science universe

7–8 RESISTORS

Resistors are one of the most common components found in electric circuits. The unit of measure for resistance is the ohm, which was named for the German scientist Georg S. Ohm. The symbol used to represent resistance is the uppercase Greek letter omega (V).

Resistors come in various sizes, types, and ratings to accommodate the needs of almost any circuit application. Resistors are commonly used to perform two functions in a circuit. One is to limit the flow of current through the circuit.

In Figure 7–17 a 30-ohm resistor is connected to a 15-volt battery. The current in this circuit is limited to a value of 0.5 ampere:

If this resistor were not present, the circuit current would be limited only by the resistance of the conductor, which would be very low and would allow a large amount of current to flow. Assume for example that the wire has a resistance of 0.0001 ohm. When the wire is connected across the 15-volt power source, a current of 150,000 amperes would try to flow through the circuit (15/0.0001 5 150,000). This is commonly known as a short circuit.

The second principal function of resistors is to produce a voltage divider, as shown in Figure 7–18. These three resistors are connected in series with a 17.5-volt battery. A volt- meter placed between different points in the circuit would indicate the following voltages:

By connecting resistors of the proper value, almost any voltage desired can be obtained. Voltage dividers were used to a large extent in vacuum tube circuits many years ago. Voltage divider circuits are still used today in applications involving field effect transistors (FETs) and in multirange voltmeter circuits.

7–9 FIXED RESISTORS

Fixed resistors have only one ohmic value that cannot be changed or adjusted. There are several different types of fixed resistors.

Carbon Resistors

One of the most common types of fixed resistors is the composition carbon resistor. These resistors are made from a compound of carbon graphite and a resin bonding material enclosed in a case of nonconductive material with connecting leads, as shown in Figure 7–19. The proportions of carbon and resin material determine the value of resistance.

Carbon resistors are very popular for most applications because they are inexpensive and readily available. They are made in standard values that range from about 1 ohm to

about 22 million ohms and can be obtained in power ratings of 1/8, 1/4, 1/2, 1, and 2 watts. The power rating of the resistor is indicated by its size. A 1/2-watt resistor is approximately 3/8 inch long and 1/8 inch in diameter. A 2-watt resistor is approximately 11/16 inch long and approximately 5/16 inch in diameter, Figure 7–20. The 2-watt resistor is larger than the 1/2-watt or 1-watt resistor because it must have a larger surface area to be able to dissipate more heat. Although carbon resistors have many desirable characteristics, they have one characteristic that is not so desirable: Carbon resistors will change their value with age or if they are overheated. Carbon resistors generally increase instead of decrease in value.

Metal Film Resistors

Another type of fixed resistor is the metal film resistor, constructed by applying a film of metal to a ceramic rod in a vacuum; see Figure 7–21. The resistance is determined by the type of metal used to form the film and the thickness of the film. Typical thickness for the film is from 0.000 01 to 0.000 000 01 inch. Leads are then attached to the film coating and the entire assembly is covered with a coating. Metal film resistors are superior to carbon resistors in several respects. They do not change their value with age, and their tolerance is generally better than carbon resistors. Also, carbon resistors commonly have a tolerance range of 20%, 10%, or 5% compared to the metal film resistor’s general range of 2% to 0.1%. The disadvantage of the metal film resistor is that it is higher in cost.

Carbon Film Resistors

Constructed in a similar manner as the metal film resistor, the carbon film resistor is made by coating a ceramic rod with a film of carbon instead of metal. Carbon film resistors are less expensive to manufacture than metal film resistors and can have a higher tolerance rating than composition carbon resistors.

Metal Glaze Resistors

Another resistor that is similar to the metal film one is the metal glaze resistor. This resistor is made by combining metal with glass. The compound is then applied to a ceramic base as a thick film. The resistance is determined by the amount of metal used in the compound. Tolerance ratings of 2% and 1% are common.

Wire Wound Resistors

Wire wound resistors are made by winding a piece of resistive wire around a ceramic core; see Figure 7–22. The resistance of a wire wound resistor is determined by the type of material used to make the resistive wire, the diameter of the wire, and the length of the wire.

Wire wound resistors can be found in various case styles and sizes. These resistors are generally used when a high power rating is needed. Wire wound resistors can operate at higher temperatures than any other type of resistor. A wire wound resistor with a hollow center is shown in Figure 7–23. The center of the resistor is hollow for a very good reason: When the resistor is mounted vertically (as it must be), the heat from the resistor produces a chimney effect and causes air to circulate through the center; see Figure 7–24.

7–10 COLOR CODE

The values of a resistor can often be determined by the color code. Many resistors have bands of color that are used to determine the resistance value, tolerance, and, in some cases, reliability. Each color in the band represents a different numerical value, as shown in Figure 7–25. The resistor shown beside the color chart illustrates how to determine the value of a resistor. Resistors can have from three to five bands of color. Resistors with a tolerance of 620% have only three color bands, but most resistors have four. For resistors with tolerances that range from 610% to 62%, the first two color bands represent numerical values. The third band is called the multiplier, which indicates how many times the first two numbers should be multiplied by 10 to obtain the resistance value. The fourth band indicates the tolerance.

For example, assume a resistor has color bands of brown, green, red, and silver, as shown in Figure 7–26. The first two colors represent the numbers 1 and 5 (brown is 1 and green is 5). The third band is red, which represents 2. Thus the number 15 should be multiplied by 10 two times, and the value of the resistor is 1,500 ohms. Another method, which is simpler to understand, is to add to the first two numbers the number of zeros indicated by the multiplier band. With the red multiplier band in our example representing a numeric value of 2, we add two zeros to the first two numbers and the number 15 becomes 1,500.

The brown fifth band indicates that this resistor has a tolerance of 61%. To determine the value of a 1% resistor, note that the first three bands are numbers and the fourth band is the multiplier. In this example, the first band is brown, which has a numerical value of 1. The next two bands are black, which represents 0. The fourth band is brown, which means add one 0 to the first three numbers. The value of this resistor is 1,000 ohms 61%.

EXAMPLE 7–9

A five-band resistor has the following color bands:

The first three bands represent numerical values: Red is 2, orange is 3, and violet is 7. The red fourth band is the multiplier; in this case red represents 2. Add two 0’s to the number 237 to find that the value of the resistor is 23,700 ohms. The brown fifth band indicates a tolerance of 61%.

Military resistors often have five color bands also. These resistors are read resistors with four color bands. The fifth band can represent different things. A fifth band of orange or yellow is used to indicate reliability. Resistors with a fifth band of orange have a reliability good enough to be used in missile systems, and those with a fifth band of yellow can be used in space flight equipment. A fifth band of white indicates that the resistor has solderable leads. Resistors with tolerance ratings ranging from 0.5% to 0.1% will generally have their values printed directly on the resistor.

Gold and Silver as Multipliers

The colors gold and silver are generally found in the fourth band of a resistor, but they can be used in the multiplier band also. A gold multiplier band means to divide the first two numbers by 10. A silver multiplier band means to divide the first two numbers by 100. For example, assume a resistor has color bands of orange, white, gold, and gold. Orange 5 3, white 5 9, gold means to divide 39 by 10 (which equals 3.9), and gold in the fourth band means 65% tolerance. The value of this resistor is 3.9 ohms with a tolerance of 65%.

