is currently limited primarily to space vehicle applications where high-energy-density batteries are required that are rugged and reliable and can withstand a high number of charge/discharge cycles over a relatively long period of time. The nickel–metal hydride cell is actually a hybrid of the nickelcadmium and nickel-hydrogen cells, combining the positive characteristics of each to create a product with a high power level in a small package that has a long cycle life. Although relatively expensive, this hybrid is a valid option for applications such as portable computers, as shown in Fig. 2.16.
Solar Cell A high-density, 40-W solar cell appears in Fig. 2.17 with some of its associated data and areas of application. Since the maximum available wattage in an average bright sunlit day is 100 mW/cm2, and since conversion efficiencies are currently between 10% and 14%, the maximum available power per square centimeter from most commercial units is between 10 mW and 14 mW. For a square meter, however, the return would be 100 W to 140 W. A more detailed description of the solar cell will appear in your electronics courses. For now it is important to realize that a fixed illumination of the solar cell will provide a fairly steady dc voltage for driving various loads, from watches to automobiles.
Ampere-Hour Rating Batteries have a capacity rating given in ampere-hours (Ah) or milliampere-hours (mAh). Some of these ratings are included in the above figures. A battery with an ampere-hour rating of 100 will theoretically provide a steady current of 1 A for 100 h, 2 A for 50 h, 10 A for 10 h, and so on, as determined by the following equation:
Life (hours) (2.9)
Two factors that affect this rating, however, are the temperature and the rate of discharge. The disc-type Eveready® BH 500 cell appearing in Fig. 2.15 has the terminal characteristics appearing in Fig. 2.18. Figure 2.18 reveals that
the capacity of a dc battery decreases with an increase in the current demand
and
the capacity of a dc battery decreases at relatively (compared to room temperature) low and high temperatures.
Forthe 1-V unit of Fig. 2.18(a), the rating is just above 500 mAh at a discharge current of 100 mA, but it drops to about 300 mAh at about 1A. Foraunit that is less than 11⁄2 in. in diameter and less than 1⁄2 in. in thickness, however, these are excellent terminal characteristics. Figure
ampere-hour rating (Ah) amperes drawn (A)
FIXED (dc) SUPPLIES  43
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10.8 V, 2.9 Ah, 600 mA (monochrome display), 900 mA (color display)
C A U T IO N J D N D K M C V L K D C J D S L S F J S K L D J F M L D K J F S J J S D J L F J F K S D M C S D J F F J S D F J F S D F S D F J S J D F A J F Z X A S D F A F D G S D D F G S D F H D F k h f d h f js h f h i u w i c s d f s d g s d fa s fg f g b f g u f u y k h e r f j h u e h f jd h k s i fh a s e jy f is h a i w e h u h a f r e a f y h
C A U T IO N


 D O
 N O T
 O P E N ,
 T H R O W
 I N
 F I R E
 O R
 S H O R T
 C I R C U I T A T T E N T IO N


 N E
 P A S
 O U V R I R ,
 J E T E R
 A U
 F E U
 N I
 M E T T R E
 E N












































 C O U R T
 C I R C U I T L E T O P !

 D E Z E
 B A T T E R I J
 N I E T
 O P E N E N ,
 V E R H I T T E N
 O F
 K O R T S L U I T T E N A C H T U N G

 N I G H T
 O F F N E N ,
 V E R B R E N N E N
 O D E R
 K U R Z S C H L I E S S E N A T T E N Z IO N E !   N O N
 A P R I R E ,
 C O R T O C I R C U I T A R E
 O
 B R U C I A R E P A S P A !


 M A
 I K K E
 A B N E S ,
 B R A E N D E S
 E L L E R
 K O R S L U T T E S A D V A R S E L

 M A
 I K K E
 A P N E S ,
 B R E N N E S
 E L L E R
 K O R T S L U T T E S P R E C A U C IO N

 N O
 A B R I R ,
 I N C I N E R A R
 N I
 C O R T O C I R C U I T A R C U ID A D O

 N A O
 A B R A ,
 N A O
 Q U E I M E ,
 N E M
 F A C A
 C U R T O C I R U I T O V A R N IN G


 R I S K
 F O R
 P E R S O N S K A D
 F A R
 I N T E
 O P P N A S ,
 B R A N N A S





































 E L L E R
 K O R T S V A R O IT U S

 A L A
 A V A A ,
 A L A
 P O L T A
 A L A K A
 O I K O S U L J E
   
 
P / N

 4 9 G 1 1 1 6
FIG. 2.16 Nickel–metal hydride (Ni-MH) battery for the IBM lap-top computer.
