Exercise Problems 2.5
I V ----, orR
= I E
R
---=
Figure 2-13(b) shows the same basic circuit, but the applied voltage is higher. The higher voltage causes more current to flow in the circuit. This should seem reasonable to you since voltage is the force that causes current to flow and resistance is what limits current flow. If there is an increased force trying to cause current flow, but the opposition to current flow (resistance) remains constant, then it should seem logical that the current flow will increase. Figure 2-13(c) illustrates the effect of reducing the voltage to a value below that in Figure 2-13(a).
The relationship between current and voltage is called linearly proportional. This impor-tant relationship is shown graphically in Figure 2-14. It is common for technical informa-tion to be expressed graphically; a technician must be able to interpret and understand graphical information. The horizontal scale of the graph shown in Figure 2-14 represents the voltage in the circuit. The vertical scale shows the resulting current flow. From any given voltage value, you can move vertically (as indicated by the dotted lines in Figure 2-14) until you intersect the resistance line, and then move horizontally from that point until you intersect the current axis. The point of intersection on the current axis indicates the amount of current that flows with the given applied voltage and the value of resistance represented by the resistance line.
Current Is Inversely Proportional to Resistance
Figure 2-15 examines the second part of Ohm’s Law, which states that current flow is inversely proportional to resistance. Figure 2-15(a) shows that a voltage source connected across a certain resistance will cause a given amount of current to flow. We could compute the value of current with Equation 2-6. Figure 2-15(b) shows that current becomes less when the resistance in the circuit is increased. This should seem reasonable since resistance
RT VT
– +
I
10 V
I
(a)
RT VT
– +
I
20 V Higher current
Lower current
(b)
RT VT
– +
I
5 V
(c) Figure 2-13. Current in a circuit is directly proportional to applied voltage.
is a measure of the opposition to current flow. Finally, Figure 2-15(c) illustrates that current in the circuit will increase if the opposition (resistance) is reduced.
The inverse relationship between current and resistance is shown graphically in Figure 2-16. As you move to the right along the horizontal scale (more resistance), you can see that the corresponding values of current flow on the vertical scale are less.
Figure 2-14. A graph showing the linearly proportional relationship between applied voltage and the resulting current flow in a fixed resistance circuit.
Current (mA)
R = 500 Ω 45
40 35 30 25 20 15 10 5 0
0 2 4 6 8 10
Voltage
12 14 16 18 20
VT R
– +
I
I Less I
Less
More I More
(a)
VT R
– +
I
(b)
VT R
– +
I
(c) Figure 2-15. More resistance causes less current flow.
Alternate Forms of Ohm’s Law
We can manipulate the basic Ohm’s Law equation (Equation 2-6), as we can with any equation, to obtain the alternate forms shown as Equations 2-7 and 2-8.
COMPUTE I WHEN V AND R ARE KNOWN
If a technician knows the values of voltage and resistance in a circuit, then he can calculate the value of current by applying Equation 2-6. The units of measure for voltage and resis-tance are volts and ohms, respectively. The unit of measure for the resulting current is amperes.
EXAMPLE SOLUTION
How much current flows through a 25-Ω resistor with 10 V across it?
EXAMPLE SOLUTION
We apply Ohm’s Law (Equation 2-6) as follows:
(2-7) (2-8) Figure 2-16. Current is inversely proportional to resistance.
Current (mA)
Voltage = 100 V 45
40 35 30 25 20 15 10 5 0
0 2 4 6 8 10
Resistance (kΩ)
12 14 16 18 20
R V
----I
=
V = IR
There are three basic equations that express Ohm’s Law:
• I = V/R
• V = IR
• R = V/I
KEY POINTS
I V ----R
= 10
25--- 0.40 A
= =
EXAMPLE SOLUTION
If an electric circuit has 120 V applied and has a total resistance of 20 Ω, how much current is flowing in the circuit?
EXAMPLE SOLUTION
We apply Ohm’s Law (Equation 2-6) as follows:
COMPUTE R WHEN V AND I ARE KNOWN
If the current and voltage in an electric circuit are known, then the resistance can be computed by applying Equation 2-7. Again, the units of measure for voltage, current, and resistance are volts, amperes, and ohms, respectively.
EXAMPLE SOLUTION
If a certain resistor allows 250 mA to flow when 35 V are across it, what is its resistance?
EXAMPLE SOLUTION
Ohm’s Law (Equation 2-7) provides our answer as follows:
EXAMPLE SOLUTION
How much resistance is required in an electric circuit to restrict the current flow to 8.5 A when 240 V are applied?
EXAMPLE SOLUTION We apply Equation 2-7.
COMPUTE V WHEN I AND R ARE KNOWN
If a technician knows the current and resistance values in an electric circuit, then she can calculate the value of applied voltage with Ohm’s Law (Equation 2-8).
