Resistive Device
- (Lamp) Conductor - + EMF FIGURE 8-16. A practical circuit.
current-limiting resistance in the circuit, it is also accomplishing the desired funtion of creating Figure 8-17 is a schematic representation of figure 8-16, in which symbols rather than pictures are used to represent the circuit components.
All components used in electrical circuits are represented in drawings, blueprints, and illustrations in schematic form by symbols. The components commonly used in basic circuits, together with their schematic symbols, are discussed to provide the necessary background for interpretation of circuit diagrams.
Source of Power The source of power, or applied voltage, for a circuit may be any one of the common sources of e.m.f, such as a mechanical source (generator), a chemical source (battery), a photoelectric source (light), or a thermal source (heat). Figure 8-18 illustrates two schematic symbols for a generator.
Most electrical components have only one symbol; however, in the case of the generator and a few others, more than one symbol has been developed to represent a single electrical component. These symbols are normally very similar
- Lamp Conductor OR FIGURE 8-18. Electrical symbols for a d.c.
generator.
in design. Figure 8-18 illustrates that the two symbols for a generator are so nearly alike there is little chance for confusion.
Another common source for the voltage applied to a circuit is the battery, a chemical source of power. Figure 8-19 shows symbols for a singlecell battery and a three-cell battery.
The following statements are true of battery symbols used in schematic diagrams (refer to figure 8-19):
Q) The shorter vertical line represents the negative terminal.
(2) The longer vertical line is the positive terminal.
(3) The horizontal lines represent the conductors connected to the terminals.
(4) Each cell of a battery has one negative and one positive terminal.
Dry cell batteries, such as those used to operate flashlights, are called primary cells. The larger storage batteries containing several primary cells are called secondary cells. The schematic symbol for the primary cell is shown in figure 8-20. The center rod is the positive terminal of the cell, and the case of the cell is the negative terminal.
When more than 1.5 volts are required, cells are connected in series. To connect the cells in series, the negative terminal of each cell is connected to the positive terminal of the succeeding cell as shown in A of figure 8-21. The voltage is then equal to the sum of the voltages of the individual cells. Since the same current must flow through each cell in succession, the current that the battery can supply is equal to the current rating of a single cell. Thus, a battery composed of cells in series provides a higher voltage, but not a greater current capacity.
Battery FIGURE 8-17. Circuit components represented FIGURE 8-19. One-cell and three-cell battery by symbols. symbols.
FIGURE 8-20. Schematic symbol for a dry cell battery.
To obtain a greater current flow than one cell is able to supply, the cells are connected in parallel.
The total current available is equal to the sum of the individual currents from each cell, but the voltage is equal to the voltage of a single cell. To connect cells in parallel, all positive terminals are connected together and all negative terminals are connected together. In A of figure 8-22, a schematic diagram of cells connected in parallel is shown.
B of figure 8-22 illustrates the symbol used to represent this group of cells connected in parallel.
Each cell must have the same voltage; otherwise, a cell with higher voltage will force current through the lower voltage cells.
Another method of arranging cells is to connect them in series-parallel. In this method, shown in figure 8-23, two groups of cells are connected in series, and then these two groups are connected in parallel. This arrangement provides both a greater voltage and a greater current output.
Conductor Another basic requirement of a circuit is the conductor or wire connecting the various electrical components. This is always represented in schematic diagrams as a line. Figure 8-24 illustrates | 1:5V
1.5V 6V
1.5V
1.5V
1.5V
1.5V
1.5V
1.5V FIGURE 8-22. Cells connected in parallel.
two different symbols used to indicate wires (conductors) that cross but are not connected.
While either of these symbols may be used, the symbol shown in B of figure 8-24 is now found more often, since it is less likely to be misinterpreted.
Figure 8-25 illustrates the two different symbols used to represent connected wires. Either of these two symbols may be used, but it is important that no conflict exists with the symbol selected to represent unconnected wires. For example, if the symbol for unconnected wires shown in A of figure 8-24 is selected, the symbol for connected wires must be that shown in A of figure
8-25.
A circuit component found in all practical circuits is the fuse. This is a safety or protective device used to prevent damage to the conductors and circuit components by excessive current flow.
1.5V 1.5V Symbol
1.5V 1.5V
1.51 1.5V 6V
1.5V FIGURE 8-21. Schematic diagram and symbol of FIGURE 8-23. Cells in series-parallel cells connected in series. arrangement.
