Chapter 2

Working with Resistors

In This Chapter

Understanding and measuring resistance

Calculating resistance with Ohm’s law

Determining resistor values and tolerance

Working with resistors in series, parallel and combination

Creating a voltage-divider circuit

Looking at how a potentiometer varies resistance

Sci-fi villains the Borg from Star Trek: The Next Generation had a saying: ‘Resistance is futile’. Captain Picard and the rest of the crew of the Enterprise eventually proved the Borg wrong of course.

Resistance isn’t useful only in battling hostile aliens – it’s also vital in electronics, which is all about manipulating the flow of current. One of the most basic ways to do so is to reduce it through resistance. Without resistance, current flows unregulated with no way to coax it into doing useful work.

In this chapter, you find out what resistance is and how to work with resistors, which are little devices that let you introduce resistance intentionally into your circuits. Along the way, you discover a fundamental relationship in the nature of electricity between voltage, current and resistance. This relationship is expressed in a simple mathematical formula called Ohm’s law. (Don’t worry, the maths isn’t complicated; if you know how to multiply and divide, you can understand Ohm’s law.) We also show you the most common ways in which resistors are used in circuits.

What Is Resistance?

As we discuss in Book I, a conductor is a material that allows current to flow and an insulator is a material that doesn’t. Good conductors allow current to flow with abandon, without impediments. Examples of good conductors include the metals copper and aluminium. Carbon is also an excellent conductor. Good insulators, on the other hand, erect solid walls that completely block current. Examples of good insulators include glass, Teflon and plastic.

The key factor that determines whether a material is a conductor or an insulator is how readily its atoms give up electrons to move charge along. Most atoms are very possessive of their electrons, and are therefore good insulators. But some atoms don’t have a strong hold on their outermost electrons. Those atoms are good conductors.

Creating resistance

If a conductor and an insulator are mixed together, the result is a compound that conducts current, but not very well. Such a compound has resistance – that is, it resists the flow of current. The degree to which the compound resists current depends on the exact mix of elements that make up the compound.

For example, a conducting material such as carbon may be mixed with an insulating material such as ceramic. If the mix is mostly carbon, the overall resistance of the mixture is low. If the mix is mostly ceramic, the overall resistance is high.

The truth is that all materials have some resistance. Even the best conductors have a small but measurable amount of resistance. The only exceptions are certain materials called superconductors that, when chilled to unbelievably low temperatures, conduct with 100% efficiency. Unfortunately, you can’t buy superconductors at your local electronic shop, and even if you could, you’d never get a freezer powerful enough to chill the stuff down to absolute zero.

Measuring resistance

Resistance is measured in units called ohms, represented by the Greek letter omega (Ω). The standard definition of 1 ohm is simple: the amount of resistance required to allow 1 ampere of current to flow when 1 V of voltage is applied to the circuit. In other words, if you connect a 1 ohm resistor across the terminals of a 1 V battery, 1 amp of current flows through the resistor (unless it is rated at less than 1 W, in which case it will go pop!).

A single ohm (1 Ω) is in fact a very small amount of resistance. Electronic circuits usually call for resistances in the hundreds, thousands or even millions of ohms.

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In Book I, Chapter 8, you discover that you can measure resistance of a circuit using an ohmmeter, which is a standard feature found in most multimeters. The procedure is simple: you disconnect all voltage sources from the circuit and then touch the ohmmeter’s two probes to the ends of the circuit and read the resistance (in ohms) on the meter.

Here are a few other points to consider about resistance and ohms:

Abbreviations: The abbreviations k (for kilo) and M (for mega) are used for thousands and millions of ohms. Thus, a 1,000-ohm resistance is written as 1 kΩ, and a 1,000,000-ohm resistance is written as 1 MΩ.

  Zero resistance: For the purposes of most electronic circuits, you can assume that the resistance value of ordinary wire is zero ohms (0 Ω). In reality, however, only superconductors have a resistance of 0 Ω. Even copper wire has some resistance. Therefore, the resistance of wire is usually measured in terms of ohms per kilometre. Though, of course, electronic circuits usually deal with wires that are at most a few centimetres or metres long, not kilometres.

Short circuits essentially have zero resistance.

  Infinite resistance: Just as you can think of ordinary wire and short circuits as having zero resistance, insulators and open circuits can be considered to have infinite resistance, though in reality no such thing exists as completely infinite resistance.

