Complete Electronics Self-Teaching Guide with Projects
Page 2
16 Resistors used in electronics generally are manufactured in standard values with regard to resistance and power rating. Appendix D shows a table of standard resistance values for 0.25- and 0.05-watt resistors. Quite often, when a certain resistance value is needed in a circuit, you must choose the closest standard value. This is the case in several examples in this book.
You must also choose a resistor with the power rating in mind. Never place a resistor in a circuit that requires that resistor to dissipate more power than its rating specifies.
Questions
If standard power ratings for carbon film resistors are 1/8, 1/4, 1/2, 1, and 2 watts, what power ratings should be selected for the resistors that were used for the calculations in problem 15?
A. For 5 watts _____
B. For 0.224 watts _____
C. For 0.5 watts _____
D. For 0.4 watts _____
Answers
A. 5 watt (or greater)
B. 1/4 watt (or greater)
C. 1/2 watt (or greater)
D. 1/2 watt (or greater)
Most electronics circuits use low-power carbon film resistors. For higher-power levels (such as the 5-watt requirement in question A), other types of resistors are available.
Small Currents
17 Although currents much larger than 1 ampere are used in heavy industrial equipment, in most electronic circuits, only fractions of an ampere are required.
Questions
A. What is the meaning of the term milliampere? __________
B. What does the term microampere mean? __________
Answers
A. A milliampere is one-thousandth of an ampere (that is, 1/1000 or 0.001 amperes). It is abbreviated mA.
B. A microampere is one-millionth of an ampere (that is, 1/1,000,000 or 0.000001 amperes). It is abbreviated μA.
18 In electronics, the values of resistance normally encountered are quite high. Often, thousands of ohms and occasionally even millions of ohms are used.
Questions
A. What does kΩ mean when it refers to a resistor? __________
B. What does MΩ mean when it refers to a resistor? __________
Answers
A. Kilohm (k = kilo, Ω = ohm). The resistance value is thousands of ohms. Thus, 1 kΩ = 1,000 ohms, 2 kΩ = 2,000 ohms, and 5.6 kΩ = 5,600 ohms.
B. Megohm (M = mega, Ω = ohm). The resistance value is millions of ohms. Thus, 1 MΩ = 1,000,000 ohms, and 2.2 MΩ = 2,200,000 ohms.
19 The following exercise is typical of many performed in transistor circuits. In this example, 6 volts is applied across a resistor, and 5 mA of current is required to flow through the resistor.
Questions
What value of resistance must be used and what power will it dissipate?
R = _____ P = _____
Answers
20 Now, try these two simple examples.
Questions
What is the missing value?
A. 50 volts and 10 mA. Find the resistance. __________
B. 1 volt and 1 MΩ. Find the current. __________
Answers
A. 5 kΩ
B. 1 μA
The Graph of Resistance
21 The voltage drop across a resistor and the current flowing through it can be plotted on a simple graph. This graph is called a V-I curve.
Consider a simple circuit in which a battery is connected across a 1 kΩ resistor.
Questions
A. Find the current flowing if a 10-volt battery is used. __________
B. Find the current when a 1-volt battery is used. __________
C. Now find the current when a 20-volt battery is used. __________
Answers
A. 10 mA
B. 1 mA
C. 20 mA
22 Plot the points of battery voltage and current flow from problem 21 on the graph shown in Figure 1.5, and connect them together.
Figure 1.5
Question
What would the slope of this line be equal to? _____
Answers
You should have drawn a straight line, as in the graph shown in Figure 1.6.
Figure 1.6
Sometimes you need to calculate the slope of the line on a graph. To do this, pick two points and call them A and B.
For point A, let V = 5 volts and I = 5 mA
For point B, let V = 20 volts and I = 20 mA
The slope can be calculated with the following formula:
In other words, the slope of the line is equal to the resistance.
Later, you learn about V-I curves for other components. They have several uses, and often they are not straight lines.
The Voltage Divider
23 The circuit shown in Figure 1.7 is called a voltage divider. It is the basis for many important theoretical and practical ideas you encounter throughout the entire field of electronics.
Figure 1.7
The object of this circuit is to create an output voltage (V0) that you can control based upon the two resistors and the input voltage. V0 is also the voltage drop across R2.
Question
What is the formula for V0? _____
Answers
R1 + R2 = RT, the total resistance of the circuit.
24 A simple example can demonstrate the use of this formula.
Question
For the circuit shown in Figure 1.8, what is V0? _____
Figure 1.8
Answers
25 Now, try these problems.
Questions
What is the output voltage for each combination of supply voltage and resistance?
