Gibilisco S. Teach Yourself Electricity and Electronics

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3. In the scenario shown by Fig. 5-9, what is the voltage across the combination of R

and R

(a) 0.22 V

(b) 0.22 mV

(d) 3.3 V

4. Suppose three resistors are connected in parallel across a battery that delivers 15 V, and the

ohmic values are R

= 470 Ω, R

= 2.2 kΩ, and R

= 3.3 kΩ, as shown in Fig. 5-10. The voltage

across the resistance R

(a) 4.4 V.

(b) 5.0 V.

(d) not determinable from the data given.

Quiz 81

5-9 Illustration for Quiz

Questions 2, 3, 8, and

9. Resistance values are

in ohms.

5-10 Illustration for Quiz

Questions 4, 5, 6, 7, 10, and

11. Resistances are in ohms,

where k indicates

multiplication by 1000.

5. In the situation shown by Fig. 5-10, what is the current through R

(a) 6.8 mA

(b) 43 mA

(d) 6.8 A

6. In the situation shown by Fig. 5-10, what is the total current drawn from the source?

(a) 6.8 mA

(b) 43 mA

(d) 6.8 A

7. In the situation shown by Fig. 5-10, suppose that resistor R

opens up. The current through

the other two resistors will

(a) increase.

(b) decrease.

(d) not change.

8. Suppose that four resistors are connected in series with a 6.0-V supply, with values shown in

Fig. 5-9. What is the power dissipated by the whole combination?

(a) 0.2 W

(b) 6.5 mW

(d) 6.5 W

9. In the situation shown by Fig. 5-9, what is the power dissipated by R

(a) 11 mW

(b) 0.11 W

(d) 6.5 mW

10. Suppose that three resistors are in parallel as shown in Fig. 5-10. What is the power dissipated

by the whole set of resistors?

(a) 5.4 W

(b) 5.4 µW

(d) 0.65 W

11. In the situation shown by Fig. 5-10, what is the power dissipated in resistance R

(a) 32 mW

(b) 0.48 W

(d) 31 W

12. Fill in the blank in the following sentence to make it true: “In a series or parallel dc circuit, the

sum of the

s in each component is equal to the total provided by the power supply.”

(a) current

(b) voltage

(d) resistance

13. Look at Fig. 5-5A. Suppose the resistors each have values of 33 Ω and the battery supplies 24

V. What is the current I

(a) 1.1 A

(b) 0.73 A

82 Direct-Current Circuit Analysis

(d) Not determinable from the information given

14. Look at Fig. 5-5B. Let each resistor have a value of 820 Ω. Suppose the top three resistors all

lead to identical light bulbs. If I

= 50 mA and I

= 70 mA, what is the power dissipated in the

resistor carrying current I

(a) 33 W

(b) 40 mW

(d) It can’t be found using the information given.

15. Refer to Fig. 5-6. Suppose the resistances R

, R

, and R

are in exactly the ratio 1:2:4:8

from left to right, and the battery supplies 30 V. What is the voltage E

(a) 4.0 V

(b) 8.0 V

(d) It is not determinable from the data given.

16. Refer to Fig. 5-6. Suppose the resistances are each 3.3 kΩ, and the battery supplies 12 V. If the

plus terminal of a dc voltmeter is placed between resistances R

and R

(with voltages E

and E

across them, respectively), and the minus terminal of the voltmeter is placed between resistances R

and R

(with voltages E

and E

across them, respectively), what will the meter register?

(a) 0.0 V

(b) 3.0 V

(d) 12 V

17. In a voltage divider network, the total resistance

(a) should be large to minimize current drain.

(b) should be as small as the power supply will allow.

(d) should be such that the current is kept to 100 mA.

18. The maximum voltage output from a voltage divider

(a) is a fraction of the power supply voltage.

(b) depends on the total resistance.

(d) depends on the ratio of resistances.

19. Refer to Fig. 5-7. Suppose the battery voltage E is 18.0 V, and there are four resistances in the

network such that R

= 100 Ω, R

= 22.0 Ω, R

= 33.0 Ω, and R

= 47.0 Ω. What is the voltage

at P

(a) 4.19 V

(b) 13.8 V

Quiz 83

(d) 2.94 V

20. Refer to Fig. 5-7. Suppose the battery voltage is 12 V, and you want to obtain intermediate

voltages of 3.0 V, 6.0 V, and 9.0 V. Suppose that a maximum of 200 mA is allowed to be drawn

from the battery. What should the resistances, R

, R

, and R

be, respectively?