I V ----R
= 120
---20 6.0 A
= =
R V
----I
= 35 250×10–3
---= 140 Ω
=
R V
----I
= 240 V
8.5 A
--- 28.24 Ω
= =
EXAMPLE SOLUTION
How much voltage must be connected across a 1.2-kΩ resistor to cause 575 µA of current to flow?
EXAMPLE SOLUTION
We apply Equation 2-8 as follows:
EXAMPLE SOLUTION
How much voltage is required to cause 20 A of current to flow through a 5-Ω resistor?
EXAMPLE SOLUTION
Practice Problems Practice Problems
Apply Ohm’s Law to solve the following problems.
1. How much current flows through a 680-kΩ resistor that has 12 V across it?
2. If a 10-kΩ resistor has 100 µA flowing through it, how much voltage is across it?
3. What value of resistance is required in a circuit to limit the current to 2.7 A when 220 V are applied?
Answers to Practice Problems
Power Calculations Based on Ohm’s Law
When working with electronic circuits, it is generally more convenient to compute power in terms of more common circuit quantities (voltage, current, and resistance). There are three basic formulas that we will use extensively for computing the electrical power in a circuit. First, the power dissipated in a component or an entire circuit is given by the product of voltage and current. This is expressed formally as Equation 2-9.
1. 17.6 µA 2. 1.0 V 3. 81.5 Ω
(2-9) V = IR
575×10–6×1.2×103
=
690 mV
=
V = IR
20 A×5 Ω 100 V
= =
P = VI
We can use this basic power equation and the Ohm’s Law relationships previously cited to develop two more important power relationships.
and,
These two important power relationships are given formally as Equations 2-10 and 2-11.
Equations 2-9, 2-10, and 2-11 are the basic power formulas that we will use throughout the remainder of this text. We will refer to these collectively as the power formulas.
In many cases, these calculations are used to determine the amount of electrical power that is converted to heat. For example, when electron current flows through a conductor, the free electrons lose energy as they collide with atoms in the material. Much of the energy loss is converted to heat, so the material heats up. Figure 2-17 shows the application of these equations to an electrical circuit.
Your electric toaster or electric oven are two excellent examples of electrical energy being consumed as power. When current passes through the heating elements, it encounters opposition or resistance. Much of the electrical energy supplied to the heating element is converted to heat; some is converted to light energy as the element glows red hot.
(2-10)
There are three basic power formulas:
Figure 2-17. The amount of electrical power in a circuit is directly related to the voltage, current, and resistance in the circuit.
EXAMPLE SOLUTION
How much power is expended in an electrical circuit when 50 V is connected across a 25-Ω resistance?
EXAMPLE SOLUTION
We can apply Equation 2-10 directly as follows:
EXAMPLE SOLUTION
How much current must flow through a 100-kΩ resistance in order to produce 5 W of power?
EXAMPLE SOLUTION
We apply Equation 2-11 as follows:
Practice Problems Practice Problems
1. How much power is dissipated when 300 mA flows through a 50-Ω resistance?
2. How much voltage is required to produce 25 W in a 150-Ω resistance?
3. If a certain electrical device has 120 V applied and has 3.5 A of current flow, how much power is dissipated?
Answers to Practice Problems
1. How much current would flow through a 10-kΩ resistor if a 12-V source were connected across it?
2. Calculate the amount of current through a 100-Ω resistor that has 1.5 V across it.
1. 4.5 W 2. 61.2 V 3. 420 W P V2
---R
= 502 V ---25 Ω
= 100 W
=
P = I2R, or
I P
R
---=
5 W 100×103Ω
--- 7.07 mA
= =
Exercise Problems 2.6 Exercise Problems 2.6
3. What value of resistance is required to limit the current in a circuit to 25 mA with 100 V applied?
4. It takes 1.2 kΩ of resistance to limit the current flow to 10 mA when a 25-V source is applied. (True or False)
5. How much voltage must be connected across a 27-kΩ resistor to cause 5 mA of current to flow?
6. Which circuit has the most resistance: a) a circuit with 12 V applied and 100 mA of current flow, or b) a circuit with 100 V applied and a current of 5 mA?
7. If 6.3 V are impressed across a 20-Ω resistance, how much power is expended?
8. How much current flows through a 51-Ω resistance if it is dissipating 200 W?
9. How much voltage is needed to cause 350 mW to be dissipated in a 2.7-kΩ resistance?
10. How much power is dissipated by an automobile radio that operates on 12 V and draws 1.2 A?
11. Which resistance would produce the most heat: 300 Ω with 25 V across it or 100 Ω with 2.5 A of current through it?
2.7 Resistors
A resistor is one of the most fundamental components used in electronic circuits. A resistor is constructed to have a specific amount of resistance to current flow. Resistors range in value from less than 1 Ω to well over 20 MΩ. They also vary in size from micro-scopic through devices that are too large to carry. In general, we can classify resistors into two categories: fixed and variable. Fixed resistors have a single value of resistance. Variable resistors are made to be adjustable so that they can provide different values of resistance.