If you connect two wires to the terminals of a battery and hold the wires apart, a voltage exists between the ends of those two wires, and a very small current travels between them – even through the air because air doesn’t have infinite resistance. This current is extraordinarily small – too small to even measure – but it’s present nonetheless. Electric currents are literally everywhere.

Looking at Ohm’s Law

The term Ohm’s law refers to one of the fundamental relationships found in electric circuits: for a given resistance, current is directly proportional to voltage. In other words, if you increase the voltage through a circuit whose resistance is fixed, the current goes up. If you decrease the voltage, the current goes down.

Ohm’s law expresses this relationship as a simple mathematical formula:

In this formula, V stands for voltage (in volts), I stands for current (in amperes) and R stands for resistance (in ohms).

Ohm’s law is incredibly useful because it lets you calculate an unknown voltage, current or resistance. In short, if you know two of these three quantities you can calculate the third.

Here’s an example of how to calculate voltage in a circuit with a lamp powered by the two AA cells. Suppose you already know that the resistance of the lamp is 12 Ω, and the current flowing through the lamp is 250 mA (which is the same as 0.25 A). Then, you can calculate the voltage as follows:

Go back (if you dare) to your school algebra class and remember that you can rearrange the terms in a simple formula such as Ohm’s law to create other equivalent formulas. In particular:

If you don’t know the voltage, you calculate it by multiplying the current by the resistance:

If you don’t know the current, you can calculate it by dividing the voltage by the resistance:

If you don’t know the resistance, you can calculate it by dividing the voltage by the current:

To convince yourself that these formulas work, look again at the circuit with a lamp that has 12 Ω of resistance connected to two AA batteries for a total voltage of 3 V. Then you can calculate the current flowing through the lamp as follows:

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If you know the battery voltage (3 V) and the current (250 mA, which is 0.25 A), you can calculate the resistance of the lamp like this:

The most important thing to remember about Ohm’s law is that you must always do the calculations in terms of volts, amperes and ohms. For example, if you measure the current in milliamps (which you usually do in electronic circuits), you have to convert the milliamps to amperes by dividing by 1,000. For example, 250 mA is 0.25 A.

As we say in the preceding section, the definition of 1 ohm is the amount of resistance that allows 1 ampere of current to flow when 1 V of potential is applied to it. This definition is based on Ohm’s law. If V is 1 and I is 1, R must also be 1:

Introducing Resistors

A resistor is a small component that’s designed to provide a specific amount of resistance in a circuit. Because resistance is an essential element of nearly every electronic circuit, you’re going to use resistors in just about every circuit you build.

Although resistors come in a variety of sizes and shapes, the most common type for hobby electronics is the carbon film resistor, shown in Figure 2-1. These resistors consist of a layer of carbon laid down on an insulating material and contained in a small cylinder, with wire leads attached to both ends.

Figure 2-1: Carbon film resistors.

Resistors are blind to the polarity in a circuit. Thus, you don’t have to worry about installing them backwards. Current can pass equally through a resistor in either direction.

  A resistor appears in schematic diagrams as an open rectangle, like the one shown here in the margin. The resistance value is typically written next to the resistor symbol. In addition, an identifier such as R1 or R2 is also sometimes written next to the symbol.

  In some schematics, particularly those drawn in America, the jagged line symbol as shown in the margin is used instead of the rectangle.

Resistors are used for many reasons in electronic circuits. The three most popular uses are:

Limiting current: You can use resistors to introduce resistance into a circuit to limit the amount of current that flows through the circuit. In accordance with Ohm’s law, if the voltage in a circuit remains the same, the current decreases if you increase the resistance.

Many electronic components have an appetite for current that has to be regulated by resistors. One of the best known is the light-emitting diode (LED), which is a special type of diode that emits visible light when current runs through it. Unfortunately, LEDs don’t know when to step away from the table when it comes to consuming current, because they have very little internal resistance. Plus LEDs don’t have much tolerance for current, so too much current burns them out. (Flip to the later section ‘Limiting Current with a Resistor’ for more on limiting currents and LEDs.)

As a result, always place a resistor in series with an LED to keep the LED from burning itself up. (You can find out a whole lot more about LEDs in Chapter 5 of this minibook.)

You can use Ohm’s law to your advantage when using current-limiting resistors. For example, if you know what the supply voltage is and you know how much current you need, you can use Ohm’s law to determine the right resistor to use for the circuit as we explain in the preceding section.