FIG. 2.17 Solar module. (Courtesy of Motorola Semiconductor Products.)
40-W, high-density solar module 100-mm 100-mm (4 4 ) square cells are used to provide maximum power in a minimum of space. The 33 series cell module provides a strong 12-V battery charging current for a wide range of temperatures ( 40°C to 60°C)
2.18(b) reveals that the maximum mAh rating (at a current drain of 50 mA) occurs at about 75°F ( 24°C), or just above average room temperature. Note that the curve drops to the right and left of this maximum value. We are all aware of the reduced “strength” of a battery at low temperatures. Note that it has dropped to almost 300 mAh at about 8°F. Another curve of interest appears in Fig. 2.19. It provides the expected cell voltage at a particular drain over a period of hours of use. It is noteworthy that the loss in hours between 50 mA and 100 mA is much greater than between 100 mA and 150 mA, even though the increase in current is the same between levels. In general,
the terminal voltage of a dc battery decreases with the length of the discharge time at a particular drain current.
44  CURRENT AND VOLTAGE
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0 200 400 600 800 1000 1200
Capacity (mAh)
Discharge current (mA)
600
500
400
300
200
100
600
500
400
300
200
100
0.9 V 1.0 V 1.1 V
Discharge current = 50 mA
0°C
°F
0 –10 0 10 20 30 40 50 60 70 80 90 100110120130
(a)
(b)
Capacity (mAh)
FIG. 2.18 Eveready® BH 500 cell characteristics: (a) capacity versus discharge current; (b) capacity versus temperature. (Courtesy of Eveready Batteries.)
150 mA
100 mA 50 mA
Discharge time (h)
Cell voltage
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.9
1.0
1.1
1.2
1.3
1.4
1.5
FIG. 2.19 Eveready® BH 500 cell discharge curves. (Courtesy of Eveready Batteries.)
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EXAMPLE 2.5 a. Determine the capacity in milliampere-hours and life in minutes for the 0.9-V BH 500 cell of Fig. 2.18(a) if the discharge current is 600 mA. b. At what temperature will the mAh rating of the cell of Fig. 2.18(b) be 90% of its maximum value if the discharge current is 50 mA?
Solutions: a. From Fig. 2.18(a), the capacity at 600 mA is about 450 mAh. Thus, from Eq. (2.9),
Life 0.75 h 45 min
b. From Fig. 2.18(b), the maximum is approximately 520 mAh. The 90% level is therefore 468 mAh, which occurs just above freezing, or 1°C, and at the higher temperature of 45°C.
Generators The dc generator is quite different, both in construction (Fig. 2.20) and in mode of operation, from the battery. When the shaft of the generator is rotating at the nameplate speed due to the applied torque of some external source of mechanical power, a voltage of rated value will appear across the external terminals. The terminal voltage and power-handling capabilities of the dc generator are typically higher than those of most batteries, and its lifetime is determined only by its construction. Commercially used dc generators are typically of the 120-V or 240-V variety. As pointed out earlier in this section, for the purposes of this text, no distinction will be made between the symbols for a battery and a generator.
Power Supplies The dc supply encountered most frequently in the laboratory employs the rectification and filtering processes as its means toward obtaining a steady dc voltage. Both processes will be covered in detail in your basic electronics courses. In total, a time-varying voltage (such as ac voltage available from a home outlet) is converted to one of a fixed magnitude.A dc laboratory supply of this type appears in Fig. 2.21. Most dc laboratory supplies have a regulated, adjustable voltage output with three available terminals, as indicated in Figs. 2.21 and 2.22(a). The symbol for ground or zero potential (the reference) is also shown in Fig. 2.22(a). If 10 V above ground potential are required, then the connections are made as shown in Fig. 2.22(b). If 15 V below ground potential are required, then the connections are made as shown in Fig. 2.22(c). If connections are as shown in Fig. 2.22(d), we say we have a “floating” voltage of 5 V since the reference level is not included. Seldom is the configuration of Fig. 2.22(d) employed since it fails to protect the operator by providing a direct low-resistance path to ground and to establish a common ground for the system. In any case, the positive and negative terminals must be part of any circuit configuration.
dc Current Sources
The wide variety of types of, and applications for, the dc voltage source has resulted in its becoming a rather familiar device, the characteristics of which are understood, at least basically, by the layperson. For example, it is common knowledge that a 12-V car battery has a terminal volt
450 mAh 600 mA
FIXED (dc) SUPPLIES  45
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120 V + –
Applied torque
“Input”
“Output” voltage
FIG. 2.20 dc generator.