FIGURE 8-24. Unconnected crossed-over wires.
The schematic symbol for a fuse is shown in figure 8-26.
Another symbol found in basic circuit schematics is the symbol for the switch, shown in figure 8-27. The open switch symbol is shown in A of figure 8-27, and in B of figure 8-27 the closed switch symbol is shown connected in a circuit. There are many different types of switches, but these symbols can represent all but the most complex.
Figure 8-28 illustrates the symbol for "ground" or thè common reference point in a circuit. This is the reference point from which most circuit B FIGURE 8-25. Connected wires.
voltages are measured. This point is normally considered to be at zero potential.
Sometimes meters for measuring current flow or voltage are temporarily connected to the circuit, and in some circuits these meters are permanent components. In figure 8-29, the symbols for an ammeter and a voltmeter are used in a simple circuit. It is important that these components be connected properly. The ammeter, which measures current flow, is always connected in series with the power source and circuit resistances. The voltmeter, which measures the voltage across a circuit component, is always FIGURE 8-27. Open and closed switch symbols.
connected across (in parallel with) a circuit component, never in a series arrangement.
Resistors The last of the basic component requirements of a complete circuit can be grouped under the FIGURE 8-28. Ground or common reference point symbol.
single heading of resistance. Resistance in a practical circuit may take the form of any electrical device, such as a motor or a lamp, which uses electrical power and produces some useful function. On the other hand, the resistance of a circuit may be in the form of resistors inserted in the circuit to limit current flow.
FIGURE 8-26. Schematic symbol for a fuse. FIGURE 8-29. Ammeter and voltmeter symbols.
Resístor Terminal Mounting Bracket FIGURE 8-30. Fixed wire-wound resistors.
A wide variety of resistors are available. Some have a fixed ohmic value and others are variable.
They are manufactured from special resistance wire, graphite (carbon), or metal film. Wirewound resistors control large currents, while carbon resistors control relatively small currents.
Wire-wound resistors are constructed by winding resistance wire on a porcelain base, attaching the wire ends to metal terminals, and coating the wire for protection and heat conduction. (See figure 8-30.
Wire-wound resistors are available with fixed taps which can be used to change the resistance value in increments or steps. They may also be provided with sliders which can be adjusted to change the resistance to any fraction of the total resistance. (See figure 8-31.) Still another type is the precision wire-wound resistors (figure 8-32) made of manganin wire. They are used where the resistance value must be very accurate.
Carbon resistors are manufactured from a rod of compressed graphite and binding material, with wire leads, called "pigtail" leads, attached to each end of the resistor. (See figure 8-33.)
Adjustable tap 7 Fixed taps.
FIGURE 8-32. Precision wire-wound resistors.
Variable resistors are used to vary the resistance while the equipment is in operation. Wire-wound variable resistors control large currents, and carbon variable resistors control small currents.
Wire-wound variable resistors are constructed by winding resistance wire on a porcelain or bakelite circular form. A contact arm which can be adjusted to any position on the circular form by means of a rotating shaft is used to select resistance settings. (See figure 8-34.)
Carbon variable resistors (see figure 8-35), used to control small currents, are constructed of a carbon compound deposited on a fiber disk. A contact on a movable arm varies the resistance as the arm shaft is turned.
The two symbols used on a schematic or circuit diagram to represent variable resistors are shown in figure 8-36.
The schematic symbol for a fixed resistor is shown in A of figure 8-37. A variation of this Pigtail lead.
FIGURE 8-31. Wire-wound resistors with fixed and adjustable taps. FIGURE 8-33. Carbon resistors.
—Cover Variable contact Resistance element terminal End terminals
- Rotating shaft Variable slider contact FIGURE 8-34. Wire-wound Variable resistor.
symbol represents the tapped resistor, which has a fixed value but is provided with taps from which selected amounts of resistance can be obtained. (See B of figure 8-37.)
Resistor Color Code The resistance value of any resistor can be measured by using an ohmmeter. But this is seldom necessary. Most wire-wound resistors have their resistance value in ohms printed on the body of the resistor. Many carbon resistors are similarly marked, but are often mounted in such a manner that it is difficult or impossible to read the resistance value. Additionally, heat often discolors the resistor body, making the printed marking illegible, and many carbon resistors are so small that a printed marking cannot be used.
Thus, a color code marking is used to identify the resistance value of carbon resistors.
