# Resistors and ohm’s law

In this chapter, you will learn how to use resistors in electric circuits to control a current. You will discover that there are different kinds of resistors for different purposes, and you will learn how to read the amount of resistance on a resistor. You will also learn about Ohm's Law, which relates the quantities of voltage, current and resistance, and you will use formulae to do calculations to find the values of voltage, current and resistance.

## Resistors and their identification codes

### What is resistance?

Electricity flows far more easily
through copper wire than through plastic wire, string or grass.
Copper wire has a low resistance to electricity flow, whereas
plastic wire has a high **resistance**. Because electricity
flows easily through copper wire, copper is a good **conductor** of electricity.

To **resist** something means to try
to prevent it. If you sit in a tree and the wind blows hard,
you can resist falling down by clinging to the branches.

To **conduct** means to allow
something to pass through.

The resistance that an object, for example a piece of wire, offers to the flow of electricity can be measured.

Resistance is measured in ohms. We use the symbol Ω

When electricity flows through a
conductor, heat is generated. Some metals, such as nickel and
chrome, resist the flow of electricity quite strongly, and heat
up when electricity is forced to flow through it. The heating
elements of stoves and kettles are normally made of a mixture
of nickel and chrome. When some metals get extremely hot, they
**emit** light.

When something **emits** light, it is a source of
light. A light bulb is a source of light, but a mirror is not
a source of light as it only reflects light.

If the resistance in a circuit is very low, for example when the terminals of a cell are connected with a piece of thick copper wire, the current will flow very strongly. This is called a "short circuit". It can result in so much heat being generated that damage is caused to the cell and other parts of the circuit, the conducting wires can melt and a fire can start.

By adding more resistance to a circuit, you can control how great the current is that flows through the circuit. In this way, you can protect the components in a circuit from too much current flowing through them. Increasing the resistance also means the cell or battery powering the circuit will last longer. You can add precise amounts of resistance by using resistors with the required resistance value.

### What is a resistor?

A resistor is a specially designed component that is normally used in a circuit to limit the current. Resistors are made of materials with a high resistance to electricity flow, and come in the form of thin wires or films. Resistors also have precise resistance values that don't change much in different environmental conditions.

The most commonly used resistors look like tubes, with two wires to connect it to the circuit. The symbol to show a resistor in a circuit diagram is an open rectangle or a zigzag line.

Low-value resistors often have their resistance value printed on them in numbers, while high-value resistors are coded, using coloured bands. The first three bands give the value of the resistor in ohms. The colour-code chart on the second page of this chapter will help you to work out the resistance value in ohms.

The fourth band on a resistor shows the accuracy rating as a percentage. This is also called the "tolerance". The band is gold or silver, depending on the tolerance. For the circuits you will be building, this is not important.

**Kilo** means multiply by a thousand, for example 1 km = 1 000 × 1 m.

**Mega** means multiply by a
million.

Resistors are the most commonly used components in electronics, as they are useful to control current. You will see how they are used in the following weeks.

**Units of measurement: ohms, kilo-ohms
and mega-ohms**

- 1 kΩ = 1 000 Ω = 10³ Ω
- 1 MΩ = 1 000 kΩ = 1 000 000 Ω = 10⁶ Ω

1. Work out and write down the resistance of each of these resistors:

(a)

(b)

(c)

(d)

2. Fill in the colour codes on these blank resistors to show the given resistance, or write the colour of each band above it if you don't have coloured pencils or pens.

(a) 200 kΩ

(b) 300 Ω

3. Describe the function of a resistor as a component in an electrical circuit.

## Ohm's law

There is a special relationship
between the voltage, current, and resistance in any circuit.
You can control any one of these three **variables** by changing the other
two variables.

Ohm's Law
states that as voltage increases, the current increases if the
resistance is **constant**.

A **variable** is a quantity that
can have different values, for example the amount of water in
a tank. A **constant**
is a quantity that always has the same value, for example
gravitational acceleration. Sometimes we call a quantity a
constant because we decide to keep it constant.