Standard Resistance Values

Fixed resistors are generally produced in standard values. The higher the tolerance value, the fewer resistance values available. Standard resistor values are listed in Figure 7–28. In the column under 10%, there are only 12 values of resistors listed. These values, however, can be multiplied by factors of 10. For example, one of the standard values listed is 33 ohms. There are also standard values in 10% resistors of 0.33; 3.3; 330; 3,300; 33,000; 330,000; and 3,300,000 ohms. The 5% column shows there are 24 resistor values and the 1% column lists 96 values. All the values listed in the chart can be multi- plied by factors of 10 to obtain other resistance values.

7–8 RESISTORS

Resistors are one of the most common components found in electric circuits. The unit of measure for resistance is the ohm, which was named for the German scientist Georg S. Ohm. The symbol used to represent resistance is the uppercase Greek letter omega (V).

Resistors come in various sizes, types, and ratings to accommodate the needs of almost any circuit application. Resistors are commonly used to perform two functions in a circuit. One is to limit the flow of current through the circuit.

In Figure 7–17 a 30-ohm resistor is connected to a 15-volt battery. The current in this circuit is limited to a value of 0.5 ampere:

If this resistor were not present, the circuit current would be limited only by the resistance of the conductor, which would be very low and would allow a large amount of current to flow. Assume for example that the wire has a resistance of 0.0001 ohm. When the wire is connected across the 15-volt power source, a current of 150,000 amperes would try to flow through the circuit (15/0.0001 5 150,000). This is commonly known as a short circuit.

The second principal function of resistors is to produce a voltage divider, as shown in Figure 7–18. These three resistors are connected in series with a 17.5-volt battery. A volt- meter placed between different points in the circuit would indicate the following voltages:

By connecting resistors of the proper value, almost any voltage desired can be obtained. Voltage dividers were used to a large extent in vacuum tube circuits many years ago. Voltage divider circuits are still used today in applications involving field effect transistors (FETs) and in multirange voltmeter circuits.

7–9 FIXED RESISTORS

Fixed resistors have only one ohmic value that cannot be changed or adjusted. There are several different types of fixed resistors.

Carbon Resistors

One of the most common types of fixed resistors is the composition carbon resistor. These resistors are made from a compound of carbon graphite and a resin bonding material enclosed in a case of nonconductive material with connecting leads, as shown in Figure 7–19. The proportions of carbon and resin material determine the value of resistance.

Carbon resistors are very popular for most applications because they are inexpensive and readily available. They are made in standard values that range from about 1 ohm to

about 22 million ohms and can be obtained in power ratings of 1/8, 1/4, 1/2, 1, and 2 watts. The power rating of the resistor is indicated by its size. A 1/2-watt resistor is approximately 3/8 inch long and 1/8 inch in diameter. A 2-watt resistor is approximately 11/16 inch long and approximately 5/16 inch in diameter, Figure 7–20. The 2-watt resistor is larger than the 1/2-watt or 1-watt resistor because it must have a larger surface area to be able to dissipate more heat. Although carbon resistors have many desirable characteristics, they have one characteristic that is not so desirable: Carbon resistors will change their value with age or if they are overheated. Carbon resistors generally increase instead of decrease in value.

Metal Film Resistors

Another type of fixed resistor is the metal film resistor, constructed by applying a film of metal to a ceramic rod in a vacuum; see Figure 7–21. The resistance is determined by the type of metal used to form the film and the thickness of the film. Typical thickness for the film is from 0.000 01 to 0.000 000 01 inch. Leads are then attached to the film coating and the entire assembly is covered with a coating. Metal film resistors are superior to carbon resistors in several respects. They do not change their value with age, and their tolerance is generally better than carbon resistors. Also, carbon resistors commonly have a tolerance range of 20%, 10%, or 5% compared to the metal film resistor’s general range of 2% to 0.1%. The disadvantage of the metal film resistor is that it is higher in cost.

Carbon Film Resistors

Constructed in a similar manner as the metal film resistor, the carbon film resistor is made by coating a ceramic rod with a film of carbon instead of metal. Carbon film resistors are less expensive to manufacture than metal film resistors and can have a higher tolerance rating than composition carbon resistors.

Metal Glaze Resistors

Another resistor that is similar to the metal film one is the metal glaze resistor. This resistor is made by combining metal with glass. The compound is then applied to a ceramic base as a thick film. The resistance is determined by the amount of metal used in the compound. Tolerance ratings of 2% and 1% are common.

Wire Wound Resistors

Wire wound resistors are made by winding a piece of resistive wire around a ceramic core; see Figure 7–22. The resistance of a wire wound resistor is determined by the type of material used to make the resistive wire, the diameter of the wire, and the length of the wire.

Wire wound resistors can be found in various case styles and sizes. These resistors are generally used when a high power rating is needed. Wire wound resistors can operate at higher temperatures than any other type of resistor. A wire wound resistor with a hollow center is shown in Figure 7–23. The center of the resistor is hollow for a very good reason: When the resistor is mounted vertically (as it must be), the heat from the resistor produces a chimney effect and causes air to circulate through the center; see Figure 7–24.

7–10 COLOR CODE

The values of a resistor can often be determined by the color code. Many resistors have bands of color that are used to determine the resistance value, tolerance, and, in some cases, reliability. Each color in the band represents a different numerical value, as shown in Figure 7–25. The resistor shown beside the color chart illustrates how to determine the value of a resistor. Resistors can have from three to five bands of color. Resistors with a tolerance of 620% have only three color bands, but most resistors have four. For resistors with tolerances that range from 610% to 62%, the first two color bands represent numerical values. The third band is called the multiplier, which indicates how many times the first two numbers should be multiplied by 10 to obtain the resistance value. The fourth band indicates the tolerance.

For example, assume a resistor has color bands of brown, green, red, and silver, as shown in Figure 7–26. The first two colors represent the numbers 1 and 5 (brown is 1 and green is 5). The third band is red, which represents 2. Thus the number 15 should be multiplied by 10 two times, and the value of the resistor is 1,500 ohms. Another method, which is simpler to understand, is to add to the first two numbers the number of zeros indicated by the multiplier band. With the red multiplier band in our example representing a numeric value of 2, we add two zeros to the first two numbers and the number 15 becomes 1,500.

The brown fifth band indicates that this resistor has a tolerance of 61%. To determine the value of a 1% resistor, note that the first three bands are numbers and the fourth band is the multiplier. In this example, the first band is brown, which has a numerical value of 1. The next two bands are black, which represents 0. The fourth band is brown, which means add one 0 to the first three numbers. The value of this resistor is 1,000 ohms 61%.

EXAMPLE 7–9

A five-band resistor has the following color bands:

The first three bands represent numerical values: Red is 2, orange is 3, and violet is 7. The red fourth band is the multiplier; in this case red represents 2. Add two 0’s to the number 237 to find that the value of the resistor is 23,700 ohms. The brown fifth band indicates a tolerance of 61%.

