Chapter 2: Voltage, Resistance, and Ohm’s Law

Keywords

1. conductor
2. diode
3. LDR
4. LED
5. potentiometer
6. resistance
7. resistor
8. thermistor
9. transistor
10. voltage

By the end of this chapter, you will be able to:

a) Understand electrical resistance, how it is measured, its relationship to current and voltage, and the factors that affect it.

b) know the function and use of a diode, transistor, thermistor, potentiometer, LDR, and LED.

Introduction

In the previous chapter, you learnt that when a conductor is connected to the terminals of an electric cell, electric current flows through the conductor. Just like any other moving object, as the electrons flow through the conductor, they meet some opposition (resistance). What causes the opposition to the movement of this charge? Do the charges face the same amount of opposition as they flow through different materials? How is the current flowing through a conductor related to the e.m.f of the cell

connected across the conductor? In this chapter, you will be able to understand the cause of the opposition to the flow of charge through different materials and how this is related to a variety of appliances.

2.2: Electrical Work and Voltage

In chapter 1, you learnt that electromotive force is the amount of work done by a cell to move 1 C of electric charge round a closed circuit connected to the cell. Using Figure 2.1, you discovered in Activity 1.9 that if the switch, S remains open, the bulb does not light and the voltmeter, reading E is the e.m.f of the cell.

Figure 2.1: Measuring e.m.f of a cell

However, when switch S is closed, based on your observations in Activity 1.9 on page 13, the bulb lights but the voltmeter reading this time changes to V the potential difference (or voltage) across the bulb. The potential difference (o voltage) across the cell represents the work done by the cell to drive the electric charges through the bulb.

DID YOU KNOW?

Did you know that: Work done = QV where Q is the amount of charge that flows through a device and V is the potential difference across the device? The work done is measured in joules (J) if charge is measured in coulombs (C and potential difference is in volts (V).

DID YOU KNOW?

Did you know that when charges flow through a conductor, they face opposition to their flow? Explain the source of this opposition.

EXAMPLE 2.1

An energy source forces a constant current of 2 A to flow through a lightbulb for 10 s. If 2.3 kJ of energy is given off by the bulb in the form of light and heat energy, calculate the voltage drop across the bulb.

EXERCISE

1. Name two instruments that can be used to measure voltage.

2. A potential difference of 5 V develops across a conductor when a certain amount of charge flows through it for 30 s. If 300 J of work is done by the battery connected to the conductor, find the current flowing through the circuit.

2.3: Electrical Resistance

When current flows through a conductor, a potential difference is developed across the conductor. The ratio of the potential difference, V, to the current, I, flowing through the conductor is called the electrical resistance, R, of the conductor. R = V The SI unit for measuring electrical resistance is the ohm (2). In an electrical circuit, the components that oppose the flow of electric current are called resistors. The circuit symbol for an electric resistor is shown in Figure 2.2.

Figure 2.2: Circuit symbol of a resistor

DID YOU KNOW?

Did you know that the instrument used to measure the resistance of a conductor is called an Ohmmeter?

EXAMPLE 2.2 A current of 1.2 A flows through a conductor for 30 s. If 400 J of work is done, find the: (i) potential difference, V, across the conductor.

ASSIGNMENT 2.1

1. Discuss the advantages and disadvantages of fixed resistors over variable resistors.

2. How is the potentiometer shown in Figure 2.4 applied in daily life situations?

3. Explain how the resistance of a photo-resistor varies.

2.5: Factors Affecting the Resistance of a Wire

Activity 2.1 Investigating the factors affecting the resistance of a wire

Key question:

What factors affect the resistance of a resistor in the form of a wire?

What you need A cell and a cell holder Three 50 cm of nickel wires of different thickness (SWG 28, 30 and 32)

What to do

Part 1

100 cm of nickel wire (SWG 28) Wire cutter Ammeter Metre rule Connecting wires 1.

With the items provided, connect the circuit shown in Figure 2.5 using nickel wire (SWG 28) of length, x = 20.0 cm.