In the formula for Ohm’s Law:

- V is the
**potential**or**voltage difference**measured in volts, -
**I**is**current**measured in amps, and -
**R**is**resistance**measured in ohms.

Figure 11 shows this relationship in a formula triangle.

When the voltage and current are known, the resistance can be calculated with:

\(R =\frac{\text{V}}{\text{I}}\).

When the resistance and current are known, the voltage can be calculated with:

\(\text{V} = \text{I} \times \text{R}\).

When the resistance and voltage are known, the current can be calculated with:

\( \text{I}=\frac{\text{V}}{\text{R}}\).

### Questions

Consider the following circuit:

1. What does Ohm's Law say will change in a circuit when the resistance is kept constant but the number of cells in series is increased?

2. How will the current change if the voltage supplied by the battery of cells is kept constant but the resistor is replaced by another resistor with a lower resistance?

3. How would you describe the relationship between the current and the voltage in a circuit?

4. How would you describe the relationship between the current and the resistance in a circuit?

5. Which of these changes will cause the current through an electrical circuit to decrease? Write down all the letters of the statements that are correct.

(a) a decrease in the voltage

(b) a decrease in the resistance

(c) an increase in the voltage

(d) an increase in the resistance

6. An electrical circuit has three 1,5 V cells in series that is connected to a lamp and a resistor in series. Which of the following things would cause the lamp to shine less brightly? Write down all the letters of the statements that are correct.

(a) an increase in the voltage of the battery (add another cell)

(b) a decrease in the voltage of the battery (remove a cell)

(c) a decrease in the resistance of the resistor

(d) an increase in the resistance of the resistor

## Calculations using ohm's law

Last week, you learnt how Ohm's Law can be used to predict what will happen when you change one or two of the following variables: current, voltage or resistance. You will now use the formulas of Ohm's Law to make predictions. Remember to use the correct units in the formula!

**Example 1**

Calculate the value of the resistance in the diagram below if the voltage across the resistor is 12 V and the current through the resistor is 2 A.

\[\begin{align} \text{R} & = \frac{\text{V}}{\text{I}} \\ & = \frac{12 \text{V}}{2 \text{A}}\\ & = 6 Ω \\ \end{align}\]

**Example 2**

Calculate the value of the voltage supply in the circuit below if the resistor has a value of 4 Ω and the current through the resistor is 2,5 A.

\[\begin{align} \text{V} & = \text{I} \times \text{R} \\ & = \text{2,5 A} \times \text{ 4 Ω} \\ & = 10 V \\ \end{align}\]

**Example 3**

Calculate the value of the current in the circuit below if the resistor has a value of 3 Ω and the voltage across the resistor is 12 V.

\[\begin{align} \text{I} & = \frac{\text{V}}{\text{R}} \\ & = \frac{12 \text{V}}{3 Ω }\\ & = 4 A \\ \end{align}\]

### Questions

1. What will the potential difference be if the current in a circuit is 10 A and the total resistance is 1 000 Ω?

2. Given V = 10 V and R = 1 kΩ, what will the value of the current be in a circuit?

3. Given V = 20 V and R = 5 kΩ, solve for the current.

4. A tumble dryer in a laundry service uses a 220 V power source. The coils of the heater provide an average resistance of 12 Ω. What is the current flowing through the heating coils?

5. A 9 V battery maintains a current of 3 A through a radio. What is the resistance in the circuit?

6. If the voltage across a circuit is increased four times, what would you expect to happen to the current through the circuit?

7. (a) In the circuit below, calculate the value of the resistor.

(b) If two more cells are added to the circuit, will the current increase or decrease? Check your prediction using the formula.

8. Calculate the battery voltage for the circuit below:

9. Look at the circuit below:

(a) Calculate the
current through R_{2}.

(b) What will the
current be through R_{1}.?

(c) What will the
voltage across R_{1}.
be?

(d) What will the
resistance value of R_{1}. be?

### Next week

In the next chapter, you will learn about components commonly used in electronic systems and their special functions.