FIG. 2.21 dc laboratory supply. (Courtesy of Leader Instruments Corporation.)
age (at least approximately) of 12 V, even though the current drain by the automobile may vary under different operating conditions. In other words, a dc voltage source will provide ideally a fixed terminal voltage, even though the current demand from the electrical/electronic system may vary, as depicted in Fig. 2.23(a). A dc current source is the dual of the voltage source; that is,
the current source will supply, ideally, a fixed current to an electrical/electronic system, even though there may be variations in the terminal voltage as determined by the system,
as depicted in Fig. 2.23(b). Do not become alarmed if the concept of a current source is strange and somewhat confusing at this point. It will be covered in great detail in later chapters. Also, additional exposure will be provided in basic electronics courses.
2.5 CONDUCTORS AND INSULATORS
Different wires placed across the same two battery terminals will allow different amounts of charge to flow between the terminals. Many factors, such as the density, mobility, and stability characteristics of a material, account for these variations in charge flow. In general, however,
conductors are those materials that permit a generous flow of electrons with very little external force (voltage) applied.
In addition,
good conductors typically have only one electron in the valence (most distant from the nucleus) ring.
Since copper is used most frequently, it serves as the standard of comparison for the relative conductivity in Table 2.1. Note that aluminum, which has seen some commercial use, has only 61% of the conductivity level of copper, but keep in mind that this must be weighed against the cost and weight factors.
Insulators are those materials that have very few free electrons and require a large applied potential (voltage) to establish a measurable current level.
46  CURRENT AND VOLTAGE
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Voltage 12 V
0
Current 10 mA
(a)
I or t
V or t0 (b)
Increasing current or time
Increasing voltage or time
FIG. 2.23 Terminal characteristics: (a) ideal voltage source; (b) ideal current source.
+
–
15 V
Jumper – (– 15 V)
15 V
+
5 V
–
+
(“Floating”)
5 V
–
+
(c) (d)
+
–
(a)
Gnd (0 V)
(b)
–
+
Jumper
10 V
–
+ (+ 10 V)10 V
FIG. 2.22 dc laboratory supply: (a) available terminals; (b) positive voltage with respect to (w.r.t.) ground; (c) negative voltage w.r.t. ground; (d) floating supply.
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A common use of insulating material is for covering current-carrying wire, which, if uninsulated, could cause dangerous side effects. Powerline repair people wear rubber gloves and stand on rubber mats as safety measures when working on high-voltage transmission lines. A number of different types of insulators and their applications appear in Fig. 2.24.
CONDUCTORS AND INSULATORS  47
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TABLE 2.1 Relative conductivity of various materials.
Metal Relative Conductivity (%)
Silver 105 Copper 100 Gold 70.5 Aluminum 61 Tungsten 31.2 Nickel 22.1 Iron 14 Constantan 3.52 Nichrome 1.73 Calorite 1.44
It must be pointed out, however, that even the best insulator will break down (permit charge to flow through it) if a sufficiently large potential is applied across it. The breakdown strengths of some common insulators are listed in Table 2.2. According to this table, for insu
(a) (b) (c)
FIG. 2.24 Insulators: (a) insulated thru-panel bushings; (b) antenna strain insulators; (c) porcelain stand-off insulators. (Courtesy of Herman H. Smith, Inc.)
TABLE 2.2 Breakdown strength of some common insulators.
Average Breakdown Material Strength (kV/cm)
Air 30 Porcelain 70 Oils 140 Bakelite 150 Rubber 270 Paper (paraffin-coated) 500 Teflon 600 Glass 900 Mica 2000
lators with the same geometric shape, it would require 270/30 9 times as much potential to pass current through rubber compared to air and approximately 67 times as much voltage to pass current through mica as through air.
2.6 SEMICONDUCTORS
Semiconductors are a specific group of elements that exhibit characteristics between those of insulators and conductors.
The prefix semi, included in the terminology, has the dictionary definition of half, partial, or between, as defined by its use. The entire electronics industry is dependent on this class of materials since electronic devices and integrated circuits (ICs) are constructed of semiconductor materials. Although silicon (Si) is the most extensively employed material, germanium (Ge) and gallium arsenide (GaAs) are also used in many important devices.
Semiconductor materials typically have four electrons in the outermost valence ring.
Semiconductors are further characterized as being photoconductive and having a negative temperature coefficient. Photoconductivity is a phenomenon where the photons (small packages of energy) from incident light can increase the carrier density in the material and thereby the charge flow level. A negative temperature coefficient reveals that the resistance (a characteristic to be described in detail in the next chapter) will decrease with an increase in temperature (opposite to that of most conductors). A great deal more will be said about semiconductors in the chapters to follow and in your basic electronics courses.