Military resistors often have five color bands also. These resistors are read resistors with four color bands. The fifth band can represent different things. A fifth band of orange or yellow is used to indicate reliability. Resistors with a fifth band of orange have a reliability good enough to be used in missile systems, and those with a fifth band of yellow can be used in space flight equipment. A fifth band of white indicates that the resistor has solderable leads. Resistors with tolerance ratings ranging from 0.5% to 0.1% will generally have their values printed directly on the resistor.

Gold and Silver as Multipliers

The colors gold and silver are generally found in the fourth band of a resistor, but they can be used in the multiplier band also. A gold multiplier band means to divide the first two numbers by 10. A silver multiplier band means to divide the first two numbers by 100. For example, assume a resistor has color bands of orange, white, gold, and gold. Orange 5 3, white 5 9, gold means to divide 39 by 10 (which equals 3.9), and gold in the fourth band means 65% tolerance. The value of this resistor is 3.9 ohms with a tolerance of 65%.

Standard Resistance Values

Fixed resistors are generally produced in standard values. The higher the tolerance value, the fewer resistance values available. Standard resistor values are listed in Figure 7–28. In the column under 10%, there are only 12 values of resistors listed. These values, however, can be multiplied by factors of 10. For example, one of the standard values listed is 33 ohms. There are also standard values in 10% resistors of 0.33; 3.3; 330; 3,300; 33,000; 330,000; and 3,300,000 ohms. The 5% column shows there are 24 resistor values and the 1% column lists 96 values. All the values listed in the chart can be multi- plied by factors of 10 to obtain other resistance values.

7–5 EFFECT OF TEMPERATURE ON RESISTANCE

Resistance depends not only on length, area, and kind of material, but also on the temperature of the material. Figure A–2 of the Appendix gives two sets of values for the resistance of copper at two different temperatures. (The resistance values given for the higher temperature are used when calculating motor and transformer windings since these windings are intended to operate warm.) These values in Figure A–2 show that as the temperature rises, the resistance of metals increases.

The graph in Figure 7–8 shows, in a general way, how the resistance of most metals increases as the temperature increases. Not only is the resistance greater, but it is also increasing at a faster rate as the temperature rises.

The resistance of carbon, however, decreases slightly with a rise in temperature. The resistance of conducting liquid solutions decreases rapidly with a temperature rise. Finally, the resistance of semiconductors, such as germanium and metal oxides, decreases very rapidly as the temperature goes up.

Not all metals increase in resistance at the same rate. The rate at normal temperatures is given as the temperature coefficient of resistance in Figure A–1 of the Appendix.

As the temperature approaches absolute 0 (–273°C), many metals and alloys lose all of their electrical resistance. This behavior is called superconductivity. When the niobium-alloy wire coils of extremely powerful electromagnets are cooled (by liquid helium) to temperatures about 4°C above absolute 0, the coils have a very low resistance. Thus, they can carry huge currents without an appreciable energy loss. Research scientists are developing super-cooled power lines that can be buried underground.

Using the Temperature Coefficient to Find Resistance at Higher Temperature

The resistance increase due to a higher temperature is equal to the original resistance multiplied by the temperature coefficient and by the rise in temperature in degrees. Ex- pressed in equation form, this statement becomes

Resistance increase 5 R x Coefficient x Degree rise

This resistance increase is added to the original resistance to give the resistance at the higher temperature.

EXAMPLE 7–7

Given: 10 feet of #30 platinum wire.

Find: The resistance of this wire if used in an oven at 500°F.

Solution

1. The resistance of 10 feet of #30 platinum wire at room temperature is found by comparison with copper: Figure A–2 (Appendix) gives the resistance of 1,000 feet of #30 copper wire as 103 ohms. Therefore, 10 feet of #30 copper wire has a resistance of 1.03 ohms. Platinum has 5.8 times as much resistance as copper. (This is derived from the Ohms Resistance per mil-foot column in Figure A–1 of the Appendix.) Therefore, 10 feet of platinum, at room temperature, has a resistance of

1.03 x 5.80 = 5.97 or 6 V

Thus, the original resistance in the formula for finding the amount of resistance increase is the value of 6 ohms at 68°F.

2. The temperature coefficient given in Figure A–1 (Appendix) is 0.003 per degree Celsius.

3. The rise of temperature in degrees must be found and expressed in degrees Celsius.

From 68°F to 500°F, there is a difference of 432°F. Since 1.8°F equals 1°C, we divide the 432°F temperature rise by 1.8 to establish that a change of 432°F is equivalent to a change of 240°C.

4. The three quantities needed to calculate the amount of change in resistance are now known. Thus, resistance increase is

6 V x 0.003 x 240°C = 4.3 V

This value is added to the original resistance of 6 ohms. As a result, the resistance of 10 feet of #30 platinum wire at 500°F is 6 ohms 1 4.3 ohms, or 10.3 ohms.

7–6 THE AMERICAN WIRE GAUGE (AWG)

It would be impractical having to calculate resistance for any given length and wire diameter. Such information is more readily available from the American Wire Gauge (AWG), also known as the Brown & Sharpe (B&S) Gauge.

The AWG was standardized in 1857 and is used mainly in the United States for measuring the diameters of round, solid, nonferrous electrical wire. The gauge size is important for determining the current carrying capacity of a conductor. Gauge sizes are determined by the number of draws necessary to produce a given diameter or wire. Electrical wire is produced by drawing it through a succession of dies, Figure 7–9.

Each time a wire passes through a die it is wrapped around a draw block several times. The draw block provides the pulling force necessary to draw the wire through the die. A 24 AWG wire would be drawn through 24 dies each having a smaller diameter. In the field, wire size can be determined with a wire gauge, Figure 7–10.

One side of the wire gauge lists the AWG size of the wire, Figure 7–11. The opposite side of the wire gauge indicates the diameter of the wire in thousandths of an inch, Figure 7–12. When determining wire size, first remove the insulation from around the conductor. The slots in the wire gauge, not the holes behind the slots, are used to determine the size, Figure 7–13.

The AWG assigns numbers from 0 to 44; see Figure A–2 of the Appendix. The table is self-explanatory, but the following observations may be useful:

• The larger the number, the smaller the wire.

• A #2 wire is nearly the size of a standard wooden pencil.

• A #44 wire is about the thickness of a fine hair.

• Wires larger than 0-gauge are labeled 00 (2/0), 000 (3/0), and 0000 (4/0), respectively.

• Wires larger than 0000 (4/0) are classified by cross-sectional area in CM, the next larger size being 250,000 CM 5 250 Kcmil (see Example 7–1).

• Odd-numbered conductors are rarely used and seldom stocked by wholesalers.

• The most prevalent wire sizes used in house wiring are #14 and #12.

• A #14-gauge wire is the smallest wire permissible by the National Electric Code® to be used for permanent installations.

• No. 8-gauge wire can be used for installing electric kitchen ranges and other heavy-duty appliances.

• No. 22-gauge wire may be used for electronic circuits.

• Ordinary lamp cords are generally made of #16 or #18 wire.