Dividing voltage: You can use resistors to reduce voltage to a level that’s appropriate for specific parts of your circuit. For example, suppose your circuit is powered by a 3 V battery but a part of your circuit needs 1.5 V. You can use two resistors of equal value to split this voltage in half, yielding 1.5 V. For more information, see the section ‘Dividing Voltage’ later in this chapter.

Resistor/capacitor networks: You can use resistors in combination with capacitors for a variety of interesting purposes. Read about this use of resistors in Chapter 3 of this minibook.

Reading Resistor Colour Codes

You can determine the resistance provided by a resistor by examining the colour codes that are painted on the resistor. These little stripes of bright colours indicate two important factoids about the resistor: its resistance in ohms and its tolerance, which indicates how close to the indicated resistance value the resistor actually is.

Most resistors have four stripes of colour. The first three stripes indicate the resistance value and the fourth one indicates the tolerance. Some resistors have five stripes of colour, with four representing the resistance value and the last one the tolerance.

If you’re uncertain from which side of the resistor to read the colours, start with the side closest to the colour stripe. The first stripe is usually painted very close to the edge of the resistor; the last stripe isn’t as close to the edge.

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Working out a resistor’s value

To read a resistor’s colour code, check out Table 2-1. Here’s the procedure for determining the value of a resistor with four stripes:

1. Turn the resistor so you can read the stripes properly.

Read the stripes from left to right. The first stripe is the one that’s closest to one end of the resistor. If this stripe is on the right side of the resistor, turn the resistor around so the first stripe is on the left.

2. Look up the colour of the first stripe to determine the value of the first digit.

For example, if the first stripe is yellow, the first digit is 4.

3. Look up the colour of the second stripe to determine the value of the second digit.

For example, if the first stripe is violet, the second digit is 7.

4. Look up the colour of the third stripe to determine the multiplier.

For example, if the third stripe is brown, the multiplier is 10.

5. Multiply the two-digit value by the multiplier to determine the resistor’s value.

For example, 47 times 10 is 470. Thus, a yellow-violet-brown resistor is 470 Ω.

If a resistor has five stripes, the first three stripes are the value digits and the fourth stripe is the multiplier. The fifth stripe is the tolerance, as described in the next section.

Table 2-1 Resistor Colour Codes (Resistance Values)

Colour	Digit	Multiplier
Black	0	1
Brown	1	10
Red	2	100
Orange	3	1 k
Yellow	4	10 k
Green	5	100 k
Blue	6	1 M
Violet	7	10 M
Grey	8	100 M
White	9	1,000 M
Gold		0.1
Silver		0.01

Here are a few examples to help you understand how to read resistor codes:

Understanding resistor tolerance

The value indicated by the stripes painted on a resistor provides an estimate of the actual resistance. The exact resistance varies by a percentage that depends on the tolerance factor of the resistor.

For example, a 22 kΩ resistor with a 5% tolerance actually has a value somewhere between 5% above and 5% below 22 kΩ, which works out to somewhere between 20.9 and 23.1 kΩ. A 470 Ω resistor with a 10% tolerance has an actual value somewhere between 423 and 517Ω.

Why the approximations? Simply because manufacturing resistors to very close tolerances costs more money, and for most electronic circuits a 5% or 10% margin of error is perfectly acceptable. For example, if you’re building a circuit to limit the current flowing through a component to 200 mA, the actual current being a little above or below 200 mA probably doesn’t matter much. Thus, a 5%- or 10%-tolerance resistor is acceptable.

If your application demands higher precision, you can spend a bit more money to buy higher-tolerance resistors. But 5%- or 10%- tolerance resistors are fine for most work, including all the circuits we present in this book (unless otherwise indicated).

The tolerance of a resistor is indicated in the resistor’s last colour stripe, as shown in Table 2-2.

Table 2-2 Resistor Colour Codes (Tolerance Values)

Colour	Tolerance (%)
Brown	1
Red	2
Yellow	5
Gold	5
Silver	10
None	20

Heating Up: Resistor Power Ratings

Resistors are like brakes for electric current. They work by applying the electrical equivalent of friction to flowing current. This friction inhibits the flow of current by absorbing some of the current’s energy and dissipating it in the form of heat. Whenever you use a resistor in a circuit, you need to make sure that the resistor is capable of handling the heat.

The power rating of a resistor indicates how much power a resistor can handle before it becomes too hot and burns up. As you can discover in Book I, Chapter 2, power is measured in units called watts. The more watts a resistor can handle, the larger and more expensive the resistor is.