2.7 AMMETERS AND VOLTMETERS
It is important to be able to measure the current and voltage levels of an operating electrical system to check its operation, isolate malfunctions, and investigate effects impossible to predict on paper. As the names imply, ammeters are used to measure current levels, and voltmeters, the potential difference between two points. If the current levels are usually of the order of milliamperes, the instrument will typically be referred to as a milliammeter, and if the current levels are in the microampere range, as a microammeter. Similar statements can be made for voltage levels. Throughout the industry, voltage levels are measured more frequently than current levels, primarily because measurement of the former does not require that the network connections be disturbed. The potential difference between two points can be measured by simply connecting the leads of the meter across the two points, as indicated in Fig. 2.25. An up-scale reading is obtained by placing the positive lead of the meter to the point of higher potential of the network and the common or negative lead to the point of lower potential. The reverse connection will result in a negative reading or a below-zero indication. Ammeters are connected as shown in Fig. 2.26. Since ammeters measure the rate of flow of charge, the meter must be placed in the network such that the charge will flow through the meter. The only way this can
48  CURRENT AND VOLTAGE
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I
+
–
E
DMM voltmeter mode
FIG. 2.25 Voltmeter connection for an up-scale ( ) reading.
+ –
+
–
E
DMM ammeter mode
I
System
FIG. 2.26 Ammeter connection for an up-scale ( ) reading.
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be accomplished is to open the path in which the current is to be measured and place the meter between the two resulting terminals. For the configuration of Fig. 2.26, the voltage source lead ( )must be disconnected from the system and the ammeter inserted as shown. An up-scale reading will be obtained if the polarities on the terminals of the ammeter are such that the current of the system enters the positive terminal. The introduction of any meter into an electrical/electronic system raises a concern about whether the meter will affect the behavior of the system. This question and others will be examined in Chapters 5 and 6 after additional terms and concepts have been introduced. For the moment, let it be said that since voltmeters and ammeters do not have internal sources, they will affect the network when introduced for measurement purposes. The design of each, however, is such that the impact is minimized. There are instruments designed to measure just current or just voltage levels. However, the most common laboratory meters include the volt-ohm-milliammeter (VOM) and the digital multimeter (DMM) of Figs. 2.27 and 2.28, respectively. Both instruments will measure voltage and current and a third quantity, resistance, to be introduced in the next chapter. The VOM uses an analog scale, which requires interpreting the position of a pointer on a continuous scale, while the DMM provides a display of numbers with decimal point accuracy determined by the chosen scale. Comments on the characteristics and use of various meters will be made throughout the text. However, the major study of meters will be left for the laboratory sessions.
AMMETERS AND VOLTMETERS  49
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FIG. 2.27 Volt-ohm-milliammeter (VOM) analog meter. (Courtesy of Simpson Electric Co.)
FIG. 2.28 Digital multimeter (DMM). (Courtesy of John Fluke Mfg. Co. Inc.)
2.8 APPLICATIONS
Throughout the text, Applications sections such as this one have been included to permit a further investigation of terms, quantities, or systems introduced in the chapter. The primary purpose of these Applications is to establish a link between the theoretical concepts of the text and the real, practical world. Although the majority of components that appear in a system may not have been introduced (and, in fact, some components will not be examined until more advanced studies), the topics were chosen very carefully and should be quite interesting to a new student of the subject matter. Sufficient comment is included to provide a surface understanding of the role of each part of the system, with the understanding that the details will come at a later date. Since exercises on the subject matter of the Applications do not appear at the end of the chapter, the content is designed not to challenge the student but rather to stimulate his or her interest and answer some basic questions such as how the system looks inside, what role specific elements play in the system, and, of course, how the system works. In essence, therefore, each Applications section provides an opportunity to begin to establish a practical background beyond simply the content of the chapter. Do not be concerned if you do not understand every detail of each application. Understanding will come with time and experience. For now, take what you can from the examples and then proceed with the material.