• A stranded wire has the same amount of copper and the same current-carrying capacity as a solid wire of the same size.

7–7 STRANDED WIRE AND CABLE

Bunch Stranding

Bunch-stranded wire is a collection of wires twisted together. These wires are not placed in specific geometrical arrangement. For example, #18 lamp cord contains 16 #30 wires that are loosely twisted together in the same direction.

Concentric Stranding

For this type of wire stranding, a center wire is surrounded by one or more definite layers of wires. Each wire layer contains six wires more than the layer immediately beneath it, Figures 7–14 and 7–15. When several wire layers are used, each layer is twisted in a direction opposite to that of the layer under it.

The diameter of the wire strands used in a cable depends on the flexibility required. Obviously, a cable made up of many fine wire strands is a lot more flexible than an equally sized cable constructed from only a few thick strands. However, since even fine wire will break if bent back and forth many times, stiffer wire may be used in addition to copper wire to increase the durability of a cable. One type of #25 microphone cable consists of four strands of #33 copperweld wire added to three strands of #33 copper wire. Steel as well as copperweld wire may be used to supply extra strength to large cables.

Rope Stranding

A rope-stranded cable consists of several concentric cables twisted together. The 7 x 19 rope-stranded cable shown in Figure 7–16 consists of seven 19-strand conductors twisted together.

Cables larger than #4/0 are rated in circular mils. Standard sizes range from 200 Kcmil to 5,000 Kcmil. These cables may be covered with any of a great variety of insulation materials.

Cables are not always circular. Flat braid is available in many shapes and sizes. The battery grounding strap on an automobile used to be made from wire in the form of a flat braid.

7–5 EFFECT OF TEMPERATURE ON RESISTANCE

Resistance depends not only on length, area, and kind of material, but also on the temperature of the material. Figure A–2 of the Appendix gives two sets of values for the resistance of copper at two different temperatures. (The resistance values given for the higher temperature are used when calculating motor and transformer windings since these windings are intended to operate warm.) These values in Figure A–2 show that as the temperature rises, the resistance of metals increases.

The graph in Figure 7–8 shows, in a general way, how the resistance of most metals increases as the temperature increases. Not only is the resistance greater, but it is also increasing at a faster rate as the temperature rises.

The resistance of carbon, however, decreases slightly with a rise in temperature. The resistance of conducting liquid solutions decreases rapidly with a temperature rise. Finally, the resistance of semiconductors, such as germanium and metal oxides, decreases very rapidly as the temperature goes up.

Not all metals increase in resistance at the same rate. The rate at normal temperatures is given as the temperature coefficient of resistance in Figure A–1 of the Appendix.

As the temperature approaches absolute 0 (–273°C), many metals and alloys lose all of their electrical resistance. This behavior is called superconductivity. When the niobium-alloy wire coils of extremely powerful electromagnets are cooled (by liquid helium) to temperatures about 4°C above absolute 0, the coils have a very low resistance. Thus, they can carry huge currents without an appreciable energy loss. Research scientists are developing super-cooled power lines that can be buried underground.

Using the Temperature Coefficient to Find Resistance at Higher Temperature

The resistance increase due to a higher temperature is equal to the original resistance multiplied by the temperature coefficient and by the rise in temperature in degrees. Ex- pressed in equation form, this statement becomes

Resistance increase 5 R x Coefficient x Degree rise

This resistance increase is added to the original resistance to give the resistance at the higher temperature.

EXAMPLE 7–7

Given: 10 feet of #30 platinum wire.

Find: The resistance of this wire if used in an oven at 500°F.

Solution

1. The resistance of 10 feet of #30 platinum wire at room temperature is found by comparison with copper: Figure A–2 (Appendix) gives the resistance of 1,000 feet of #30 copper wire as 103 ohms. Therefore, 10 feet of #30 copper wire has a resistance of 1.03 ohms. Platinum has 5.8 times as much resistance as copper. (This is derived from the Ohms Resistance per mil-foot column in Figure A–1 of the Appendix.) Therefore, 10 feet of platinum, at room temperature, has a resistance of

1.03 x 5.80 = 5.97 or 6 V

Thus, the original resistance in the formula for finding the amount of resistance increase is the value of 6 ohms at 68°F.

2. The temperature coefficient given in Figure A–1 (Appendix) is 0.003 per degree Celsius.

3. The rise of temperature in degrees must be found and expressed in degrees Celsius.

From 68°F to 500°F, there is a difference of 432°F. Since 1.8°F equals 1°C, we divide the 432°F temperature rise by 1.8 to establish that a change of 432°F is equivalent to a change of 240°C.

4. The three quantities needed to calculate the amount of change in resistance are now known. Thus, resistance increase is

6 V x 0.003 x 240°C = 4.3 V

This value is added to the original resistance of 6 ohms. As a result, the resistance of 10 feet of #30 platinum wire at 500°F is 6 ohms 1 4.3 ohms, or 10.3 ohms.

7–6 THE AMERICAN WIRE GAUGE (AWG)

It would be impractical having to calculate resistance for any given length and wire diameter. Such information is more readily available from the American Wire Gauge (AWG), also known as the Brown & Sharpe (B&S) Gauge.

The AWG was standardized in 1857 and is used mainly in the United States for measuring the diameters of round, solid, nonferrous electrical wire. The gauge size is important for determining the current carrying capacity of a conductor. Gauge sizes are determined by the number of draws necessary to produce a given diameter or wire. Electrical wire is produced by drawing it through a succession of dies, Figure 7–9.

Each time a wire passes through a die it is wrapped around a draw block several times. The draw block provides the pulling force necessary to draw the wire through the die. A 24 AWG wire would be drawn through 24 dies each having a smaller diameter. In the field, wire size can be determined with a wire gauge, Figure 7–10.

One side of the wire gauge lists the AWG size of the wire, Figure 7–11. The opposite side of the wire gauge indicates the diameter of the wire in thousandths of an inch, Figure 7–12. When determining wire size, first remove the insulation from around the conductor. The slots in the wire gauge, not the holes behind the slots, are used to determine the size, Figure 7–13.

The AWG assigns numbers from 0 to 44; see Figure A–2 of the Appendix. The table is self-explanatory, but the following observations may be useful:

• The larger the number, the smaller the wire.

• A #2 wire is nearly the size of a standard wooden pencil.

• A #44 wire is about the thickness of a fine hair.

• Wires larger than 0-gauge are labeled 00 (2/0), 000 (3/0), and 0000 (4/0), respectively.

• Wires larger than 0000 (4/0) are classified by cross-sectional area in CM, the next larger size being 250,000 CM 5 250 Kcmil (see Example 7–1).

• Odd-numbered conductors are rarely used and seldom stocked by wholesalers.

• The most prevalent wire sizes used in house wiring are #14 and #12.

• A #14-gauge wire is the smallest wire permissible by the National Electric Code® to be used for permanent installations.

• No. 8-gauge wire can be used for installing electric kitchen ranges and other heavy-duty appliances.

• No. 22-gauge wire may be used for electronic circuits.

• Ordinary lamp cords are generally made of #16 or #18 wire.