Most resistors are designed to handle ¹⁄₈ W or ¹⁄₄ W. You can also find resistors rated for ¹⁄₂ W or 1 W, but they’re rarely needed in the types of electronic projects we’re describing for you. Unless otherwise stated, all the resistors used in this book are rated at ¹⁄₄ W.

Unfortunately, you can’t tell a resistor’s power rating just by looking at it. Unlike resistance and tolerance, wattages don’t have colour codes (see the preceding section). The size of the resistor, however, is a good indicator of its power rating and the ratings are written on the packaging when you buy new resistors. After you work with them for a while, you can quickly recognise the size difference between resistors of different power ratings.

If you want to be safe, you can calculate the power demands required of a particular resistor in your circuits. To start, use Ohm’s law to calculate the voltage across the resistor and the current that’s going to pass through the resistor. For example, if a 100 Ω resistor will have 3 V across it, you can calculate that 30 mA of current will flow through the resistor by dividing the voltage by the resistance (3 V ÷ 1,000 Ω = 0.03 A, which is 30 mA).

When you know the voltage and the current, you can calculate the power that’s going to be dissipated by the resistor by using the power formula we describe in Book I, Chapter 2:

P = I × V

Thus, the power dissipated by the resistor is just 0.09 W, well under the maximum that a ¹⁄₄ W (0.25 W) resistor can handle. (A ¹⁄₈ W resistor should be able to handle this amount of power too, but with power ratings erring on the large side is best.)

Limiting Current with a Resistor

One of the most common uses for resistors is to limit the current flowing through a component. Some components, such as light-emitting diodes, are very sensitive to current. A few milliamps of current is enough to make an LED glow; a few hundred milliamps is enough to destroy the LED.

Project 2-1 shows you how to build a simple circuit that demonstrates how a resistor can be used to limit current to an LED. The finished circuit, which you assemble on a small solderless breadboard, is shown in Figure 2-2.

Figure 2-2: The LED circuit assembled on a breadboard.

Before we get into the construction of the circuit, here’s a simple question: why use a 120 Ω resistor? Why not a larger or a smaller value? In other words, how do you determine what size resistor to use in a circuit like this?

The answer is simple: Ohm’s law, which can easily tell you what size resistor to use. But you first have to know the voltage and current (see the earlier section ‘Looking at Ohm’s Law’). In this case, the voltage is easy to figure out: you know that two AA batteries provide 3 V. To figure out the current, you just need to decide how much current is acceptable for your circuit. The technical specifications of the LED tell you how much current the LED can handle. In the case of a standard 5 mm red LED (the kind you can buy for about 60 pence), the maximum allowable current is 28 mA. To be safe and make sure that you don’t destroy the LED with too much current, round the maximum current down to 25 mA.

To calculate the desired resistance, you divide the voltage (3 V) by the current (0.025 A). The result is 120 Ω.

Do not connect the LED directly to the battery without a resistor. If you do, the LED flashes brightly – and may go bang – and then it’s dead forever.

Building Resistance in Combination

Suppose that you design the perfect circuit, and it calls for a 1,100 Ω resistor in a critical spot. Then you discover that you can’t find a 1,100 Ω resistor anywhere. You can buy 1 kΩ resistors and 100 Ω resistors, but no one seems to have any 1,100 Ω resistors.

Do you have to settle for a 1 kΩ resistor and hope that it’s close enough? Certainly not!

All you have to do is use two or more resistors in combination to create the necessary resistance. Such a combination of resistors is sometimes called a resistor network. You can freely substitute a resistor network for a single resistor whenever you want.

You can combine resistors in two basic ways: in series (strung end to end) and in parallel (side by side). This section explains how you calculate the total resistance of a network of resistors in series and in parallel, and shows you how to mix the two arrangements.

Combining resistors in series

Calculating the total resistance for two or more resistors strung end to end – that is, in series – is straightforward: you simply add the resistance values to get the total resistance.

For example, if you need 1,100 ohms of resistance and can’t find a 1,100 Ω resistor, you can combine a 1,000 Ω resistor and a 100 Ω resistor in series. Adding these two resistances together gives you a total resistance of 1,100 Ω.

You can place more than two resistors in series if you want. You just keep adding up all the resistances to get the total resistance value. For example, if you need 1,800 Ω of resistance, you can use a 1 kΩ resistor and eight 100 Ω resistors in series.