There is only one color code for carbon resistors, but there are two systems or methods used to paint this color code on resistors. One is the bodyend-dot system, and the other is the end-to-center band system.
In each color code system, three colors are used to indicate the resistance value in ohms, and a tourth color is sometimes used to indicate the tolerance of the resistor. By reading the colors in the correct order and by substituting numbers from the color code, the resistance value of a resistor can be determined.
Cover End terminals Variable slider contact
- Resistance Variable contact element terminal
- Rotating shaft FIGURE 8-35. Carbon variable resistor.
Resistor color code Color Number Tolerance Black Brown 1% Red 2% Orange 3% FIGURE 8-36. Symbols for variable resistors. Yelow Green 4 5 4% 5% Blue 6% Violet 7 7% It is very difficult to manufacture a resistor to Gray 8% an exact standard of ohmic values. Fortunately, White 9 9% most circuit requirements are not extremely Gold Silver 10% 5% critical. For many uses the actual resistance in No color 20% ohms can be 20 percent higher or lower than the value marked on the resistor without causing FIGURE 8-38. Resistor color code.
difficulty. The percentage variation between the marked value and the actual value of a resistor is known as the "tolerance" of a re- second bands, except in the following two cases:
sistor. A resistor coded for a 5-percent tolerance will not be more than 5 percent higher or lower than the value indicated by the color code.
The resistor color code (see figure 8-38) is made up of a group of colors, numbers, and tolerance values. Each color is represented by a number and in most cases by a tolerance value.
When the color code is used with the end-tocenter band marking system, the resistor is normally marked with bands of color at one end of the resistor. The body or base color of the resistor has nothing to do with the color code, and in no way indicates a resistance value. To prevent confusion, this body will never be the same color as any of the bands indicating resistance When the end-to-center band marking system is used, the resistor will be marked by either three or four bands. The first color band (nearest the end of the resistor) will indicate the first digit in the numerical resistance value. This band will never be gold or silver in color.
The second color band (refer to figure 8-39) will always indicate the second digit of ohmic value.
It will never be gold or silver in color. The third color band indicates the number of zeros to be added to the two digits derived from the first and
(1) If the third band is gold in color, the first two digits must be multiplied by 10 percent.
(2) If the third band is silver in color, the first two digits must be multiplied by 1 percent.
If there is a fourth color band, it is used as a multiplier for percentage of tolerance, as indicated in the color code chart in figure 8-38. If there is no fourth band, the tolerance is understood to be 20 percent.
Figure 8-39 illustrates the rules for reading the resistance value of a resistor marked with the end-to-center band system. This resistor is marked with three bands of color, which must be read from the end toward the center.
These are the values that should be obtained:
Numerical Color Value Significance Ist band-Red Ist digit 2nd band-Green 5 2nd digit 3rd band--Yellow No. of zeros to add There is no fourth color band, so the tolerance is understood to be 20 percent. 20 percent of 250,000 = 50,000.
Since the 20 percent tolerance is plus or minus, Maximum resistance = 250,000 + 50,000 B = 300,000 ohms Minimum resistance = 250,000 - 50,000 FIGURE 8-37. Symbols for fixed resistors. = 200,000 ohms.
2nd Band Ist Band 3rd Band White - Blue Brown + Gold Red - • Yellow 5% Green FIGURE 8-41. Resistor color code example.
FIGURE 8-39. End-to-center band marking.
Green - Red Figure 8-40 contains a resistor with another Red - - Red set of colors. This resistor code should be read as follows:
The resistance of this resistor is 86,000 +10 5 00 2% percent ohms. The maximum resistance is 94,600 FIGURE 8-42. Resistor with 2 percent tolerance.
ohins and the minimum resistance is 77,400 ohms.
As another example, the resistance of the Brown - Black - - Black f Brown resistor in figure 8-41 is 960 + 5 percent ohms.
The maximum resistance is 1,008 ohms, and the minimum resistance is 912 ohms.
1% Sometimes circuit considerations dictate that the tolerance must be smaller than 20 percent. FIGURE 8-43, Resistor with black third color band.
Figure 8-42 shows an example of a resistor with a 2 percent tolerance. The resistance value of this resistor is 2,500 + 2 percent ohms. The maximum Gold (Multiplier) Black resistance is 2,450 ohms. resistance is 2,550 ohms, and the minimum Brown • FRed Figure 8-43 contains an example of a resistor with a black third color band. The color code value of black is zero, and the third band indicates 0 10% 2% the number of zeros to be added to the first two FIGURE 8-44. Resistor with a gold third band.
digits.