A. VS = 1 volt, R1 = 1 ohm, R2 = 1 ohm
V0 = _____
B. VS = 6 volts, R1 = 4 ohms, R2 = 2 ohms
V0 = _____
C. VS = 10 volts, R1 = 3.3. kΩ, R2 = 5.6 kΩ
V0 = _____
D. VS = 28 volts, R1 = 22 kΩ, R2 = 6.2 kΩ
V0 = _____
Answers
A. 0.5 volts
B. 2 volts
C. 6.3 volts
D. 6.16 volts
26 The output voltage from the voltage divider is always less than the applied voltage. Voltage dividers are often used to apply specific voltages to different components in a circuit. Use the voltage divider equation to answer the following questions.
Questions
A. What is the voltage drop across the 22 k resistor for question D of problem 25? __________
B. What total voltage do you get if you add this voltage drop to the voltage drop across the 6.2 k resistor? __________
Answers
A. 21.84 volts
B. The sum is 28 volts.
The voltages across the two resistors add up to the supply voltage. This is an example of Kirchhoff's Voltage Law (KVL), which simply means that the voltage supplied to a circuit must equal the sum of the voltage drops in the circuit. In this book, KVL is often used without actual reference to the law.
Also the voltage drop across a resistor is proportional to the resistor's value. Therefore, if one resistor has a greater value than another in a series circuit, the voltage drop across the higher-value resistor is greater.
Using Breadboards
A convenient way to create a prototype of an electronic circuit to verify that it works is to build it on a breadboard. You can use breadboards to build the circuits used in the projects later in this book. As shown in the following figure, a breadboard is a sheet of plastic with several contact holes. You use these holes to connect electronic components in a circuit. After you verify that a circuit works with this method, you can then create a permanent circuit using soldered connections.
Breadboards contain metal strips arranged in a pattern under the contact holes, which are used to connect groups of contacts together. Each group of five contact holes in a vertical line (such as the group circled in the figure) is connected by these metal strips. Any components plugged into one of these five contact holes are, therefore, electrically connected.
Ea
ch row of contact holes marked by a “+” or “−” are connected by these metal strips. The rows marked “+” are connected to the positive terminal of the battery or power supply and are referred to as the +V bus. The rows marked “−” are connected to the negative terminal of the battery or power supply and are referred to as the ground bus. The 1V buses and ground buses running along the top and bottom of the breadboard make it easy to connect any component in a circuit with a short piece of wire called a jumper wire. Jumper wires are typically made of 22-gauge solid wire with approximately 1/4 inch of insulation stripped off each end.
The following figure shows a voltage divider circuit assembled on a breadboard. One end of R1 is inserted into a group of contact holes that is also connected by a jumper wire to the 1V bus. The other end of R1 is inserted into the same group of contact holes that contains one end of R2. The other end of R2 is inserted into a group of contact holes that is also connected by a jumper wire to the ground bus. In this example, a 1.5 kΩ resistor was used for R1, and a 5.1 kΩ resistor was used for R2.
A terminal block is used to connect the battery pack to the breadboard because the wires supplied with battery packs (which are stranded wire) can't be inserted directly into breadboard contact holes. The red wire from a battery pack is attached to the side of the terminal block that is inserted into a group of contact holes, which is also connected by a jumper wire to the 1V bus. The black wire from a battery pack is attached to the side of the terminal block that is inserted into a group of contact holes, which is also connected by a jumper wire to the ground bus.
To connect the output voltage, Vo, to a multimeter or a downstream circuit, two additional connections are needed. One end of a jumper wire is inserted in the same group of contact holes that contain both R1 and R2 to supply Vo. One end of another jumper wire is inserted in a contact hole in the ground bus to provide an electrical contact to the negative side of the battery. When connecting test equipment to the breadboard, you should use a 20-gauge jumper wire because sometimes the 22-gauge wire is pulled out of the board when attaching test probes.
The Current Divider
27 In the circuit shown in Figure 1.9, the current splits or divides between the two resistors that are connected in parallel.
Figure 1.9
IT splits into the individual currents I1 and I2, and then these recombine to form IT.
Questions
Which of the following relationships are valid for this circuit?
A. VS = R1I1
B. VS = R2I2
C. R1I1 = R2I2
D. I1/I2 = R2/R1
Answers
All of them are valid.
28 When solving current divider problems, follow these steps:
1. Set up the ratio of the resistors and currents:
I1/I2 = R2/R1
2. Rearrange the ratio to give I2 in terms of I1:
3. From the fact that IT = I1 + I2, express IT in terms of I1 only.
4. Now, find I1.
5. Now, find the remaining current (I2).
Question
The values of two resistors in parallel and the total current flowing through the circuit are shown in Figure 1.10. What is the current through each individual resistor?