Figure 2-3 shows how serial resistors work. Here, the two circuits have identical resistances. The circuit on the left accomplishes the job with one resistor; the circuit on the right does it with three. Therefore, the circuits are equivalent.

Any time you see two or more resistors in series in a circuit, you can substitute a single resistor whose value is the sum of the individual resistors. Similarly, any time you see a single resistor in a circuit, you can substitute two or more resistors in series as long as their values add up to the desired value.

Figure 2-3: Combining resistors in series.

The total resistance of resistors in series is always greater than the resistance of any of the individual resistors, because each resistor adds its own resistance to the total.

Combining resistors in parallel

You can combine resistors in parallel to create equivalent resistances, but calculating the total resistance for such resistors is a bit more complicated than calculating the resistance for resistors in series, and so you may need to dust off your thinking cap. Although Ohm’s law is simple enough, the calculations required to work out parallel resistors can get a little complex. The maths isn’t horribly complicated, but it isn’t trivial either.

As the circuit in Figure 2-4 illustrates, when you combine two resistors in parallel, current can flow through both resistors at the same time. Although each resistor does its job to hold back the current, the total resistance of two resistors in parallel is always less than the resistance of either of the individual resistors because the current has two pathways through which to go.

Figure 2-4: Resistors in parallel.

So how do you calculate the total resistance for resistors in parallel? Very carefully. Here are the rules:

Resistors of equal value in parallel: In this, the simplest case, you can calculate the total resistance by dividing the value of one of the individual resistors by the number of resistors in parallel. For example, the total resistance of two 1 kΩ resistors in parallel is 500 Ω and the total resistance of four 1 kΩ resistors is 250 Ω.

Unfortunately, this is the only case that’s simple. The maths when resistors in parallel have unequal values is more complicated.

Two resistors of different values in parallel: With only two involved, the calculation isn’t too bad:

In this formula, R1 and R2 are the values of the two resistors.

Here’s an example, based on a 2 kΩ and a 3 kΩ resistor in parallel:

Three or more resistors of different values in parallel: Here the calculation begins to look like rocket science:

The dots at the end of the expression indicate that you keep adding up the reciprocals of the resistances for as many resistors as you have.

In case you’re crazy enough to want to do this kind of maths, here’s an example for three resistors whose values are 2 kΩ, 4 kΩ and 8 kΩ:

As you can see, the final result is 1,142.857 Ω. That’s more precision than you can possibly want, and so you can probably safely round it off to 1,143 Ω, or maybe even 1,150 Ω.

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Mixing series and parallel resistors

Resistors can be combined to form complex networks in which some of the resistors are in series and others are in parallel. For example, Figure 2-5 shows a network of three 1 kΩ resistors and one 2 kΩ resistor. These resistors are arranged in a mixture of serial and parallel connections.

To calculate the total resistance of this type of network, you divide and conquer. Look for simple series or parallel resistors, calculate their total resistance and then substitute a single resistor with an equivalent value. For example, you can replace the two 1 kΩ resistors that are in series with a single 2 kΩ resistor. Now, you have two 2 kΩ resistors in parallel. Remembering that the total resistance of two resistors with the same value is half the resistance value, you can replace these two 2 kΩ resistors with a single 1 kΩ resistor. You’re now left with two 1 kΩ resistors in series. Thus, the total resistance of this circuit is 2 kΩ.

Deceptively simple, isn’t it?

Figure 2-5: Resistors in series and parallel.

Assembling resistors in series and parallel

Project 2-2 lets you do a little hands-on work with some simple series and parallel resistor connections so that you can see firsthand how the calculations we describe in the previous three sections work in the real world.

You may well find that the individual variations of resistors (due to their manufacturing tolerances) mean that the calculated resistances don’t always match the resistance of the circuits. But in most cases, the variations aren’t significant enough to affect the operation of your circuits.

In this project, you assemble five resistors into three different configurations: the first has all five resistors in series; the second has them all in parallel; and the third creates a network of two sets of parallel resistors that are connected in series. Figure 2-6 shows how these three configurations appear when assembled.

Figure 2-6: The assembled resistors for Project 2-2.

Dividing Voltage with Resistors

One interesting and useful property of resistors is that if you connect two resistors together in series, you can tap into the voltage at the point between the two resistors to get a voltage that’s a fraction of the total voltage across both resistors. This type of circuit is called a voltage divider, and is a common way to reduce voltage in a circuit. Figure 2-7 shows a typical voltage-divider circuit.