In this case, a zero number of zeros must be added to the first two digits; therefore, no zeros are Green -Silver (Multiplier) added. Thus, the resistance value is 10 ‡ 1 Yellow - — Silver percent ohms. The maximum resistance is 10.1 ohms, and the minimum resistance is 9.9 ohms.
There are two exceptions to the rule stating the 5 1% 10% third color band indicates the number of zeros.
The first of these exceptions is illustrated in FIGURE 8-45. Resistor with a silver third band.
figure 8-44. When the third band is gold in color, Body color red (2) End color green (5) Blue • Orange Gray Silver Dot color yellow (4) 6 000 10% FICURE 8-46. Resistor coded with body-end-dot system.
FIGURE 8-40. Resistor color code example.
it indicates that the first two digits must be multiplied by 10 percent. The value of this resistor is 10 X .10 + 2% = 1 + .02 ohms.
When the third band is silver, as is the case in figure 8-45, the first two digits must be multiplied by 1 percent. The value of the resistor is .45 + 10 percent ohms.
Body-End-Dot System The body-end-dot system of marking is rarely used today. A few examples will explain it. The location of the colors has the following significance:
Body color Ist digit of ohmic value End color . 2nd digit of ohmic value Dot color . Number of zeros to be added If only one end of the resistor is painted, it indicates the second figure of the resistor value, and the tolerance will be 20 percent. The other two tolerance values are gold (5 percent) and silver (10 percent). The opposite end of the resistor will be painted to indicate a tolerance other than 20 percent. Figure 8-46 shows a resistor coded by the body-end-dot system.
The values are as follows:
Body-1st digit-2.
End--2nd digit-5.
Dot--No. of zeros- 0000 (4).
The resistor value is 250,000 + 20 percent ohms. The tolerance is understood to be 20 percent because no second dot is used.
If the same color is used more than once, the body, end, and dot may all be the same color, or any two may be the same; but the color code is used in exactly the same way. For example, a 33,000-ohm resistor will be entirely orange.
OHM'S LAW The most important law applicable to the study of electricity is Ohm's law. This law, which outlines the relationship between voltage, current, and resistance in an electrical circuit, was first stated by the German physicist, George Simon Ohm (1787-1854). This law applies to all directcurrent circuits. In a modified form it may be applied to the alternating circuits to be studied later in this text. Ohm's experiments showed that current flow in an electrical circuit is directly proportional to the amount of voltage applied to the circuit. Stated in different words, this law says that as the voltage increases, the current increases; and when the voltage decreases, the current flow decreases. It should be added that this relationship is true only if the resistance in the circuit remains constant. For it can be readily seen that if the resistance changes, current also changes.
Ohm's law may be expressed as an equation, as follows:
E Where I is current in amperes, E is the potential difference measured in volts, and R is the resistance measured in ohms (designated by the Greek letter omega, whose symbol is N).
If any two of these circuit quantities are known, the third may be found by simple algebraic transposition.
The circuit shown in figure 8-47 contains a voltage source of 24 volts and a resistance of 3 ohms.
If an ammeter is inserted in the circuit, as shown in figure 8-47, the intensity of current flowing in the circuit can be read directly. Assuming that no ammeter is available, the intensity of current fow can be determined by using Ohm's law as follows:
E = R 1 = 30 I = 8 amperes.
Some features of figure 8-47 that are typical of all electrical circuits drawn in schematic form should be reviewed. The electrical pressure or potential difference appiled to the circuit is rep- 302 24 volts Ammeter FIGURE 8-47. Electrical circuit demonstrating Ohm's law.
R = ?
Ammeter 24 volts o amperes FIGURE 8-48. A circuit with unknown resistance.
resented in schematic form by the symbol for a battery. The negative sign is located near one side to indicate the negative terminal of the source, or battery. The opposite side is marked positive with a + symbol. Arrows are sometimes used to indicate the direction of current flow from the negative terminal, through the conducting wires and other circuit devices, to the positive terminal of the source.
Figure 8-48 shows that the values of voltage and current are known. To find the quantity of resistance in the circuit, Ohm's law can be transposed to solve for R.
Transposing the basic formula I = to R = and substituting the known circuit values in the equation, R = 8 amperes 24 volts - = 3 ohms, or 3 g.