We will examine both classes of resistors in the following paragraphs.
Fixed Resistors
There are many types of fixed resistors, but they all have at least three characteristics that are important to a technician:
• value
• power rating
• tolerance
All of these characteristics are determined at the time the resistor is manufactured. They cannot be altered by the user. The value of the resistor indicates the nominal or ideal amount of resistance exhibited by the resistor. Like all resistance, it is measured in ohms.
Figure 2-18 shows several types of fixed resistors.
RESISTOR POWER RATING
When current flows through a resistor, it encounters opposition, which creates heat. If a resistor dissipates too much heat, it will be damaged. The damage may range from a slight change in the resistance value to complete physical disintegration of the resistor body.
A resistor is a fundamen-tal component used in electronic circuits to pro-vide a definite amount of opposition to current flow.
KEY POINTS
The value of a fixed resistor cannot be changed once it has been manufactured.
KEY POINTS
Every resistor has a power rating. This indicates the amount of power that can be dissi-pated for an indefinite amount of time without degrading the performance of the resistor.
The power rating of a resistor is largely, but not solely, determined by the physical size of the resistor. The greater the surface area of the resistor, the more power it can dissipate.
Thus, as a general rule, the physical size of a resistor is an indication of its power rating.
Resistor power ratings range from less than 0.1 W to many hundreds of watts. The most common power ratings are 1/8, 1/4, 1/2, 1, and 2 W. Figure 2-19 shows resistors with several different power ratings.
RESISTOR TOLERANCE
Manufacturers cannot make resistors with exactly the right value. There is a certain degree of variation between resistors that are ideally the same value. The manufacturer guarantees that the actual value of the resistor will be within a certain percentage of its nominal or marked value. The allowable variation—expressed as a percent—is called the resistor tolerance.
Figure 2-18. There are many types of fixed resistors.
The power rating of a resistor specifies the max-imum power that can be safely dissipated by the resistor without damage.
KEY POINTS
Resistor power ratings are given in watts.
KEY POINTS
Figure 2-19. The power rating of a resistor is largely affected by its physical size.
Resistors cannot be man-ufactured to exact values, so they are given a toler-ance rating.
KEY POINTS
The most common resistor tolerances are 1%, 2%, 5%, 10%, and 20%. As a general rule, tighter tolerance resistors are more expensive. Resistors with tolerances lower than 2% are often called precision resistors. Resistors with a 20% tolerance are rarely used in modern designs. The tolerance may be either positive or negative. That is, the actual resistor value may be smaller (negative tolerance) or larger (positive tolerance) than the marked value.
The maximum deviation between actual and marked values for a particular resistor is computed by multiplying the tolerance percentage by the marked value of the resistor.
This computation is given by Equation 2-12.
We can determine the highest resistance value that a particular resistor can have and still be within tolerance by adding the maximum deviation to the marked value. The minimum acceptable resistance value is computed by subtracting the maximum deviation from the marked value. Thus, the range of resistance values is given by Equation 2-13.
EXAMPLE SOLUTION
A certain resistor is marked as 1,000 Ω with a 10% tolerance. Compute the maximum deviation and the range of possible resistance values.
EXAMPLE SOLUTION
First we apply Equation 2-12 to determine the maximum deviation.
We now apply Equation 2-13 to calculate the range of resistor values that are within the toler-ance specification.
Practice Problems Practice Problems
1. A certain resistor is marked as 330 Ω with a 20% tolerance. Compute the maxi-mum deviation and the range of possible resistance values.
2. Determine the highest and lowest resistor value that a 22-kΩ resistor can have, if it has a 5% tolerance.
3. If a resistor that was marked as 39 kΩ, 10% actually measured 37,352 Ω, would it be within tolerance?
(2-12)
(2-13) maximum deviation = tolerance×marked value
resistance range= marked value ± maximum deviation
maximum deviation = tolerance×marked value 0.1×1,000 Ω 100 Ω
= =
resistance range = marked value±maximum deviation lowest value = 1,000–100 = 900 Ω
highest value = 1,000+100 = 1,100 Ω
Answers to Practice Problems
RESISTOR TECHNOLOGY
We shall examine four major classes of fixed resistor technology:
• carbon-composition resistors
• film resistors
• wirewound resistors
• surface-mount technology (SMT) CARBON-COMPOSITION RESISTORS
Carbon-composition resistors are one of the oldest types of resistors used today. They are far from obsolete, however. Figure 2-20 shows a cutaway view of a carbon-composition resistor. They are manufactured by making a slurry of finely ground carbon (fairly low-resistance material), a powdered filler (high-low-resistance material), and a liquid binder. The slurry is pressed into cylindrical forms and the leads are attached. Finally, the resistor is coated with a hard nonconductive coating and then color banded to indicate its value.