Figure 1.10
Answers
Work through the steps as shown here:
1. I1/I2 = R2/R1 = 1/2
2. I2 = 2I1
3. IT = I1 + I2 = I1 + 2I1 = 3I1
4. I1 = IT/3 = 2/3 ampere
5. I2 = 2I1 = 4/3 amperes
29 Now, try these problems. In each case, the total current and the two resistors are given. Find I1 and I2.
Questions
A. IT = 30 mA, R1 = 12 kΩ, R2 = 6 kΩ __________
B. IT = 133 mA, R1 = 1 kΩ, R2 = 3 kΩ __________
C. What current do you get if you add I1 and I2? __________
Answers
A. I1 = 10 mA, I2 = 20 mA
B. I1 = 100 mA, I2 = 33 mA
C. They add back together to give you the total current supplied to the parallel circuit.
Question C is actually a demonstration of Kirchhoff's Current Law (KCL). Simply stated, this law says that the total current entering a junction in a circuit must equal the sum of the currents leaving that junction. This law is also used on numerous occasions in later chapters. KVL and KCL together form the basis for many techniques and methods of analysis that are used in the application of circuit analysis.
Also, the current through a resistor is inversely proportional to the resistor's value. Therefore, if one resistor is larger than another in a parallel circuit, the current flowing through the higher value resistor is the smaller of the two. Check your results for this problem to verify this.
30 You can also use the following equation to calculate the current flowing through a resistor in a two-branch parallel circuit:
Question
Write the equation for the current I2. _____
Check the answers for the previous problem using these equations.
Answer
The current through one branch of a two-branch circuit is equal to the total current times the resistance of the opposite branch, divided by the sum of the resistances of both branches. This is an easy formula to remember.
Using the Multimeter
A multimeter is a must-have testing device for anyone's electronics toolkit. A multimeter is aptly named because it can be used to measure multiple parameters. Using a multimeter, you can measure current, voltage, and resistance by setting the rotary switch on the multimeter to the parameter you want to measure, and connecting each mulitmeter probe to a wire in a circuit. The following figure shows a multimeter connected to a voltage divider circuit to measure voltage. Following are the details of how you take each of these measurements.
Voltage
To measure the voltage in the circuit shown in the figure, at the connection between R1 and R2, use jumper wire to connect the red probe of a multimeter to the row of contact holes containing leads from both R1 and R2. Use another jumper wire to connect the black probe of the multimeter to the ground bus. Set the rotary switch on the multimeter to measure voltage, and it returns the results.
Note The circuit used in a multimeter to measure voltage places a large-value resistor in parallel with R2 so that the test itself does not cause any measurable drop in the current passing through the circuit.
Tip Whenever you perform tests on a circuit, attach alligator clips or test clips with plastic covers to the ends of the probes. This aids the probes in grabbing the jumper wires with little chance that they'll cause a short.
Current
The following figure shows how you connect a multimeter to a voltage divider circuit to measure current. Connect a multimeter in series with components in the circuit, and set the rotary switch to the appropriate ampere range, depending upon the magnitude of the expected current. To connect the multimeter in series with R1 and R2, use a jumper wire to connect the +V bus to the red lead of a multimeter, and another jumper wire to connect the black lead of the multimeter to R1. These connections force the current flowing through the circuit to flow through the multimeter.
Note The circuit used in a multimeter to measure current passes the current through a low-value resistor so that the test itself does not cause any measurable drop in the current.
Resistance
You typically use the resistance setting on a multimeter to check the resistance of individual components. For example, in measuring the resistance of R2 before assembling the circuit shown in the previous figure, the result was 5.0 kΩ, slightly off the nominal 5.1 kΩ stated value.
You can also use a multimeter to measure the resistance of a component in a circuit. A multimeter measures resistance by applying a small current through the components being tested, and measuring the voltage drop. Therefore, to prevent false readings, you should disconnect the battery pack or power supply from the circuit before using the multimeter.
Switches
; 31 A mechanical switch is a device that completes or breaks a circuit. The most familiar use is that of applying power to turn a device on or off. A switch can also permit a signal to pass from one place to another, prevent its passage, or route a signal to one of several places.
In this book, you work with two types of switches. The first is the simple on-off switch, also called a single pole single throw switch. The second is the single pole double throw switch. Figure 1.11 shows the circuit symbols for each.
Figure 1.11
Keep in mind the following two important facts about switches:
A closed (or ON) switch has the total circuit current flowing through it. There is no voltage drop across its terminals.
An open (or OFF) switch has no current flowing through it. The full circuit voltage appears between its terminals.
The circuit shown in Figure 1.12 includes a closed switch.
Figure 1.12
Questions
A. What is the current flowing through the switch? __________
B. What is the voltage at point A and point B with respect to ground? __________
C. What is the voltage drop across the switch? __________