Ohm's law can also be transposed to determine the voltage applied to a circuit when current flow and resistance are known, as shown in figure 8-49.
In this circuit the unknown circuit quantity, the voltage, is represented by the symbol E. The value of resistance is 3 ohms, and the current flow is 8 amperes. (The word amperes is often shortened to "amps.") Transposing Onm's law from its basic formula, the equation to solve for E becomes E = I X R.
R = 30 Ammeter E = ?
8 amperes FIGURE 8-49. Circuit with unknown voltage.
Amperes (I)
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5 R - 20 Ohms
2.0 (Constant)
1.5
1.0
0.5 10 20 30 40 50 60 70 80 90 100 110120 Volts (E) FIGURE 8-50. Voltage vs. current in a constant-resistance circuit.
Substituting the known values in the equation, E = 8X3 È = 24 volts or 24 V.
The relationship between the various circuit quantities can be further demonstrated if the resistance in a circuit is held constant. In such a case, the current will increase or decrease in direct proportion to the increase or decrease of voltage appled to the circuit. For example, if the voltage applied to a circuit is 120 volts and the resistance of the circuit is 20 ohms, the current flow will be 120 20' or 6 amperes. If this resistance remains constant at 20 ohms, a graph of voltage-current relationship, as shown in figure 8-50, can be ploted.
The relationship between voltage and current in this example shows voltage plotted horizontally along the X axis in values from 0 to 120 volts, and the corresponding values of current are plotted vertically in values from 0 to 6.0 amperes along the Y axis. A straight line drawn through all the points where the voltage and current lines meet represents the equation I = 20 E and is called a linear relationship. The constant, 283
Electromotive force Current = Resistance Volts I= = Amperes = R Ohms Electromotive force Resistance = Current R=I E Ohms = - Volts Amperes Electromotive force = current X resistance E = IR Volts = amperes × ohms FIGURE 8-51. Ohm's law.
20, represents the resistance, which is assumed not to change in this example. This graph represents an important characteristic of the basic law, that the current varies directly with the applied voltage if the resistance remains constant.
The basic equations derived from Ohm's law are summarized, together with the units of measurements of circuit quantities, in figure 8-51.
The various equations which may be derived by transposing the basic law can be easily obtained by using the triangles in figure 8-52.
The triangles containing E, I, and R are divided into two parts, with E above the line and I X R below it. To determine an unknown circuit quantity when the other two are known, cover the unknown quantity with a thumb.
The location of the remaining uncovered letters in the triangle will indicate the mathematical operation to be performed. For example, to find I, refer to (a) of figure 8-52, and cover I with the thumb. The uncovered letters indicate that E is to be divided by R, or 1 = R To find R, refer to
(b) of figure 8-52, and cover R with the thumb. The result indicates that E is to be divided by Lor R = - To find E, refer to (e) of figure 8-52, and cover E with the thumb. The result indicates I is to be multiplied by R, or E = I X R.
This chart is useful when learning to use Ohm's law. It should be used to supplement the beginner's knowledge of the algebraic method.
Power In addition to the volt, ampere, and ohm, there is one other unit frequently used in electrical circuit calculations. This is the unit of power.
The unit used to measure power in d.c. electrical circuits is the watt. Power is defined as the rate of doing work and is equal to the product of the voltage and current in a d.c. circuit. When the current in amperes (I) is multiplied by e.m.f. in volts (E), the result is power measured in watts (P). This indicates that the electrical power delivered to a circuit varies directly with the applied voltage and current flowing in the circuit.
Expressed as an equation, this becomes P = IE.
This equation may be transposed to determine any one of the three circuit quantities as long as the other two are known. Thus, if the power is read directly from a wattmeter and the voltage is measured with a voltmeter, the intensity of the current (I) flowing in the circuit can be determined P by transposing the basic equation to I = Similarly, the voltage (E) can be found by transposing the basic power formula to E = T P Since some of the values used to determine the power delivered to a circuit are the same as those used in Ohm's law, it is possible to substitute Ohm's law values for equivalents in the power formula.
In Cher's law; I = If this vales I" is substituted for I in the power formula, it becomes P= IXE;P = EX ROP = R This equation, P = R' illustrates that the power in watts delivered to a circuit varies directly with the square of the applied voltage and inversely with the circuit resistance.
R To find I (amperes) place thumb over I and To find R (ohms) place thumb over R and divide E by R as indicated. divide as indicated.