• A stranded wire has the same amount of copper and the same current-carrying capacity as a solid wire of the same size.

7–7 STRANDED WIRE AND CABLE

Bunch Stranding

Bunch-stranded wire is a collection of wires twisted together. These wires are not placed in specific geometrical arrangement. For example, #18 lamp cord contains 16 #30 wires that are loosely twisted together in the same direction.

Concentric Stranding

For this type of wire stranding, a center wire is surrounded by one or more definite layers of wires. Each wire layer contains six wires more than the layer immediately beneath it, Figures 7–14 and 7–15. When several wire layers are used, each layer is twisted in a direction opposite to that of the layer under it.

The diameter of the wire strands used in a cable depends on the flexibility required. Obviously, a cable made up of many fine wire strands is a lot more flexible than an equally sized cable constructed from only a few thick strands. However, since even fine wire will break if bent back and forth many times, stiffer wire may be used in addition to copper wire to increase the durability of a cable. One type of #25 microphone cable consists of four strands of #33 copperweld wire added to three strands of #33 copper wire. Steel as well as copperweld wire may be used to supply extra strength to large cables.

Rope Stranding

A rope-stranded cable consists of several concentric cables twisted together. The 7 x 19 rope-stranded cable shown in Figure 7–16 consists of seven 19-strand conductors twisted together.

Cables larger than #4/0 are rated in circular mils. Standard sizes range from 200 Kcmil to 5,000 Kcmil. These cables may be covered with any of a great variety of insulation materials.

Cables are not always circular. Flat braid is available in many shapes and sizes. The battery grounding strap on an automobile used to be made from wire in the form of a flat braid.

Resistance

7–1 CONDUCTANCE VS. RESISTANCE

It is well known that some materials, especially metals, permit electrical currents to easily flow through them. These materials, whose atomic structures readily provide free electrons, are referred to as good conductors.

Silver is the best of such conductors, but it is seldom used because of its high cost. Copper is almost as good a conductor as silver, is relatively inexpensive, and serves for most types of wiring. Aluminum, a fairly good conductor, is used where weight reduction is an important factor.

By contrast, other materials tend to prevent current from flowing through them. Such substances are known as nonconductors or insulators. Examples of insulators are glass, rubber, and nylon.

It is important to realize that not all materials can be so easily classified. The degree of conductivity varies over an extremely wide range. Conductors and insulators merely represent two extremes between which a great variety of materials are classified as poor conductors or semiconductors.

Among these poor conductors are metals and alloys that find use as resistance wire in heat-producing appliances such as electric ranges and heaters. Nickel-chromium, often called nichrome, is an example of such wire.

But even the extremes do not represent absolute perfection. Every conductor, no matter how good, still offers some resistance. Just how much resistance a conductor has de- pends on four factors, namely:

1. The type of material from which it is made

2. The conductor’s length

3. Its cross-sectional area (thickness)

4. Its temperature

These factors will be explored in the following sections.

7–2 RESISTIVITY OF MATERIALS

The resistance rating of different materials is based on a comparison of the number of ohms measured in a standard-sized sample of the material. In the metric sys- tem, for instance, the standard is a 1-centimeter cube whose resistance is measured in millionths of an ohm (microhms). Look at Figure A–1 in the Appendix, and com- pare the resistivity in microhm-centimeters. This resistivity is also known as specific resistance.

In the English system of measurement, the standard of resistivity is called the mil-foot. This standard is based on the resistance of a piece of wire 1 foot long with a diameter of 0.001 inch (1 mil 5 1/1,000). Figure 7–1 illustrates the concept of a mil-foot, and the chart in Figure 7–2 shows some characteristic values of resistivity.

7–3 LENGTH OF A CONDUCTOR

The resistance of any conductor is directly proportional to its length. For example, if 50 feet of wire has a resistance of 1 ohm, then 100 feet of the same wire will have a resistance of 2 ohms. In other words, the longer the wire, the more resistance it has. This simple fact must be taken into account whenever electricians plan the installation of a long supply line.

7–4 CROSS-SECTIONAL AREA (CSA) OF A CONDUCTOR IN CIRCULAR MILS

Resistance is inversely proportional to the cross-sectional area of the wire. This is a way of saying that the thicker the wire, the lower its resistance. A thick wire, as shown in Figure 7–3, allows many electrons to move through it easily, just as a wide road can carry many cars per hour or a large pipe can allow a large volume of water to flow through it.

Because the use of square inches or square feet results in complicated calculations and inconveniently small numbers for ordinary sizes of wire, a more convenient unit of area (thickness) is used. The circle in Figure 7–4 represents the end of a wire that is 1/1,000 of an inch thick. This distance, 0.001 inch, is 1 mil. The area of this circle, which is 1 mil in diameter, is 1 circular mil (CM). A circular mil is a unit of area (A) measurement. It is the same type of measurement as a square foot or an acre but more convenient to use.

For example, what is the area of a circle with a diameter of 0.002 inch? As Figure 7–5 illustrates, such a circle has an area exactly four times larger than a circle with a diameter of inch. If either the radius or the diameter of any flat surface is doubled, then the area will increase four times. Let us look at an example using the formula for finding the area of a circle, A 5 πr2. If the radius r of circle X is 5, then the area r2 is 25π. If the radius r of circle Y is 10 (double that of circle X), then the area of circle Y is 100π (four times that of circle X). There- fore, to answer the question about the area of a circle that has a diameter of 0.002 inch, we can say that the area is four times greater than that of a 1-mil circle, or 4 circular mils.

What is the area of a circle that has a diameter of 0.003 inch? Three-thousandths of an inch is 3 mils: 32 is 9. This circle is nine times as large in area as a 1-mil circle. The area of the circle, therefore, is 9 circular mils. The area of a circle, using circular mils, can be found by the following steps:

1. Write the diameter of the circle in mils.

2. Square this number (multiply it by itself); the result is the area of the circle in circular mils.

Note: 250,000 CM is also expressed as 250 Kcmil (formerly known as 250 MCM).

If the circular mils of a wire is known, it is a simple matter to reverse the mathematical procedure and find the diameter.

EXAMPLE 7–2

Given: A conductor with cross-sectional area of 100 circular mils.

Find: Its diameter in inches.

Solution

Not all conductors are circular in shape. Solid rectangular conductors (bus bars) are used to carry large currents. Bus bars are often easier to assemble and take up less space than the large-sized round conductors required to carry the same current. In addition, the flat shape of the bus bar provides more surface area from which heat can radiate.

The cross-sectional area of such a bus bar is figured in square mils rather than in circular mils. A square mil is defined as the area of a square with sides of 0.001 inch, as illustrated in Figure 7–6.

EXAMPLE 7–3

Given: A bus bar 4 inches wide and 0.25 inch thick, as shown in Figure 7–7.

Find: Its cross-sectional area in square mils.

Calculating the Resistance of a Wire

As previously stated, the resistance of a wire is a function of its resistivity (K); see Figure 7–2. Furthermore, it is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). This statement can be written mathematically as

EXAMPLE 7–6

Given: A two-wire power line is to be erected between poles 1,200 feet apart (the length of the wire is 2,400 feet). Resistance of the line should not be more than 1.7 ohms.