Flashlight
Although the flashlight employs one of the simplest of electrical circuits, a few fundamentals about its operation do carry over to more sophisticated systems. First, and quite obviously, it is a dc system with a lifetime totally dependent on the state of the batteries and bulb. Unless it is the rechargeable type, each time you use it, you take some of the life out of it. For many hours the brightness will not diminish noticeably. Then, however, as it reaches the end of its ampere-hour capacity, the light will become dimmer at an increasingly rapid rate (almost exponentially). For the standard two-battery flashlight appearing in Fig. 2.29(a) with its electrical schematic in Fig. 2.29(b), each 1.5-V battery has an ampere-hour rating of about 16 as supported by Fig. 2.12. The single-contact miniature flange-base bulb is rated at 2.5 V and 300 mA with good brightness and a lifetime of about 30 hours. Thirty hours may not seem like a long lifetime, but you have to consider how long you usually use a flashlight on each occasion. If we assume a 300-mA drain from the battery for the bulb when in use, the lifetime of the battery, by Eq. (2.9), is about 53 hours. Comparing the 53-hour lifetime of the battery to the 30-hour life expectancy of the bulb suggests that we normally have to replace bulbs more frequently than batteries. However, most of us have experienced the opposite effect: We can change batteries two or three times before we need to replace the bulb. This is simply one example of the fact that one cannot be guided solely by the specifications of each component of an electrical design. The operating conditions, terminal characteristics, and details about the actual response of the system for short and long periods of time must be taken into account. As mentioned earlier, the battery loses some of its power each time it is used. Although the terminal voltage may not change much at first, its ability to provide the same level of current will
50  CURRENT AND VOLTAGE
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drop with each usage. Further, batteries will slowly discharge due to “leakage currents” even if the switch is not on. The air surrounding the battery is “not clean” in the sense that moisture and other elements in the air can provide a conduction path for leakage currents through the air, through the surface of the battery itself, or through other nearby surfaces, and the battery will eventually discharge. How often have we left a flashlight with new batteries in a car for a long period of time only to find the light very dim or the batteries dead when we need the flashlight the most? An additional problem is acid leaks that appear as brown stains or corrosion on the casing of the battery. These leaks will also affect the life of the battery. Further, when the flashlight is turned on, there is an initial surge in current that will drain the battery more than continuous use for a period of time. In other words, continually turning the flashlight on and off will have a very detrimental effect on its life. We must also realize that the 30-hour rating of the bulb is for continuous use, that is, 300 mA flowing through the bulb for a continuous 30 hours. Certainly, the filament in the bulb and the bulb itself will get hotter with time, and this heat has a detrimental effect on the filament wire. When the flashlight is turned on and off, it gives the bulb a chance to cool down and regain its normal characteristics, thereby avoiding any real damage. Therefore, with normal use we can expect the bulb to last longer than the 30 hours specified for continuous use. Even though the bulb is rated for 2.5-V operation, it would appear that the two batteries would result in an applied voltage of 3 V which suggests poor operating conditions. However, a bulb rated at 2.5 V can easily handle 2.5 V to 3 V. In addition, as was pointed out in this chapter, the terminal voltage will drop with the current demand and usage. Under normal operating conditions, a 1.5-V battery is considered to be in good condition if the loaded terminal voltage is 1.3 V to 1.5 V. When it drops to 1 V to 1.1 V, it is weak, and when it drops to 0.8 V to 0.9 V, it has lost its effectiveness. The levels can be related directly to the test band now appearing on Duracell® batteries, such as on the one shown
APPLICATIONS  51
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FIG. 2.29 (a) Eveready® D cell flashlight; (b) electrical schematic of flashlight of part (a); (c) Duracell® Powercheck™ D cell battery.
(b)
3 V
+
–
Bulb
Switch
Ibulb
Bulb
Reflector
Metal support
1.5-V D battery
1.5-V D battery
Spring
Sliding switch
Contact
+
–
1.5 V
+
–
1.5 V
(a)
(c)
in Fig. 2.29(c). In the test band on this battery, the upper voltage area (green on the actual battery) is near 1.5 V (labeled 100%); the lighter area to the right, from about 1.3 V down to 1 V; and the replace area (red) on the far right, below 1 V. Be aware that the total supplied voltage of 3 V will be obtained only if the batteries are connected as shown in Fig. 2.29(b). Accidentally placing the two positive terminals together will result in a total voltage of 0 V, and the bulb will not light at all. Forthe vast majority of systems with more than one battery, the positive terminal of one battery will always be connected to the negative terminal of another. For all low-voltage batteries, the end with the nipple is the positive terminal, and the end with the flat end is the negative terminal. In addition, the flat or negative end of a battery is always connected to the battery casing with the helical coil to keep the batteries in place. The positive end of the battery is always connected to a flat spring connection or the element to be operated. If you look carefully at the bulb, you will find that the nipple connected to the positive end of the battery is insulated from the jacket around the base of the bulb. The jacket is the second terminal of the battery used to complete the circuit through the on/off switch. If a flashlight fails to operate properly, the first thing to check is the state of the batteries. It is best to replace both batteries at once. A system with one good battery and one nearing the end of its life will result in pressure on the good battery to supply the current demand, and, in fact, the bad battery will actually be a drain on the good battery. Next check the condition of the bulb by checking the filament to see whether it has opened at some point because a long-term, continuous current level occurred or because the flashlight was dropped. If the battery and bulb seem to be in good shape, the next area of concern is the contacts between the positive terminal and the bulb and the switch. Cleaning both with emery cloth will often eliminate this problem.