(a) 15 Ω, 30 Ω, 45 Ω, and 60 Ω

(b) 60 Ω, 45 Ω, 30 Ω, and 15 Ω

(d) There isn’t enough information given here to design the circuit.

84 Direct-Current Circuit Analysis

ALL ELECTRICAL COMPONENTS, DEVICES, AND SYSTEMS HAVE SOME RESISTANCE. IN EVERYDAY PRACTICE,

there is no such thing as a perfect electrical conductor. You’ve seen some examples of circuits con-

taining components that are deliberately designed to oppose the flow of current. These components

are resistors. In this chapter, you’ll learn all about them.

Purpose of the Resistor

Resistors play diverse roles in electrical and electronic equipment. Here are a few of the more com-

mon ways they are used.

Voltage Division

You’ve learned how voltage dividers can be designed using resistors. The resistors dissipate some

power in doing this job, but the resulting voltages can provide the proper biasing of electronic cir-

cuits. This ensures, for example, that an amplifier or oscillator will function in the most efficient, re-

liable way possible.

Bias

The term bias means, in the case of a bipolar transistor, a field-effect transistor, or a vacuum tube, that

the control electrode—the base, gate, or grid—is provided with a certain voltage, or made to carry a

certain current, relative to the emitter, source, or cathode. Networks of resistors can accomplish this.

A radio transmitting amplifier is biased differently than an oscillator or a low-level receiving

amplifier. Sometimes voltage division is required for biasing. Other times it isn’t necessary. Figure

6-1 shows a bipolar transistor whose base is biased using a pair of resistors in a voltage divider con-

figuration.

Current Limiting

Resistors interfere with the flow of electrons in a circuit. Sometimes this is essential to prevent

damage to a component or circuit. A good example is a receiving amplifier. A resistor can keep the

CHAPTER

Resistors

transistor from using up a lot of power just getting hot. Without resistors to limit or control the cur-

rent, the transistor can be overstressed carrying direct current that doesn’t contribute to the signal.

Figure 6-2 shows a current-limiting resistor between the emitter of a bipolar transistor and electri-

cal ground.

Power Dissipation

The dissipation of power in the form of heat is not always a bad thing. Sometimes a resistor can be

used as a dummy component, so a circuit sees the resistor as if it were something more complicated.

When testing a radio transmitter, for example, a resistor can be used to take the place of an antenna.

This keeps the transmitter from interfering with communications on the airwaves. The transmitter

output heats the resistor without radiating any signal. But as far as the transmitter knows, it’s con-

nected to a real antenna (Fig. 6-3)—and a perfect one, too, if the resistor has just the right ohmic

value!

86 Resistors

6-1 A pair of resistors can

act as a voltage divider

to bias the base of a

transistor.

6-2 A resistor can limit the

current that passes

through the emitter of

a transistor.

Another situation in which power dissipation is useful is at the input of a power amplifier, such

as the sort used in high-fidelity audio equipment. Sometimes the circuit driving the amplifier (sup-

plying its input signal) has too much power. A resistor, or network of resistors, can dissipate this

excess so that the amplifier doesn’t get too much drive. In any type of amplifier, overdrive (an exces-

sively strong input signal) can cause distortion, inefficiency, and other problems.

Bleeding Off Charge

In a high-voltage, dc power supply, capacitors are used to smooth out the fluctuations in the out-

put. These capacitors acquire an electric charge, and they store it for a while. In some power sup-

plies, these filter capacitors hold the full output voltage of the supply, say something like 750 V, even

after the supply has been turned off, and even after it is unplugged from the wall outlet. If you at-

tempt to repair such a power supply, you can be electrocuted by this voltage. Bleeder resistors, con-

nected across the filter capacitors, drain their stored charge so that servicing the supply is not

dangerous. In Fig. 6-4, the bleeder resistor, R, should have a value high enough so that it doesn’t in-

terfere with the operation of the power supply, but low enough so it will discharge the capacitor, C,

in a short time after the power supply has been shut down.

Purpose of the Resistor 87

6-3 At A, a radio transmitter is connected to a real

antenna. At B, the same transmitter is connected

to a resistive dummy antenna.

It’s a good idea to short out all filter capacitors, using a screwdriver with an insulated handle and

wearing heavy, insulated gloves, before working on a dc power supply. Even if the supply has bleeder

resistors, they might take a while to get rid of the residual charge. In addition, bleeder resistors can,

and sometimes do, fail.

Impedance Matching

A more sophisticated application for resistors is in the coupling in a chain of amplifiers, or in the

input and output circuits of amplifiers. In order to produce the greatest possible amplification, the

impedances must agree between the output of a given amplifier and the input of the next. The same

is true between a source of signal and the input of an amplifier. Also, this applies between the out-

put of an amplifier and a load, whether that load is a speaker, a headset, or whatever.