(a) (b) R To find E (volts) place thumb over X and multiply as indicated.
(c) E = volts 1 = amperes R = ohms FIGURE 8-52. Ohm's law chart.
The watt is named for James Watt, the inventor of the steam engine. Watt devised an experiment to measure the power of a horse in order to find a means of measuring the mechanical power of his steam engine. One horsepower is required to move 33,000 pounds 1 foot in 1 minute. Since power is the rate of doing work, it is equivalent to the work divided by time. Stated as a formula, this is 33,000 ft.-lb.
Power = 60 sec. (1 min.) ' Or P = 550 ft.-lb./sec.
Electrical power can be rated in a similar manner. For example, an electric motor rated as a 1-horsepower motor requires 746 watts of electrical energy. But the watt is a relatively small unit of power. Much more common is the kilowatt or 1,000 watts. (The prefix kilo means 1,000.) In measuring amounts of electrical energy consumed, the kilowatt hour is used. For example, if a 100- watt bulb consumes electrical energy for 20 hours, it has used 2,000 watt hours or 2 kilowatt hours of electrical energy.
Electrical power that is lost in the form of heat when current flows through an electrical device is often referred to as power loss. This heat is usually dissipated into the surrounding air and serves no useful purpose, except when used for heating. Since all conductors possess some resistance, circuits are designed to reduce these losses. Referring again to the basic power formula, P = I X E, it is possible to substitute the Ohm's law values for E in the power formula to obtain a power formula that directly reflects the power losses in a resistance.
P= IXE; E = IXR.
Substituting the Ohm's law value for E (I X R) in the power formula, P = IXIXR.
Collecting terms, this gives, P = PR.
From this equation, it can be seen that the power in watts in a circuit varies as the square of the circuit current in amperes and varies directly with the circuit resistance in ohms.
Finally, the power delivered to a circuit can be expressed as a function of current and resistance by transposing the power equation P = I R.
Transposing to solve for current gives 12 = R and by extracting the square root of both sides of the equation, 1 = 1 Thus, the current through a 500-watt, 100-ohm load (resistance) is as follows:
1 = VR - 100 500 = 2.24 amperes.
The electrical equations derived from Ohm's law and the basic power formula do not reveal all about the behavior of circuits. They do indicate the numerical relation between the volt, ampere, ohm, and watt. Figure 8-53 provides a summary of all the possible transpositions of these formulas in a 12-segment circle.
SERIES D. C. CIRCUITS The series circuit is the most basic of electrical circuits. All other types of circuits are elaborations or combinations of series circuits. Figure 8-54 is an example of a simple series circuit. It is a circuit because it provides a complete path for current to flow from the negative to the positive terminal of the battery. It is a series circuit because there is only one possible path in which current can flow, as indicated by the arrows showing the direction of electron movement. It is also called a series circuit because current must pass through the circuit components, the battery and the resistor, one after the other, or "in series."
The circuit shown in figure 8-55 contains the basic components required for any circuit: a source of power (battery), a load or current-limiting resistance (resistor), and a conductor (wire). Most practical circuits contain at least two other items:
a control device (switch) and a safety device (fuse). With all five components in the circuit it would appear as shown in figure 8-55, which is a d.c. series circuit.
IR FIGURE 8-53. Summary of basic equations using the volt, ampere, ohm, and watt.
In the d.c. or direct-current circuit, current flows in one direction from the negative terminal of the battery through the switch (which must be closed) through the load resistance and the fuse to the positive terminal of the battery.
To discuss the behavior of electric current in a
d.c. series circuit, figure 8-56 is redrawn in figure 8-57 to include three ammeters and two resistors. Since an ammeter measures the intensity of current flow, three have been located in the circuit to measure the current flowing at various points in the circuit.
With the switch closed to complete the circuit, all three ammeters will indicate the same amount of current. This is an important characteristic of all series circuits: No matter how many components are included in a series circuit, the current is the same intensity throughout the circuit.
While it is true that an increase in the number of circuit components will increase the resistance to current flow in the circuit, whatever the value of current flowing in the circuit, it will be the same value at all points in the circuit.
In figure 8-56, the current through resistor R1 is labeled 11 and the current through resistor R2 is labeled I2. If the total current in the circuit is Ir, the formula describing the current flow is, 17 = 11 = 12.
If the number of resistors is increased to five, the formula will be IT = 11 = 12 = 13 = 14 = 15.