A Figure 2.5: V Wire element Factors affecting resistance of a wire

2. Read and record the ammeter reading, I, and the voltmeter reading, V.

3. Repeat procedures 1 and 2 for x = 30.0, 40.0, 50.0 and 60.0 cm.

4. Tabulate your results including values of

5. Plot a graph of against x.

6. Determine the slope of your graph and explain the significance of this slope.

7. Explain the observation to show how resistance varies with length.

Part 2

1. Connect the circuit shown in Figure 2.5 using nickel wire (SWG 32) of length x = 40 cm.

2. Read and record the ammeter reading, I, and the voltmeters reading V.

3. Repeat steps (1) and (2) using nickel wires with SWG 30 and 28.

4. Tabulate your results and include values of V

5. Plot a graph of against SWG number.

6. Determine the slope of your graph and explain the significance of this slope. Explain how the results obtained can be used to show how resistance varies with length.

DID YOU KNOW?

Did you know that the electrical resistance, R, of a conductor in the form of a wire increases with length and reduces with increase in cross-sectional area?

EXERCISE 2.3

A uniform wire of length 120 cm and diameter 21 mm is made of a material of resistivity 5.0 x 104 Q2 m. Determine the:

1. Cross sectional area of the wire.

2. Resistance of the wire.

3. Current flowing through the wire if a potential difference of 10 V is applied across its ends.

ASSIGNMENT 2.2

Using the Internet or textbooks in your library, find out how resistors can be arranged in an electric circuit. 2.6: Arrangement of Resistors in Circuits 2.6.1: Series Arrangement of Resistors Activity 2.2 Investigating the properties of resistors in a series arrangement

Key question:

What are the properties of resistors in a series arrangement?

What you need One dry cell (1.5V size 3D) Three torch bulbs (as resistors) Three switches labelled K,, K, and K, 3 3 Three ammeters labelled A,, A, and A Four voltmeters labelled V1, V2, V, and V4 Seven connecting wires

What to do Part 1

1. Connect the circuit shown in Figure 2.6.

Figure 2.6: Series connection of resistors Voltage, Resistance and Ohm’s Law

2. Close switch K,. What do you observe?

3. Open switch K,. 4. Repeat procedures 2 and 3 for switches K, and K,.

5. Now, close all the three switches K,, K, and K. What do you observe?

6. Remove bulb R, from the circuit and close all the switches. Compare the brightness of bulbs R, and R, before and after removing bulb R..

7. Remove bulb R2 so that only bulb R, remains in the circuit. Close all the switches and compare the brightness of bulb R, to its brightness in cases 5 and 6 above.

8. What conclusions can you draw from your observations in 5, 6 and 7?

Part 2

1. Replace all the switches with ammeters as shown in the Figure 2.7:

Figure: Current through resistors in series arrangement

2. Compare the readings of ammeters A,, A, and A. What scientific conclusion can you draw?

3. Now, remove the ammeters and connect voltmeters to the circuit as shown in Figure 2.8:

Voltage across resistors in series arrangement 3

4. Compare the readings of voltmeters V,, V2, V, and V.

What scientific conclusion can you draw?

DID YOU KNOW?

Did you know that when resistors are connected in series:

1. Total resistence, R = R, + R2 + R2?

2. The same current, I, flows through each of the resistors?

3. Total e.m.f of the supply cell, V, = V2 + V2 + V1? When resistors are connected in series: Total resistance R = R1 + R2 + R ̧ 2 The same current I flows through each of the resistors. Total e.m.f of the supply cell, V, = V2 + V3 +V 4·

2.6.2: Resistors in Parallel

Activity 2.3 2 4′ Investigating the properties of resistors in a parallel arrangement

Key question:

What are the properties of resistors in a parallel arrangement?

What you need One dry cell (1.5V size 3D) Three torch bulbs (as resistors R1, R2 and R3) Four switches labelled K1, K2, K3, and K4 Four ammeters labelled A1, A2, A3, and A4 Four voltmeters labelled V1,V2, V3, and V4 Seven connecting wires

3. Connect the circuit shown in Figure 2.11:

Figure 2.11: Potential difference across resistors in parallel arrangement

4. Compare the readings of Voltmeters V,, V, V, and V4. What conclusion can you draw?

5. Discuss the advantages and disadvantages of a series connection over the parallel connection of resistors.

Note that

The potential drop across each of the resistors in a parallel network is the same, that is to say, V1 = V2 = V3. 2 3′

The current flowing through each resistor is inversely proportional to the resistance of the resistor. This means that less current flows through components with higher resistance.

The current in the circuit is the algebraic sum of the currents flowing through the individual resistors i.e. | = 1, + 11⁄2 + 1⁄2· 2 3″ Total resistance, R, is given by:

EXAMPLE 2.3

Figure 2.12 shows resistors connected in series across a 12 V d.c supply.