12-V Car Battery Charger
Battery chargers are a common household piece of equpiment used to charge everything from small flashlight batteries to heavy-duty, marine, lead-acid batteries. Since all are plugged into a 120-V ac outlet such as found in the home, the basic construction of each is quite similar. In every charging system a transformer (Chapter 21) must be included to cut the ac voltage to a level appropriate for the dc level to be established. A diode (also called rectifier) arrangement must be included to convert the ac voltage which varies with time to a fixed dc level such as described in this chapter. Diodes and/or rectifiers will be discussed in detail in your first electronics course. Some dc chargers will also include a regulator to provide an improved dc level (one that varies less with time or load). Since the car battery charger is one of the most common, it will be described in the next few paragraphs. The outside appearance and the internal construction of a Sears 6/2 AMP Manual Battery Charger are provided in Fig. 2.30. Note in Fig. 2.30(b) that the transformer (as in most chargers) takes up most of the internal space. The additional air space and the holes in the casing are there to ensure an outlet for the heat that will develop due to the resulting current levels.
52  CURRENT AND VOLTAGE
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The schematic of Fig. 2.31 includes all the basic components of the charger. Note first that the 120 V from the outlet are applied directly across the primary of the transformer. The charging rate of 6 A or 2 A is determined by the switch, which simply controls how many windings of the primary will be in the circuit for the chosen charging rate. If the battery is charging at the 2-A level, the full primary will be in the circuit, and the ratio of the turns in the primary to the turns in the sec
APPLICATIONS  53
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FIG. 2.30 Battery charger: (a) external appearance; (b) internal construction.
(a)
(b)
Control switch
Grounded to chassis
Circuit breaker
Meter leads
Heat sink
Rectifier (diode) configuration
Transformer
ondary will be a maximum. If it is charging at the 6-A level, fewer turns of the primary are in the circuit, and the ratio drops. When you study transformers, you will find that the voltage at the primary and secondary is directly related to the turns ratio. If the ratio from primary to secondary drops, then the voltage drops also. The reverse effect occurs if the turns on the secondary exceed those on the primary. The general appearance of the waveforms appears in Fig. 2.31 for the 6-A charging level. Note that so far, the ac voltage has the same wave shape across the primary and secondary. The only difference is in the peak value of the waveforms. Now the diodes take over and convert the ac waveform which has zero average value (the waveform above equals the waveform below) to one that has an average value (all above the axis) as shown in the same figure. For the moment simply recognize that diodes are semiconductor electronic devices that permit only conventional current to flow through them in the direction indicated by the arrow in the symbol. Even though the waveform resulting from the diode action has a pulsing appearance with a peak value of about 18 V, it will charge the 12-V battery whenever its voltage is greater than that of the battery, as shown by the shaded area. Below the 12-V level the battery cannot discharge back into the charging network because the diodes permit current flow in only one direction. In particular, note in Fig. 2.30(b) the large plate that carries the current from the rectifier (diode) configuration to the positive terminal of the battery. Its primary purpose is to provide a heat sink (a place for the heat to be distributed to the surrounding air) for the diode configuration. Otherwise the diodes would eventually melt down and self-destruct due to the resulting current levels. Each component of Fig 2.31 has been carefully labeled in Fig. 2.30(b) for reference. When current is first applied to a battery at the 6-A charge rate, the current demand as indicated by the meter on the face of the instrument may rise to 7 A or almost 8 A. However, the level of current will decrease as the battery charges until it drops to a level of 2 A or 3 A. For units such as this that do not have an automatic shutoff, it is impor
54  CURRENT AND VOLTAGE
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FIG. 2.31 Electrical schematic for the battery charger of Fig. 2.30.
120 V ac 2 A
6 A
Transformer (step-down)
13 V +
Diodes (rectifiers)
Circuit breaker
Current meter
Negative clamp of charger
Positive clamp of charger
Peak = 18 V
12 V
–
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tant to disconnect the charger when the current drops to the fully charged level; otherwise, the battery will become overcharged and may be damaged. A battery that is at its 50% level can take as long as 10 hours to charge, so don’t expect it to be a 10-minute operation. In addition, if a battery is in very bad shape with a lower than normal voltage, the initial charging current may be too high for the design. To protect against such situations, the circuit breaker will open and stop the charging process. Because of the high current levels, it is important that the directions provided with the charger be carefully read and applied.
Answering Machines/Phones dc Supply
A wide variety of systems in the home and office receive their dc operating voltage from an ac/dc conversion system plugged right into a 120-V ac outlet. Lap-top computers, answering machines/phones, radios, clocks, cellular phones, CD players, and so on, all receive their dc power from a packaged system such as appearing in Fig. 2.32. The conversion from ac to dc occurs within the unit which is plugged directly into the outlet. The dc voltage is available at the end of the long wire which is designed to be plugged into the operating unt. As small as the unit may be, it contains basically the same components as appearing in the battery charger of Fig. 2.30.
APPLICATIONS  55
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FIG. 2.33 Internal construction of the 9-V dc supply of Fig. 2.32.
FIG. 2.32 Answering machine/phone 9-V dc supply.
