by Earl Boysen
Answers
A.
B. VA = VB = 10 volts
C. 0 V (There is no voltage drop because both terminals are at the same voltage.)
32 The circuit shown in Figure 1.13 includes an open switch.
Figure 1.13
Questions
A. What is the voltage at point A and point B? __________
B. How much current is flowing through the switch? __________
C. What is the voltage drop across the switch? __________
Answers
A. VA = 10 volts; VB = 0 volts.
B. No current is flowing because the switch is open.
C. 10 volts. If the switch is open, point A is the same voltage as the positive battery terminal, and point B is the same voltage as the negative battery terminal.
33 The circuit shown in Figure 1.14 includes a single pole double throw switch. The position of the switch determines whether lamp A or lamp B is lit.
Figure 1.14
Questions
A. In the position shown, which lamp is lit? __________
B. Can both lamps be lit simultaneously? __________
Answers
A. Lamp A.
B. No, one or the other must be off.
Capacitors in a DC Circuit
34 Capacitors are used extensively in electronics. They are used in both alternating current (AC) and DC circuits. Their main use in DC electronics is to become charged, hold the charge, and, at a specific time, release the charge.
The capacitor shown in Figure 1.15 charges when the switch is closed.
Figure 1.15
Question
To what final voltage will the capacitor charge? _____
Answers
It will charge up to 10 volts. It will charge up to the voltage that would appear across an open circuit located at the same place where the capacitor is located.
35 How long does it take to reach this voltage? This is an important question with many practical applications. To find the answer you must know the time constant (τ) (Greek letter tau) of the circuit.
Questions
A. What is the formula for the time constant of this type of circuit? __________
B. What is the time constant for the circuit shown in Figure 1.15? __________
C. How long does it take the capacitor to reach 10 volts? __________
D. To what voltage level does it charge in one time constant? __________
Answers
A. τ = R × C.
B. τ = 10 kΩ × 10 μF = 10,000 Ω × 0.00001 F = 0.1 seconds. (Convert resistance values to ohms and capacitance values to farads for this calculation.)
C. Approximately 5 time constants, or about 0.5 seconds.
D. 63 percent of the final voltage, or about 6.3 volts.
36 The capacitor does not begin charging until the switch is closed. When a capacitor is uncharged or discharged, it has the same voltage on both plates.
Questions
A. What is the voltage on plate A and plate B of the capacitor in Figure 1.15 before the switch is closed? __________
B. When the switch is closed, what happens to the voltage on plate A? __________
C. What happens to the voltage on plate B? __________
D. What is the voltage on plate A after one time constant? __________
Answers
A. Both will be at 0 volts if the capacitor is totally discharged.
B. It will rise toward 10 volts.
C. It will stay at 0 volts.
D. About 6.3 volts.
37 The capacitor charging graph in Figure 1.16 shows how many time constants a voltage must be applied to a capacitor before it reaches a given percentage of the applied voltage.
Figure 1.16
Questions
A. What is this type of curve called? __________
B. What is it used for? __________
Answers
A. It is called an exponential curve.
B. It is used to calculate how far a capacitor has charged in a given time.
38 In the following examples, a resistor and a capacitor are in series. Calculate the time constant, how long it takes the capacitor to fully charge, and the voltage level after one time constant if a 10-volt battery is used.
Questions
A. R = 1 kΩ, C = 1,000 μF __________ B. R = 330 kΩ, C = 0.05 μF __________
Answers
A. τ = 1 second; charge time = 5 seconds; VC = 6.3 volts.
B. τ = 16.5 ms; charge time = 82.5 ms; VC = 6.3 volts. (The abbreviation “ms” indicates milliseconds.)
39 The circuit shown in Figure 1.17 uses a double pole switch to create a discharge path for the capacitor.
Figure 1.17
Questions
A. With the switch in position X, what is the voltage on each plate of the capacitor? __________
B. When the switch is moved to position Y, the capacitor begins to charge. What is its charging time constant? __________
C. How long does it take to fully charge the capacitor?
Answers
A. 0 volts
B. τ = R × C = (100 kΩ) (100 μF) = 10 secs
C. Approximately 50 seconds
40 Suppose that the switch shown in Figure 1.17 is moved back to position X after the capacitor is fully charged.
Questions
A. What is the discharge time constant of the capacitor? __________
B. How long does it take to fully discharge the capacitor? __________
Answers
A. τ = R × C = (50 kΩ) (100 μF) = 5 seconds (discharging through the 50 kΩ resistor)
B. Approximately 25 seconds
The circuit powering a camera flash is an example of a capacitor's capability to store a charge and then discharge upon demand. While you wait for the flash unit to charge, the camera uses its battery to charge a capacitor. When the capacitor is charged, it holds that charge until you click the Shutter button, causing the capacitor to discharge, which powers the flash.