Figure 2.12: Series arrangement of resistors Given that R, = 6, R2 = 8 and R1 = 2 Q, calculate the: 1. Effective resistance in the circuit. 2. Total current in the circuit.

3. P.d across the 8 resistor.

Given that R, = 10 Q, R2 = 8 Q, R2 = 2 and R1 = 4, determine the: 4

(i) Effective resistance in the circuit and the ammeter reading when K, is open and K, is closed.

(ii) Effective resistance in the circuit and the ammeter reading when K, is closed and K, is open.

(iii) Effective resistance in the circuit and the ammeter reading when both K, and K, are closed.

(iv) Potential difference across resistor R, when both K, and K, are closed.

2.7: Internal Resistance of a Cell

DID YOU KNOW? Did you know that the cell uses energy to drive electric current within itself?

Activity 2.4 Determining internal resistance of a dry cell

Key question:

What do you understand by the “internal resistance of a cell”?

What you need

1 dry cell A single cell holder 1 voltmeter (0-3V) 1000 variable resistor 1 ammeter Switch What to do

1. Connect the circuit shown in Figure 2.15:

Figure 2.15: Determining internal resistance of a cell

2. With switch, K, open, read and record the voltmeter reading E.

3. Close switch K.

4. Adjust the value of the variable resistor, R, until the voltmeter reading, V = 0.2 V.

5. Note and record the reading, I, of the ammeter.

6. Repeat procedures 4 and 5 for V = 0.4, 0.6, 0.8 and 1.0 V.

7. Tabulate your results in a suitable table.

8. Plot a graph of V against I.

9. Calculate the slope, s, of your graph.

10. What is the significance of the slope obtained in (9) above?

Note that

When a cell is connected to a resistor of resistance, R, the total resistance in the circuit is r + R, where r is the internal resistance of the cell. If the e.m.f of the cell is E, then E = I(r+ R), where I is the current flowing in the circuit. If V is the potential difference across the resistor, R, then V = E – Ir, which is in the form y = mx + c (the equation of a straight line graph).

EXAMPLE 2.6

A cell of e.m.f 2.0 V and internal resistance 0.5, supplies a current of 0.2 A in a closed circuit connected to it. Determine the load resistance in the circuit.

2.8: Relationship Between Current, Voltage and Resistance

The relationship between the current flowing through a conductor and the potential difference across it was first investigated by a scientist called Ohm. The result of this investigation is called Ohm’s law, which states that:

“the current flowing through a metallic conductor is directly proportional to the applied voltage across its ends provided temperature and other physical factors remain constant”.

Activity 2.5Verifying Ohm’s law

Key question: What is the relationship between the current flowing through a conductor and the potential difference between its ends?

What you need

A cell and cell holder Switch A resistor Ammeter Voltmeter Connecting wires Resistance meter Variable resistor

What to do

Figure 2.16: Verifying Ohm’s law

1. Set up the apparatus as shown in Figure 2.16.

2. Adjust the variable resistor such that the current, I, flowing through the ammeter is 0.10 A.

3. Read and record the voltmeter reading, V.

4. Repeat procedures 2 and 3 for I = 0.12, 0.14, 0.16 and 0.18 A.

5. Tabulate your results.

6. Plot a graph of voltage, V, against current, I. 7. Find the slope of the graph and state its units.

8. Now measure the resistance, R, of the resistor using a resistance meter and compare your result with the slope of the graph above.

9. From your graph, state the variation of voltage with current and compare your statement with the statement for Ohm’s law.

10. Write a mathematical expression of Ohm’s law. What do you think is the constant of proportionality?

11. Discuss how you can use the results to bring out the relationship between V and I.

2.8.1: Water Pipe Analogy for Ohm’s Law

Ohm’s Law describes the current that flows through a resistance when different electric potentials (voltage) are applied at the ends of the resistor. Since we cannot see electrons, the water-pipe analogy helps us to understand electric circuits better.

Figure 2.17: Illustrating Ohms law using water-pipe analogy

Here, the voltage is analogous to water pressure, the current is the amount of water flowing through the pipe, and the resistance is the size of the pipe. More water (current) will flow through the pipe where more pressure (voltage) is applied and the pipe has a wider cross-sectional area (lower the resistance).