Find: The size of the aluminum wire to be used.

Solution

Resistance

7–1 CONDUCTANCE VS. RESISTANCE

It is well known that some materials, especially metals, permit electrical currents to easily flow through them. These materials, whose atomic structures readily provide free electrons, are referred to as good conductors.

Silver is the best of such conductors, but it is seldom used because of its high cost. Copper is almost as good a conductor as silver, is relatively inexpensive, and serves for most types of wiring. Aluminum, a fairly good conductor, is used where weight reduction is an important factor.

By contrast, other materials tend to prevent current from flowing through them. Such substances are known as nonconductors or insulators. Examples of insulators are glass, rubber, and nylon.

It is important to realize that not all materials can be so easily classified. The degree of conductivity varies over an extremely wide range. Conductors and insulators merely represent two extremes between which a great variety of materials are classified as poor conductors or semiconductors.

Among these poor conductors are metals and alloys that find use as resistance wire in heat-producing appliances such as electric ranges and heaters. Nickel-chromium, often called nichrome, is an example of such wire.

But even the extremes do not represent absolute perfection. Every conductor, no matter how good, still offers some resistance. Just how much resistance a conductor has de- pends on four factors, namely:

1. The type of material from which it is made

2. The conductor’s length

3. Its cross-sectional area (thickness)

4. Its temperature

These factors will be explored in the following sections.

7–2 RESISTIVITY OF MATERIALS

The resistance rating of different materials is based on a comparison of the number of ohms measured in a standard-sized sample of the material. In the metric sys- tem, for instance, the standard is a 1-centimeter cube whose resistance is measured in millionths of an ohm (microhms). Look at Figure A–1 in the Appendix, and com- pare the resistivity in microhm-centimeters. This resistivity is also known as specific resistance.

In the English system of measurement, the standard of resistivity is called the mil-foot. This standard is based on the resistance of a piece of wire 1 foot long with a diameter of 0.001 inch (1 mil 5 1/1,000). Figure 7–1 illustrates the concept of a mil-foot, and the chart in Figure 7–2 shows some characteristic values of resistivity.

7–3 LENGTH OF A CONDUCTOR

The resistance of any conductor is directly proportional to its length. For example, if 50 feet of wire has a resistance of 1 ohm, then 100 feet of the same wire will have a resistance of 2 ohms. In other words, the longer the wire, the more resistance it has. This simple fact must be taken into account whenever electricians plan the installation of a long supply line.

7–4 CROSS-SECTIONAL AREA (CSA) OF A CONDUCTOR IN CIRCULAR MILS

Resistance is inversely proportional to the cross-sectional area of the wire. This is a way of saying that the thicker the wire, the lower its resistance. A thick wire, as shown in Figure 7–3, allows many electrons to move through it easily, just as a wide road can carry many cars per hour or a large pipe can allow a large volume of water to flow through it.

Because the use of square inches or square feet results in complicated calculations and inconveniently small numbers for ordinary sizes of wire, a more convenient unit of area (thickness) is used. The circle in Figure 7–4 represents the end of a wire that is 1/1,000 of an inch thick. This distance, 0.001 inch, is 1 mil. The area of this circle, which is 1 mil in diameter, is 1 circular mil (CM). A circular mil is a unit of area (A) measurement. It is the same type of measurement as a square foot or an acre but more convenient to use.

For example, what is the area of a circle with a diameter of 0.002 inch? As Figure 7–5 illustrates, such a circle has an area exactly four times larger than a circle with a diameter of inch. If either the radius or the diameter of any flat surface is doubled, then the area will increase four times. Let us look at an example using the formula for finding the area of a circle, A 5 πr2. If the radius r of circle X is 5, then the area r2 is 25π. If the radius r of circle Y is 10 (double that of circle X), then the area of circle Y is 100π (four times that of circle X). There- fore, to answer the question about the area of a circle that has a diameter of 0.002 inch, we can say that the area is four times greater than that of a 1-mil circle, or 4 circular mils.

What is the area of a circle that has a diameter of 0.003 inch? Three-thousandths of an inch is 3 mils: 32 is 9. This circle is nine times as large in area as a 1-mil circle. The area of the circle, therefore, is 9 circular mils. The area of a circle, using circular mils, can be found by the following steps:

1. Write the diameter of the circle in mils.

2. Square this number (multiply it by itself); the result is the area of the circle in circular mils.

Note: 250,000 CM is also expressed as 250 Kcmil (formerly known as 250 MCM).

If the circular mils of a wire is known, it is a simple matter to reverse the mathematical procedure and find the diameter.

EXAMPLE 7–2

Given: A conductor with cross-sectional area of 100 circular mils.

Find: Its diameter in inches.

Solution

Not all conductors are circular in shape. Solid rectangular conductors (bus bars) are used to carry large currents. Bus bars are often easier to assemble and take up less space than the large-sized round conductors required to carry the same current. In addition, the flat shape of the bus bar provides more surface area from which heat can radiate.

The cross-sectional area of such a bus bar is figured in square mils rather than in circular mils. A square mil is defined as the area of a square with sides of 0.001 inch, as illustrated in Figure 7–6.

EXAMPLE 7–3

Given: A bus bar 4 inches wide and 0.25 inch thick, as shown in Figure 7–7.

Find: Its cross-sectional area in square mils.

Calculating the Resistance of a Wire

As previously stated, the resistance of a wire is a function of its resistivity (K); see Figure 7–2. Furthermore, it is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). This statement can be written mathematically as

EXAMPLE 7–6

Given: A two-wire power line is to be erected between poles 1,200 feet apart (the length of the wire is 2,400 feet). Resistance of the line should not be more than 1.7 ohms.

Find: The size of the aluminum wire to be used.

Solution

6–4 ELECTRICAL METER CONNECTION

The proper techniques of connecting electrical meters should be demonstrated and practiced in a laboratory setting. It is assumed that the reader has access to such facilities. However, the following guidelines are offered for your review and consideration:

1. When using multifunction test instruments, be sure that the test leads are correctly inserted into the proper jacks (terminal openings) designated for the task.

2. Always connect voltmeters parallel to a load or source; see Figure 6–11.

3. Always connect ammeters in series. To establish such a connection, break the circuit and then insert the meter into the break; see Figure 6–12.

4. DC meters are polarized: positive (+) and negative (–). Take care to connect the positive (red-colored) test lead toward the positive end of the source. If mistakes are made in the polarization, the pointer will deflect downhill, that is, to the left of 0.

5. When ohmmeters are applied to a circuit, be sure that the power is turned off. Better yet, disconnect one side of the resistance to be measured.

6. When meters with multiple ranges are employed, protect the meter by switching to the highest range first to prevent overloading.

SUMMARY

• Analog meters are instruments in which numerical data are represented by the position of a moving pointer over a scale.

• Multimeters, such as VOMs, serve different functions with multiple ranges.

• The range of a meter at maximum deflection must not be exceeded.

• DC meters must be correctly polarized.