Inside the Capacitor
Capacitors store an electrical charge on conductive plates that are separated by an insulating material, as shown in the following figure. One of the most common types of capacitor is a ceramic capacitor, which has values ranging from a few μF up to approximately 47 μF. The name for a ceramic capacitor comes from the use of a ceramic material to provide insulation between the metal plates.
Another common type of capacitor is an electrolytic capacitor, available with capacitance values ranging from 0.1 μF to several thousand μF. The name electrolytic comes from the use of an electrolytic fluid, which, because it is conductive, acts as one of the “plates,” whereas the other plate is made of metal. The insulating material is an oxide on the surface of the metal.
Unlike ceramic capacitors, many electrolytic capacitors are polarized, which means that you must insert the lead marked with a “+” in the circuit closest to the positive voltage source. The symbol for a capacitor indicates the direction in which you insert polarized capacitors in a circuit. The curved side of the capacitor symbol indicates the negative side of the capacitor, whereas the straight side of the symbol indicates the positive side of the capacitor. You can see this orientation later in this chapter in Figure 1.22.
Units of capacitance are stated in pF (picofarad), μF (microfarad), and F (farad). One μF equals 1,000,000 pF and one F equals 1,000,000 μF. Many capacitors are marked with their capacitance value, such as 220 pF. However, you'll often find capacitors that use a different numerical code, such as 224. The first two numbers in this code are the first and second significant digits of the capacitance value. The third number is the multiplier, and the units are pF. Therefore, a capacitor marked with 221 has a value of 220 pF, whereas a capacitor with a marking of 224 has a value of 220,000 pF. (You can simplify this to 0.22 μF.)
41 Capacitors can be connected in parallel, as shown in Figure 1.18.
Figure 1.18
Questions
A. What is the form
ula for the total capacitance? __________
B. What is the total capacitance in circuit 1? __________
C. What is the total capacitance in circuit 2? __________
Answers
A. CT = C1 + C2 + C3 + … + CN
B. CT = 1 + 2 = 3 μF
C. CT = 1 + 2 + 3 = 6 μF
In other words, the total capacitance is found by simple addition of the capacitor values.
42 Capacitors can be placed in series, as shown in Figure 1.19.
Figure 1.19
Questions
A. What is the formula for the total capacitance? __________
B. In Figure 1.19, what is the total capacitance? __________
Answers
A.
B.
43 In each of these examples, the capacitors are placed in series. Find the total capacitance.
Questions
A. C1 = 10 μF, C2 = 5 μF __________
B. C1 = 220 μF, C2 = 330 μF, C3 = 470 μF __________
C. C1 = 0.33 μF, C2 = 0.47 μF, C3 = 0.68 μF __________
Answers
A. 3.3 μF
B. 103.06 μF
C. 0.15 μF
Summary
The few simple principles reviewed in this chapter are those you need to begin the study of electronics. Following is a summary of these principles:
The basic electrical circuit consists of a source (voltage), a load (resistance), and a path (conductor or wire).
The voltage represents a charge difference.
If the circuit is a complete circuit, then electrons flow, which is called current flow. The resistance offers opposition to current flow.
The relationship between V, I, and R is given by Ohm's law:
Resistance could be a combination of resistors in series, in which case you add the values of the individual resistors together to get the total resistance.
Resistance can be a combination of resistors in parallel, in which case you find the total by using the following formula:
You can find the power delivered by a source by using the following formula:
You can find the power dissipated by a resistance by using the following formula:
If you know the total applied voltage, VS, you can find the voltage across one resistor in a series string of resistors by using the following voltage divider formula:
You can find the current through one resistor in a two resistor parallel circuit with the total current known by using the current divider formula:
Kirchhoff's Voltage Law (KVL) relates the voltage drops in a series circuit to the total applied voltage.
Kirchhoff's Current Law (KCL) relates the currents at a junction in a circuit by saying that the sum of the input currents equals the sum of the output currents. For a simple parallel circuit, this becomes the following, where IT is the input current:
A switch in a circuit is the control device that directs the flow of current or, in many cases, allows that current to flow.
Capacitors are used to store electric charge in a circuit. They also allow current or voltage to change at a controlled pace. The circuit time constant is found by using the following formula:
At one time constant in an RC circuit, the values for current and voltage have reached 63 percent of their final values. At five time constants, they have reached their final values.
Capacitors in parallel are added to find the total capacitance.
Capacitors in series are treated the same as resistors in parallel to find a total capacitance.
DC Pre-Test
The following problems and questions test your understanding of the basic principles presented in this chapter. You need a separate sheet of paper for your calculations. Compare your answers with the answers provided following the test. You can work many of the problems in more than one way.
Questions 1–5 use the circuit shown in Figure 1.20. Find the unknown values indicated using the values given.