Transformer
Capacitor
Diodes (2)
120-V ac plug
9-V dc output
In Fig. 2.33 you can see the transformer used to cut the voltage down to appropriate levels (again the largest component of the system). Note that two diodes establish a dc level, and a capacitive filter (Chapter 10) is added to smooth out the dc as shown. The system can be relatively small because the operating current levels are quite small, permitting the use of thin wires to construct the transformer and limit its size. The lower currents also reduce the concerns about heating effects, permitting a small housing structure. The unit of Fig. 2.33, rated at 9 V at200 mA, is commonly used to provide power to answering machines/phones. Further smoothing of the dc voltage will be accomplished by a regulator built into the receiving unit. The regulator is normally a small IC chip placed in the receiving unit to separate the heat that it generates from the heat generated by the transformer, thereby reducing the net heat at the outlet close to the wall. In addition, its placement in the receiving unit will reduce the possibility of picking up noise and oscillations along the long wire from the conversion unit to the operating unit, and it will ensure that the full rated voltage is available at the unit itself, not a lesser value due to losses along the line.
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V56  CURRENT AND VOLTAGE
9. If 465 C of charge pass through a wire in 2.5 min, find the current in amperes.
10. If a current of 40 A exists for 1 min, how many coulombs of charge have passed through the wire?
11. How many coulombs of charge pass through a lamp in 2 min if the current is constant at 750 mA?
12. If the current in a conductor is constant at 2 mA, how much time is required for 4600 10 6 C to pass through the conductor? 13. If 21.847 10 18 electrons pass through a wire in 7 s, find the current.
14. How many electrons pass through a conductor in 1 min if the current is 1 A?
15. Will a fuse rated at 1 A “blow” if 86 C pass through it in 1.2 min? *16. If 0.784 10 18 electrons pass through a wire in 643 ms, find the current.
*17. Which would you prefer? a. A penny for every electron that passes through a wire in 0.01 ms at a current of 2mA, or b. A dollar for every electron that passes through a wire in 1.5 ns if the current is 100 mA.
SECTION 2.3 Voltage
18. What is the voltage between two points if 96 mJ of energy are required to move 50 1018 electrons between the two points?
19. If the potential difference between two points is 42 V, how much work is required to bring 6 C from one point to the other?
20. Find the charge Q that requires 96 J of energy to be moved through a potential difference of 16 V.
21. How much charge passes through a battery of 22.5 V if the energy expended is 90 J?
22. If a conductor with a current of 200 mA passing through it converts 40 J of electrical energy into heat in 30 s, what is the potential drop across the conductor?
*23. Charge is flowing through a conductor at the rate of 420 C/min. If 742 J of electrical energy are converted to heat in 30 s, what is the potential drop across the conductor?
*24. The potential difference between two points in an electric circuit is 24 V. If 0.4 J of energy were dissipated in a period of 5 ms, what would the current be between the two points?
SECTION 2.4 Fixed (dc) Supplies
25. What current will a battery with an Ah rating of 200 theoretically provide for 40 h?
26. What is the Ah rating of a battery that can provide 0.8 A for 76 h?
27. For how many hours will a battery with an Ah rating of 32 theoretically provide a current of 1.28 A?
PROBLEMS
SECTION 2.1 Atoms and Their Structure
1. The numbers of orbiting electrons in aluminum and silver are 13 and 47, respectively. Draw the electronic configuration, including all the shells and subshells, and discuss briefly why each is a good conductor.
2. Find the force of attraction between a proton and an electron separated by a distance equal to the radius of the smallest orbit followed by an electron (5 10 11 m) in a hydrogen atom.
3. Find the force of attraction in newtons between the charges Q1 and Q2 in Fig. 2.34 when a. r 1 m b. r 3 m c. r 10 m (Note how quickly the force drops with an increase in r.)
FIG. 2.34 Problem 3.
*4. Find the force of repulsion in newtons between Q1 and Q2 in Fig. 2.35 when a. r 1 mi b. r 0.01 m c. r 1/16 in.
FIG. 2.35 Problem 4.
*5. Plot the force of attraction (in newtons) versus separation (in meters) for two charges of 2 mC and 4 mC. Set r to 0.5 m and 1 m, followed by 1-m intervals to 10 m. Comment on the shape of the curve. Is it linear or nonlinear? What does it tell you about the force of attraction between charges as they are separated? What does it tell you about any function plotted against a squared term in the denominator? 6. Determine the distance between two charges of 20 mC if the force between the two charges is 3.6 104 N. *7. Two charged bodies, Q1 and Q2, when separated by a distance of 2 m, experience a force of repulsion equal to 1.8 N. a. What will the force of repulsion be when they are 10 m apart? b. If the ratio Q1/Q2 1/2, find Q1 and Q2 (r 10 m).