Resistors of different values are made by altering the ratio of carbon to filler material. The higher the percentage of carbon, the lower the resistance of the resistor. The power rating is made higher by increasing the physical size of the resistor.
FILM RESISTORS
Film resistors come in several varieties. A film resistor is made by depositing a thin layer of resistive material onto an insulating tube or rod called the substrate. The general range of resistance is established by the resistivity of the material used. Leads are attached to end caps which contact the ends of the resistive film.
Once the resistive layer has been deposited, it is trimmed with a high-speed industrial laser. As the laser etches away portions of the deposited film, the resistance of the device increases. The laser normally trims the resistor to the correct value by cutting a spiral
1. maximum deviation: 66 Ω;
range: 264 Ω to 396 Ω 2. 20.9 kΩ and 23.1 kΩ 3. Yes.
Carbon-composition resistors use a mixture of carbon and an insulating filler as the resistive ele-ment; this mixture is pressed into a cylindrical form.
KEY POINTS
Figure 2-20. A cutaway view of a carbon-composition resistor.
Film resistors are made by depositing a thin layer of resistive material on an insulating rod.
KEY POINTS
pattern along the length of the resistor body. This method of trimming is called spiraling.
The laser, in combination with automatic test fixtures can produce resistors that are very close to the desired value.
Several types of materials are used as the film material in film resistors: carbon (carbon film), nickel-chromium (metal film), metal and glass mixture (metal glaze), metal and oxide (metal oxide). Each technology provides advantages over the others, including such things as power ratings, ability to withstand momentary surges, reaction to environmental extremes, resistance to physical abuse, and changes in resistance with aging. Figure 2-21 shows a cutaway view of a typical film resistor.
WIREWOUND RESISTORS
Wirewound resistors are made by winding resistive wire around an insulating rod. The ends of the wire are connected to leads, and the body of the resistor is coated with a hard insulative jacket. The value of a particular wirewound resistor is determined by the type of wire, diameter of the wire, and the length of the wire used to wind the resistor. Wirewound resistors are generally used for their high power ratings, but they are sometimes selected because of their precise values (precision resistors). Figure 2-22 shows a cutaway view of a wirewound resistor. Sometimes a wide colored band is painted on the resistor body to identify it as a wirewound type.
SURFACE-MOUNT RESISTORS
Because there is a continuing demand for smaller electronic products, there is an associ-ated demand for smaller electronic components. One common method for reducing the size of an electronic product is to utilize SMT. Surface-mount resistors have no leads.
Their contacts solder directly to pads on the printed circuit board. Surface-mount resistors are manufactured by spreading a resistive layer onto a ceramic substrate. The resistive
Solder coated copper wire
Metal film on ceramic core
Multiple coating
Figure 2-21. A cutaway view of a film resistor.
(a)
(b)
Wirewound resistors are made by wrapping resis-tive wire around an insu-lating rod.
KEY POINTS
Wirewound resistors have higher power ratings for a given physical size than the other resistor types.
KEY POINTS
Surface-mount resistors have no external leads and are used when small size is an important con-sideration.
KEY POINTS
coating is then covered with a layer of glass for protection. Figure 2-23 shows a cutaway view of a surface-mount resistor.
RESISTOR COLOR CODE (THREE- ANDFOUR-BAND)
Since many resistors are physically small, it is impractical to print their value with numbers big enough to read. Instead, manufacturers often mark resistors with three to five colored bands to indicate their value. The colors are assigned according to a code standardized by the Electronic Industries Association (EIA). It is essential for a technician to memorize this code and know how to use it.
All-welded cap and lead assembly
Heat-conducting ceramic substrate
Silicone conformal coating
Alpha-digital marking Alloy resistance wire wound to specific
parameters including TCRs from +20 to +5500 ppm/°C
–
Figure 2-22. A cutaway view of a wirewound resistor.
Nickel Tin/lead solder
Organic protection
Thick-film conductor
Wraparound terminations for soldering
Figure 2-23. (a) A cutaway view of a surface-mount resistor. (b) Typical surface mount resistors. The head of a straight pin is shown for perspective.
(a) (b)
Table 2-1 shows the relationship between a particular digit and its corresponding color in the standard color code. Figure 2-24 shows how to interpret the colored bands on a three- or four-band resistor.
Three- or four-band resistors can be interpreted by applying the following procedure:
1. The first two bands represent the first two digits of the resistance value.
2. Multiply the digits obtained in step one by the value of the third (multiplier) band.
3. If there is a fourth band, it indicates the tolerance, otherwise tolerance is ±20%.