Figure 2-7: A voltage-divider circuit.

When the two resistors in the voltage divider are of the same value, the voltage is cut in half. For example, imagine that your circuit is powered by a 9 V battery, but your circuit only needs 4.5 V. You can use a pair of resistors of equal value across the battery leads to provide the necessary 4.5 V.

When the resistors are of different values, you need to do a little maths to calculate the voltage at the centre of the divider. The formula is as follows:

For example, suppose that you’re using a 9 V battery, but your circuit requires 6 V. In this case, you can create a voltage divider using a 1 kΩ resistor for R1 and a 2 kΩ resistor for R2. Here’s the maths:

As you can see, these resistor values cut the voltage down to 6 V.

In Project 2-3, you build a simple-voltage divider circuit on a solderless breadboard to provide either 3 V or 6 V from a 9 V battery. The assembled circuit is shown in Figure 2-8.

Figure 2-8: The assembled voltage-divider circuit.

Varying Resistance with a Potentiometer

Many circuits call for a resistance that the user can vary. For example, most audio amplifiers include a volume control that lets you turn the volume up or down, and similarly you can create a simple light dimmer by varying the resistance in series with a lamp.

A variable resistor is called a potentiometer (or just pot for short). A potentiometer is simply a resistor with three terminals. Two of the terminals are permanently fixed on each end of the resistor, but the middle terminal is connected to a wiper that slides in contact with the entire surface of the resistor. Thus, the amount of resistance between this centre terminal and either of the two side terminals varies as the wiper moves.

Figure 2-9 shows how a typical potentiometer looks from the outside. The resistive track and slider (properly called the wiper) are enclosed within the metal can and the three terminals are beneath it. The rod that protrudes from the top of the metal can is connected to the wiper so that when the user turns the rod, the wiper moves across the resistor to vary the resistance.

Figure 2-9: A potentiometer.

Figure 2-10 shows how a potentiometer works on the inside. Here, you can see that the resistor is made of a semicircular piece of resistive material such as carbon. The two outer terminals are connected to either end of the resistor. The wiper, to which the third terminal is connected, is mounted so that it can rotate across the resistor. When the wiper moves, the resistance between the centre terminal and the other two terminals changes.

Figure 2-10: How a potentiometer works.

  The symbol used for a potentiometer in schematic diagrams is shown in the margin. As you can see, the centre tap of the resistor is indicated by an arrow that’s meant to reflect that the value of the resistance at this terminal varies when the wiper moves.

Potentiometers are rated by their total resistance. The resistance between the centre terminal and the two other terminals always adds up to the total resistance rating of the potentiometer. For example, the two resistances split by a 100 kΩ potentiometer always add up to 100 Ω. When the dial is exactly in the centre, both resistances are 50 Ω. As you move the wiper one way or the other, one resistance increases while the other decreases; but in all cases, the total of the two resistances always adds up to 100 Ω.

Here are a few other thoughts to keep in mind about potentiometers, plus a few different types:

Variety: Potentiometers come in a wide variety of shapes and sizes. With a little hunting around in shops or on the Internet, you can find the perfect potentiometer for every need.

Trim pots: These potentiometers are very small and can be adjusted only by the use of a tiny screwdriver. They’re designed to make occasional fine-tuning adjustments to your circuits.

Switches: Some potentiometers have switches incorporated into them, so that when you turn the knob all the way to one side or pull it out, the switch operates to open or close the circuit.

  Wipers: When the wiper reaches one end of the resistor or the other, the resistance between the centre terminal and the terminal on that end is essentially zero. Keep this point in mind when you’re designing circuits. Putting a small resistor in series with a potentiometer is a common way to avoid circuit paths with no resistance.

Linear tapers: In these potentiometers, the resistance varies evenly as you turn the dial. For example, if the total resistance is 10 kΩ, the resistance at the halfway mark is 5 kΩ and the resistance at the one-quarter mark is 2.5 kΩ. They’re called linear taper potentiometers because the resistance change is linear.

Logarithmic tapers: Many potentiometers aren’t linear. For example, potentiometers designed for audio applications usually have a logarithmic taper, which means that the resistance doesn’t vary evenly as you move the dial.

  Rheostats: These variable resistors have only two terminals – one on an end of the resistor itself, the other attached to the wiper. Although properly called a rheostat, most people use the term potentiometer or pot to refer to both two- and three-terminal variable resistors.