SECTION 2.2 Current
8. Find the current in amperes if 650 C of charge pass through a wire in 50 s.
Q1 r Q2
8   C
40   C ++
Q1 r Q2
–
1   C
2   C
+
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28. Find the mAh rating of the Eveready® BH 500 battery at 100°F and 0°C at a discharge current of 50 mA using Fig. 2.18(b). 29. Find the mAh rating of the 1.0-V Eveready® BH 500 battery if the current drain is 550 mA using Fig. 2.18(a). How long will it supply this current?
30. For how long can 50 mA be drawn from the battery of Fig. 2.19 before its terminal voltage drops below 1 V? Determine the number of hours at a drain current of 150 mA, and compare the ratio of drain current to the resulting ratio of hours of availability.
31. A standard 12-V car battery has an ampere-hour rating of 40 Ah, whereas a heavy-duty battery has a rating of 60 Ah. How would you compare the energy levels of each and the available current for starting purposes?
*32. Using the relevant equations of the past few sections, determine the available energy (in joules) from the Eveready battery of Fig. 2.15(b).
*33. A portable television using a 12-V, 3-Ah rechargeable battery can operate for a period of about 5.5 h. What is the average current drawn during this period? What is the energy expended by the battery in joules?
34. Discuss briefly the difference among the three types of dc voltage supplies (batteries, rectification, and generators).
35. Compare the characteristics of a dc current source with those of a dc voltage source. How are they similar and how are they different?
SECTION 2.5 Conductors and Insulators
36. Discuss two properties of the atomic structure of copper that make it a good conductor.
37. Name two materials not listed in Table 2.1 that are good conductors of electricity.
38. Explain the terms insulator and breakdown strength.
39. List three uses of insulators not mentioned in Section 2.5.
SECTION 2.6 Semiconductors
40. What is a semiconductor? How does it compare with a conductor and an insulator?
41. Consult a semiconductor electronics text and note the extensive use of germanium and silicon semiconductor materials. Review the characteristics of each material.
SECTION 2.7 Ammeters and Voltmeters
42. What are the significant differences in the way ammeters and voltmeters are connected?
43. If an ammeter reads 2.5 A for a period of 4 min, determine the charge that has passed through the meter.
44. Between two points in an electric circuit, a voltmeter reads 12.5 V for a period of 20 s. If the current measured by an ammeter is 10 mA, determine the energy expended and the charge that flowed between the two points.
GLOSSARY
Ammeter An instrument designed to read the current through elements in series with the meter. Ampere (A) The SI unit of measurement applied to the flow of charge through a conductor. Ampere-hour rating (Ah) The rating applied to a source of energy that will reveal how long a particular level of current can be drawn from that source. Cell A fundamental source of electrical energy developed through the conversion of chemical or solar energy. Conductors Materials that permit a generous flow of electrons with very little voltage applied. Copper A material possessing physical properties that make it particularly useful as a conductor of electricity. Coulomb (C) The fundamental SI unit of measure for charge. It is equal to the charge carried by 6.242 1018 electrons. Coulomb’s law An equation defining the force of attraction or repulsion between two charges. dc current source A source that will provide a fixed current level even though the load to which it is applied may cause its terminal voltage to change. dc generator A source of dc voltage available through the turning of the shaft of the device by some external means. Direct current Current having a single direction (unidirectional) and a fixed magnitude over time.
Electrolytes The contact element and the source of ions between the electrodes of the battery. Electron The particle with negative polarity that orbits the nucleus of an atom. Free electron An electron unassociated with any particular atom, relatively free to move through a crystal lattice structure under the influence of external forces. Insulators Materials in which a very high voltage must be applied to produce any measurable current flow. Neutron The particle having no electrical charge, found in the nucleus of the atom. Nucleus The structural center of an atom that contains both protons and neutrons. Positive ion An atom having a net positive charge due to the loss of one of its negatively charged electrons. Potential difference The algebraic difference in potential (or voltage) between two points in an electrical system. Potential energy The energy that a mass possesses by virtue of its position. Primary cell Sources of voltage that cannot be recharged. Proton The particle of positive polarity found in the nucleus of an atom. Rectification The process by which an ac signal is converted to one that has an average dc level. Secondary cell Sources of voltage that can be recharged.
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Semiconductor A material having a conductance value between that of an insulator and that of a conductor. Of significant importance in the manufacture of semiconductor electronic devices. Solar cell Sources of voltage available through the conversion of light energy (photons) into electrical energy. Specific gravity The ratio of the weight of a given volume of a substance to the weight of an equal volume of water at 4°C.
Volt (V) The unit of measurement applied to the difference in potential between two points. If one joule of energy is required to move one coulomb of charge between two points, the difference in potential is said to be one volt. Voltmeter An instrument designed to read the voltage across an element or between any two points in a network.