• Voltmeters are connected in parallel.

• Ammeters are connected in series.

• Resistors must be disconnected from the circuit before an ohmmeter is attached.

Achievement Review

PART I DC VOLTMETER READING

Look at the scale of a DC voltmeter shown on page 75. Then assume that the pointer deflects to the individual settings as shown in the chart on page 74 and that the range selector is in the position indicated. Your instructor will give further instruction as necessary.

PART II DC AMMETER READING

Look at the scale of a DC ammeter shown on page 77. Next, assume that the pointer deflects to the individual settings shown in the chart on page 76 and that the range selector is in the position indicated. Your instructor will give further explanation if necessary.

PART III CIRCUIT CHECKS

Following are schematics of a number of circuits with instruments attached. Some of these schematics have mistakes incorporated. Your task is to check each circuit for mistakes. Circle the mistake(s) as you see them, and briefly explain what is wrong. If no mistakes are found, label the drawing OK and state what is being measured, for example, RT, I2, E1.

6–4 ELECTRICAL METER CONNECTION

The proper techniques of connecting electrical meters should be demonstrated and practiced in a laboratory setting. It is assumed that the reader has access to such facilities. However, the following guidelines are offered for your review and consideration:

1. When using multifunction test instruments, be sure that the test leads are correctly inserted into the proper jacks (terminal openings) designated for the task.

2. Always connect voltmeters parallel to a load or source; see Figure 6–11.

3. Always connect ammeters in series. To establish such a connection, break the circuit and then insert the meter into the break; see Figure 6–12.

4. DC meters are polarized: positive (+) and negative (–). Take care to connect the positive (red-colored) test lead toward the positive end of the source. If mistakes are made in the polarization, the pointer will deflect downhill, that is, to the left of 0.

5. When ohmmeters are applied to a circuit, be sure that the power is turned off. Better yet, disconnect one side of the resistance to be measured.

6. When meters with multiple ranges are employed, protect the meter by switching to the highest range first to prevent overloading.

SUMMARY

• Analog meters are instruments in which numerical data are represented by the position of a moving pointer over a scale.

• Multimeters, such as VOMs, serve different functions with multiple ranges.

• The range of a meter at maximum deflection must not be exceeded.

• DC meters must be correctly polarized.

• Voltmeters are connected in parallel.

• Ammeters are connected in series.

• Resistors must be disconnected from the circuit before an ohmmeter is attached.

Achievement Review

PART I DC VOLTMETER READING

Look at the scale of a DC voltmeter shown on page 75. Then assume that the pointer deflects to the individual settings as shown in the chart on page 74 and that the range selector is in the position indicated. Your instructor will give further instruction as necessary.

PART II DC AMMETER READING

Look at the scale of a DC ammeter shown on page 77. Next, assume that the pointer deflects to the individual settings shown in the chart on page 76 and that the range selector is in the position indicated. Your instructor will give further explanation if necessary.

PART III CIRCUIT CHECKS

Following are schematics of a number of circuits with instruments attached. Some of these schematics have mistakes incorporated. Your task is to check each circuit for mistakes. Circle the mistake(s) as you see them, and briefly explain what is wrong. If no mistakes are found, label the drawing OK and state what is being measured, for example, RT, I2, E1.

Electrical Quantity Measurement

6–1 TYPES OF METERS

The traditional meters have a pointer moving across the face of a scale (similar to the speedometer in many cars). Such instruments are classified as analog meters. Readings from analog meters are generally limited to three-digit accuracy. The third digit must often be estimated and, therefore, is uncertain.

Most electrical measuring devices, from panel meters for permanent installations to portable test instruments, have made use of such analog scales. Throughout most of the twentieth century, one of the widely used portable test instruments has been the VOM (short for volt-ohm-milliamperes). Figure 6–1 shows such an instrument, while Figure 6–2 displays a magnified view of its frontal features. Compare the two figures and note that the setting of the selector switch (the large knob in the center) reveals the function and range of the instrument, which, in turn, determines the proper scale to be read. Careful inspection will reveal that the selector switch can be set to read DC volts in the upper left-hand quadrant of the circle and AC volts in the upper right-hand quadrant. Current readings in milliamperes or amperes, either DC or AC, are obtained by settings in the lower right-hand quadrant, and ohms readings are found in the lower left-hand section, as indicated by the Greek letter omega (Ω).

Note that the top scale, reading ohms, is inverted with the zero reading on the right-hand side of the scale. In preparation for a resistance reading the test leads must be shorted (touched together), whereupon the instrument pointer should move toward the 0-ohm position. If the needle does not quite reach the zero position, the instrument must be “nulled” or “zeroed in” by turning the control labeled ADJ.

By contrast, Figure 6–3 is the picture of a modern DMM (digital multimeter), which directly displays the numerical results of the measurement. Digital instruments such as this are the first choice in today’s market for new acquisitions and installations, but analog

meters will still be with us for a long time to come. Therefore, students are urged to practice reading meter scales.

6–2 AMMETER AND VOLTMETER SCALE INTERPRETATION

The skill of interpreting various analog scales is a necessary and valuable asset to any technician. Students are therefore encouraged to carefully follow the examples given in the following pages, even though they may be using predominantly digital instruments in the laboratory.

A portion of an easy-to-read meter scale is shown in Figure 6–4. Note that the space between whole-number values is divided into 10 parts so that each small division is equal to 0.1 (one-tenth). If the pointer is at position 1, the indicated amount is 0.3. At position 2, the pointer is halfway between 1.70 and 1.80, so the indicated reading is At position 3, the pointer is at the 2.6 mark.

Always be careful to note the value by the small divisions on the scale. On the meter in Figure 6–5, each small division is equal to 0.2. At position 1, the pointer is at 0.6; at position 2, the pointer is at 3.5; and at position 3, the pointer indicates 5.2.

It is customary to use decimals rather than common fractions to record the values of meter readings. For example, a scale reading is given as 8.75 rather than 83⁄4, or as 7.4 rather than 72⁄5.

The scale of Figure 6–6 represents a dual-range ammeter. Such an instrument would generally have three terminals for making the connections labeled COM, 3 A, and 30 A. (The abbreviation COM denotes the terminal, which is common to all measurements.)

For the 30-ampere range (top scale), the test leads are connected to the COM and 30 A terminals. For the 3-ampere range (bottom scale), connections are made to the COM and the 3 A terminals.

The range of a meter is the maximum amount of the instrument at full-scale deflection. For the protection of the meter, the range should never be exceeded. Therefore, it is wise to measure unknown quantities on the higher range first before switching to a lower range for the sake of greater accuracy.

Notice that in our example, Figure 6–6, each pointer position has two different interpretations.

The scale in Figure 6–7 shows pointers indicating values at 0.08, 0.35, 1.04, and 1.49, the smallest divisions representing 0.02 ampere.