Figure 1.20
1. R1 = 12 ohms, R2 = 36 ohms, VS = 24 volts
RT = _____ , I = _____
2. R1 = 1 kΩ, R2 = 3 kΩ, I = 5 mA
V1 = _____ , V2 = _____ , VS = _____
3. R1 = 12 kΩ, R2 = 8 kΩ, VS = 24 volts
V1 = _____ , V2 = _____
4. VS = 36 V, I = 250 mA, V1 = 6 volts
R2 = _____
5. Now, go back to problem 1. Find the power dissipated by each resistor and the total power delivered by the source.
P1 = _____ , P2 = _____ , PT = _____
Questions 6–8 use the circuit shown in Figure 1.21. Again, find the unknowns using the given values.
Figure 1.21
6. R1 = 6 kΩ, R2 = 12 kΩ, VS = 20 volts
RT = _____ , I = _____
7. I = 2 A, R1 = 10 ohms, R2 = 30 ohms
I1 = _____ , I2 = _____
8. VS = 12 volts, I = 300 mA, R1 = 50 ohms
R2 = _____ , P1 = _____
9. What is the maximum current that a 220- ohm resistor can safely have if its power rating is 1/4 watt?
IMAX = _____
10. In a series RC circuit the resistance is 1 kΩ, the applied voltage is 3 volts, and the time constant should be 60 μsec.
A. What is the required value of C?
C = _____
B. What is the voltage across the capacitor 60 μsec after the switch is closed?
VC = _____
C. At what time will the capacitor be fully charged?
T = _____
11. In the circuit shown in Figure 1.22, when the switch is at position 1, the time constant should be 4.8 ms.
Figure 1.22
A. What should be the value of resistor R1?
R1 = _____
B. What will be the voltage on the capacitor when it is fully charged, and how long will it take to reach this voltage?
VC = _____, T = _____
C. After the capacitor is fully charged, the switch is thrown to position 2. What is the discharge time constant, and how long will it take to completely discharge the capacitor?
τ = _____ , T = _____
12. Three capacitors are available with the following values:
C1 = 8 μF; C2 = 4 μF; C3 = 12 μF.
A. What is CT if all three are connected in parallel?
CT = _____
B. What is CT if they are connected in series?
CT = _____
C. What is CT if C1 is in series with the parallel combination of C2 and C3?
CT = _____
Answers to DC Pre-Test
If your answers do not agree with those provided here, review the problems indicated in parentheses before you go to Chapter 2, “The Diode.” If you still feel uncertain about these concepts, go to a website such as www.BuildingGadgets.com and work through DC tutorials listed there.
It is assumed that Ohm's law is well known, so problem 4 will not be referenced.
1. RT = 48 ohms, I = 0.5 ampere (problem 9)
2. V1 = 5 volts, V2 = 15 volts, VS = 20 volts (problems 23 and 26)
3. V1 = 14.4 volts, V2 = 9.6 volts (problems 23 and 26)
4. R2 = 120 ohms (problems 9 and 23)
5. P1 = 3 watts, P2 = 9 watts, PT = 12 watts (problems 9 and 13)
6. RT = 4 kΩ, I = 5 mA (problem 10)
7. I1 = 1.5 amperes, I2 = 0.5 ampere (problems 28 and 29)
8. R2 = 200 ohms, P1 = 2.88 watts (problems 10 and 13)
9. IMAX = 33.7 mA (problems 13, 15, and 16)
10A. C = 0.06 μF (problems 34 and 35)
10B. VC = 1.9 volts (problem 35)
10C. T = 300 μsec (problems 34–38)
11A. R1 = 30 kΩ (problems 33, 39, and 40)
11B. VC = 15 V, T = 24 ms (problem 35)
11C. τ = 1.6 ms, T = 8.0 ms (problems 39–40)
12A. CT = 24 μF (problems 41 and 42)
12B. CT = 2.18 μF (problem 42)
12C. CT = 5.33 μF (problems 42–43)
Chapter 2
The Diode
The main characteristic of a diode i
s that it conducts electricity in one direction only. Historically, the first vacuum tube was a diode; it was also known as a rectifier. The modern diode is a semiconductor device. It is used in all applications where the older vacuum tube diode was used, but it has the advantages of being much smaller, easier to use, and less expensive.
A semiconductor is a crystalline material that, depending on the conditions, can act as a conductor (allowing the flow of electric current) or an insulator (preventing the flow of electric current). Techniques have been developed to customize the electrical properties of adjacent regions of semiconductor crystals, which allow the manufacture of small diodes, as well as transistors and integrated circuits.
When you complete this chapter, you can do the following:
Specify the uses of diodes in DC circuits.
Determine from a circuit diagram whether a diode is forward- or reverse-biased.
Recognize the characteristic V-I curve for a diode.
Specify the knee voltage for a silicon or a germanium diode.
Calculate current and power dissipation in a diode.