2.8.2: Ohmic and Non-Ohmic Conductors

All conductors can be classified into two categories, namely; ohmic conductors and non-ohmic conductors. Ohmic conductors are conductors that obey Ohm’s law. That is, the current flowing through ohmic conductors is directly proportional to the applied potential difference across their ends provided the physical conditions of the conductors remains unchanged. Non-ohmic conductors do not obey Ohm’s law.

ASSIGNMENT 2.3

1. Identify three examples of ohmic conductors and three examples of non- ohmic conductors.

2. Draw the current-voltage graphs for ohmic and non-ohmic conductors and explain their differences and similarities.

2.9: Thermistors, Transistors, Diodes, LDR, LED and Potentiometer

2.9.1: Thermistors

A thermistor is a heat sensitive device. It is usually made of a semi-conductor material whose resistance changes very rapidly with change in temperature. A thermistor has the following important properties: The resistance of a thermistor changes very rapidly with change of temperature. The temperature coefficient of a thermistor is very high i.e. it can absorb release a lot of heat before its temperature changes. Or The temperature coefficient of a thermistor can be both positive and negative.

ASSIGNMENT 2.4 thermistor is applied. Identify devices that apply a thermistor in their operations and explain how the

2.9.2: Diode

A diode is an electronic component, which can allow electric current to flow through it in only one direction. The circuit symbol of a diode is as shown in Figure 2.19;

Watch the video below to understand how diode works

Figure 2.18: Circuit diagram of a diode

Activity 2.6 Understanding how a diode works

Key question:

How does a diode work?

What you need

A diode • Connecting wires • A bulbou • Two dry cells What to do

1. Identify the positive terminal of the diode and connect the circuit shown in Figure 2.19.

Figure 2.19: How a diode works

2. Note down what happens to the bulb.

3. Now, reverse the terminals of the diode in Figure 2.19 and observe what happens to the bulb.

4. Basing on your observations in 2 and 3, describe what you understand by forward biased and reverse biased as applied to diodes.

5. Write short notes about the application of diodes.

ASSIGNMENT 2.5

Search for information on the different types of diodes and explain their characteristics. Also, give examples of where these diodes are applied.

2.9.3: Light Dependent Resistor (LDR) or Photo-resistor

A photo-resistor or light dependent resistor is an electronic component whose resistance depends on the intensity of light incident on it. This means that it is sensitive to light. A light-dependent resistor (LDR) is a non-ohmic conductor. Its resistance is high when the intensity of light falling on it is low.

Figure 2.20: Property of an LDR and its circuit symbol

ASSIGNMENT 2.6

Explain some applications of LDRs included in streetlights.

2.9.4: Transistor

A transistor is a semi-conductor device with three terminals, capable of amplification and rectification. Amplification is the process of transforming weak currents (signals) into strong ones while rectification is the process of converting an alternating current or voltage into the direct current or voltage. The circuit symbol of a transistor is shown in Figure 2.21.

Project work 2.1

1. Explain how a transistor is used for amplification of weak signals.

2. Design and construct an electronic circuit using three transistors.

3. Test and explain the output of your circuit.

2.9.5: Light Emitting Diode (LED)

A light emitting diode (LED) is an electric component that emits light when an electric current flows through it. When electric current flows through the LEDs, they experience a specific drop in voltage. The drop in voltage determines the energy lost by the diode and hence the colour of the emitted light. Project work 2.2 Using a LDR and 12 LEDs, construct a model streetlights and test your model for functionality.

2.9.6: A Potentiometer

A potentiometer is a passive electronic component. Potentiometers work by varying the position of a sliding contact across a uniform resistance. The supply voltage is applied across the whole length of the resistor, and the output voltage is obtained between the fixed and sliding contact as shown in Figure 2.23.

Figure 2.23: A potentiometer

Chapter Summary

In this chapter, you have learnt that

voltage or potential difference is the measure of potential energy between two points in a circuit. voltage is measured in volts and has the symbol V. electric current is the rate of continuous flow of charges around a circuit and is measured in amperes. Its symbol is I. electrical resistance is the opposition to current flowing around a circuit. a good conductor has a low value of resistance while an insulator has a high value of resistance. Ohm’s law: For a conductor at constant temperature, the current flowing through the conductor is proportional to the potential difference across its ends. the electrical resistance of a semi-conductor decreases with increasing temperature.

Watch the video below to learn more about Voltage, Resistance, and Ohm’s Law