Figure 6–8 represents the scale of a 50-ampere ammeter. The smallest divisions here represent 0.5 ampere. The first position of the pointer indicates 22 amperes. De- pending on the accuracy of the meter mechanism, the next indicated position may be called 38.25 because the pointer is halfway between 38.0 and 38.5. However, if the accuracy of the meter is to within 2% of the full-scale reading, then the meter is accurate to within only 1 ampere. Therefore, there is no point in worrying about determining the meter reading to an accuracy of 0.5 ampere. To justify a meter reading of 38.5, the meter must have an accuracy of 1% or better, and to justify the 38.25, an accuracy of 0.5%.

When reading an analog dial, the observer’s line of sight should be perpendicular to the surface of the scale. If it is not perpendicular, a reading error known as parallax is

introduced, Figure 6–9. Therefore, highly accurate meters have a narrow mirror strip along the scale to help prevent such reading errors. The VOM depicted in Figure 6–1 is equipped with a scale mirror. On this kind of scale, the correct alignment is achieved when the mirror image of the pointer disappears behind the pointer itself.

6–3 OHMMETER SCALE INTERPRETATION

We are accustomed to reading analog meters with their numbers arranged from left to right and with the 0 digit on the left-hand side of the scale.

Most ohmmeters have the numbers of their scales arranged from right to left, with the 0 on the right-hand side of the scale, Figure 6–10. Recall that such instruments must be adjusted to the zero position by means of a special control (see explanation in Section 6–1).

Note that this is a nonlinear scale where equal spaces do not represent equal values. Note, for instance, that the space from 0 to 1 is greater than the space between 10 and 20. This makes the meter readings much more accurate toward the lower end of the scale (the right-hand side).

Ohmmeters generally have a range switch indicating multiplier values, such as 3 1, 3 100, 3 1K, 3 100K. This means that each reading taken on the scale must be multi- plied by the value indicated on the range switch.

Electrical Quantity Measurement

6–1 TYPES OF METERS

The traditional meters have a pointer moving across the face of a scale (similar to the speedometer in many cars). Such instruments are classified as analog meters. Readings from analog meters are generally limited to three-digit accuracy. The third digit must often be estimated and, therefore, is uncertain.

Most electrical measuring devices, from panel meters for permanent installations to portable test instruments, have made use of such analog scales. Throughout most of the twentieth century, one of the widely used portable test instruments has been the VOM (short for volt-ohm-milliamperes). Figure 6–1 shows such an instrument, while Figure 6–2 displays a magnified view of its frontal features. Compare the two figures and note that the setting of the selector switch (the large knob in the center) reveals the function and range of the instrument, which, in turn, determines the proper scale to be read. Careful inspection will reveal that the selector switch can be set to read DC volts in the upper left-hand quadrant of the circle and AC volts in the upper right-hand quadrant. Current readings in milliamperes or amperes, either DC or AC, are obtained by settings in the lower right-hand quadrant, and ohms readings are found in the lower left-hand section, as indicated by the Greek letter omega (Ω).

Note that the top scale, reading ohms, is inverted with the zero reading on the right-hand side of the scale. In preparation for a resistance reading the test leads must be shorted (touched together), whereupon the instrument pointer should move toward the 0-ohm position. If the needle does not quite reach the zero position, the instrument must be “nulled” or “zeroed in” by turning the control labeled ADJ.

By contrast, Figure 6–3 is the picture of a modern DMM (digital multimeter), which directly displays the numerical results of the measurement. Digital instruments such as this are the first choice in today’s market for new acquisitions and installations, but analog

meters will still be with us for a long time to come. Therefore, students are urged to practice reading meter scales.

6–2 AMMETER AND VOLTMETER SCALE INTERPRETATION

The skill of interpreting various analog scales is a necessary and valuable asset to any technician. Students are therefore encouraged to carefully follow the examples given in the following pages, even though they may be using predominantly digital instruments in the laboratory.

A portion of an easy-to-read meter scale is shown in Figure 6–4. Note that the space between whole-number values is divided into 10 parts so that each small division is equal to 0.1 (one-tenth). If the pointer is at position 1, the indicated amount is 0.3. At position 2, the pointer is halfway between 1.70 and 1.80, so the indicated reading is At position 3, the pointer is at the 2.6 mark.

Always be careful to note the value by the small divisions on the scale. On the meter in Figure 6–5, each small division is equal to 0.2. At position 1, the pointer is at 0.6; at position 2, the pointer is at 3.5; and at position 3, the pointer indicates 5.2.

It is customary to use decimals rather than common fractions to record the values of meter readings. For example, a scale reading is given as 8.75 rather than 83⁄4, or as 7.4 rather than 72⁄5.

The scale of Figure 6–6 represents a dual-range ammeter. Such an instrument would generally have three terminals for making the connections labeled COM, 3 A, and 30 A. (The abbreviation COM denotes the terminal, which is common to all measurements.)

For the 30-ampere range (top scale), the test leads are connected to the COM and 30 A terminals. For the 3-ampere range (bottom scale), connections are made to the COM and the 3 A terminals.

The range of a meter is the maximum amount of the instrument at full-scale deflection. For the protection of the meter, the range should never be exceeded. Therefore, it is wise to measure unknown quantities on the higher range first before switching to a lower range for the sake of greater accuracy.

Notice that in our example, Figure 6–6, each pointer position has two different interpretations.

The scale in Figure 6–7 shows pointers indicating values at 0.08, 0.35, 1.04, and 1.49, the smallest divisions representing 0.02 ampere.

Figure 6–8 represents the scale of a 50-ampere ammeter. The smallest divisions here represent 0.5 ampere. The first position of the pointer indicates 22 amperes. De- pending on the accuracy of the meter mechanism, the next indicated position may be called 38.25 because the pointer is halfway between 38.0 and 38.5. However, if the accuracy of the meter is to within 2% of the full-scale reading, then the meter is accurate to within only 1 ampere. Therefore, there is no point in worrying about determining the meter reading to an accuracy of 0.5 ampere. To justify a meter reading of 38.5, the meter must have an accuracy of 1% or better, and to justify the 38.25, an accuracy of 0.5%.

When reading an analog dial, the observer’s line of sight should be perpendicular to the surface of the scale. If it is not perpendicular, a reading error known as parallax is

introduced, Figure 6–9. Therefore, highly accurate meters have a narrow mirror strip along the scale to help prevent such reading errors. The VOM depicted in Figure 6–1 is equipped with a scale mirror. On this kind of scale, the correct alignment is achieved when the mirror image of the pointer disappears behind the pointer itself.

6–3 OHMMETER SCALE INTERPRETATION

We are accustomed to reading analog meters with their numbers arranged from left to right and with the 0 digit on the left-hand side of the scale.

Most ohmmeters have the numbers of their scales arranged from right to left, with the 0 on the right-hand side of the scale, Figure 6–10. Recall that such instruments must be adjusted to the zero position by means of a special control (see explanation in Section 6–1).

Note that this is a nonlinear scale where equal spaces do not represent equal values. Note, for instance, that the space from 0 to 1 is greater than the space between 10 and 20. This makes the meter readings much more accurate toward the lower end of the scale (the right-hand side).

Ohmmeters generally have a range switch indicating multiplier values, such as 3 1, 3 100, 3 1K, 3 100K. This means that each reading taken on the scale must be multi- plied by the value indicated on the range switch.