Impedance is the ac “big brother” of dc resistance. You will learn about impedance in Part 2 of

this book.

Fixed Resistors

There are several ways in which fixed resistors (units whose resistance does not change, or cannot be

adjusted) are manufactured. Here are the most common types.

Carbon-Composition Resistors

The cheapest method of making a resistor is to mix up powdered carbon (a fair electrical conduc-

tor) with some nonconductive substance, press the resulting claylike stuff into a cylindrical shape,

and insert wire leads in the ends (Fig. 6-5). The resistance of the final product depends on the ratio

88 Resistors

6-4 A bleeder resistor (R) is

connected across the

filter capacitor (C) in a

power supply.

6-5 Construction of a

carbon-composition

resistor.

of carbon to the nonconducting material, and also on the physical distance between the wire leads.

This results in a carbon-composition resistor.

Carbon-composition resistors can be manufactured in a wide range of resistance values. This

kind of resistor also has the advantage of being nonreactive, meaning that it introduces almost

pure resistance into the circuit, and not much capacitance or inductance. This makes carbon-

composition resistors useful in radio receivers and transmitters.

Carbon-composition resistors dissipate power according to how big, physically, they are. Most

of the carbon-composition resistors you see in electronics stores can handle

⁄4 W or

⁄2 W. There are

⁄8-W units available for miniaturized, low-power circuitry, and 1- or 2-W units for circuits where

some electrical ruggedness is needed. Occasionally you’ll see a carbon-composition resistor with a

much higher power rating, but these are rare.

Wirewound Resistors

Another way to get resistance is to use a length of wire that isn’t a good conductor. The wire can be

wound around a cylindrical form as a coil (Fig. 6-6). The resistance is determined by how well the

wire metal conducts, by its diameter or gauge, and by its stretched-out length. This type of compo-

nent is called a wirewound resistor.

Fixed Resistors 89

6-6 Construction of a

wirewound resistor.

Wirewound resistors can be manufactured to have values within a very close range. They are

precision components. Also, wirewound resistors can be made to handle large amounts of power. A

disadvantage of wirewound resistors, in some applications, is that they act like inductors. This

makes them unsuitable for use in most radio-frequency circuits. Wirewound resistors usually have

low to moderate values of resistance.

Film-Type Resistors

Carbon, resistive wire, or some mixture of ceramic and metal can be applied to a cylindrical form as

a film, or thin layer, in order to obtain a specific resistance. This type of component is called a car-

bon-film resistor or metal-film resistor. Superficially, it looks like a carbon-composition resistor, but

the construction is different (Fig. 6-7).

The cylindrical form is made of an insulating substance, such as porcelain. The film is deposited

on this form by various methods, and the value tailored as desired. Metal-film resistors can be made

to have nearly exact values. Film-type resistors usually have low to medium-high resistance.

A major advantage of film-type resistors is that they, like carbon-composition resistors, do not

have much inductance or capacitance. A disadvantage, in some applications, is that they can’t han-

dle as much power as carbon-composition or wirewound types.

Integrated-Circuit (IC) Resistors

Resistors can be fabricated on a semiconductor wafer known as an integrated circuit (IC), also called

a chip. The thickness, and the types and concentrations of impurities added, control the resistance

of the component. Integrated-circuit resistors can handle only a tiny amount of power because of

their small size.

The Potentiometer

Figure 6-8 is a simplified drawing of the construction of a potentiometer, or variable resistor. A resis-

tive strip, similar to that found on film-type fixed resistors, is bent into a nearly complete circle, and

terminals are connected to either end. This forms a fixed resistance. To obtain the variable resist-

ance, a sliding contact is attached to a rotatable shaft and bearing, and is connected to a third ter-

minal. The resistance between the middle terminal and either of the end terminals can vary from

zero up to the resistance of the whole strip.

Some potentiometers use a straight strip of resistive material, and the control moves up and

down or from side to side. This type of variable resistor, called a slide potentiometer, is used in hi-fi

audio graphic equalizers, as the volume controls in some hi-fi audio amplifiers, and in other applica-

tions when a linear scale is preferable to a circular scale. Potentiometers are manufactured to handle

low levels of current, at low voltage.

Linear-Taper Potentiometer

One type of potentiometer uses a strip of resistive material whose density is constant all the way

around. This results in a linear taper. The resistance between the center terminal and either end ter-

minal changes at a steady rate as the control shaft is turned.

90 Resistors

6-7 Construction of a

film-type resistor.