Introduction

This unit is intended to develop your understanding of current, voltage, and resistance. From the beginning, you should try to use these words precisely in describing circuits. You will discover how to connect meters to make measurements of circuit behaviour. In addition, you are going to find out what happens when components are connected in series and in parallel.

Measuring current
An electric
current
Current I is a flow of charged particles, usually electrons.
current
is a flow of charged particles, usually electrons. In simulations, the flow of current is shown by arrows which appear when a
circuit
A circuit is a closed conducting path.
circuit
is completed.

Click on the figure below to interact with the model.

 Figure 1.  Torch simulation.

The direction of current flow in a circuit is thought of as being from the positive terminal (+) of the
battery
A battery consists of two or more cells. The cells may be connected in series or in parallel.
battery
towards the negative terminal (−). This is called
conventional current
In a circuit, current is thought of as flowing from the positive terminal of the power supply towards the negative terminal. This is the direction of flow for a positively charged particle.
conventional current
. (As explained in Introducing Circuits, this is opposite in direction to the flow of electrons in the circuit, but confusion is avoided by consistently thinking about current in the conventional direction.)

Current is measured in units called amperes, or amps. One amp, written as 1 A, is quite a large current and the currents flowing in most electronic circuits are smaller. Other common units include milliamps (mA), that is, thousandths of an amp, and microamps (μA), millionths of an amp.

 To measure the current flowing in the circuit, an ammeter is needed.
 To connect this instrument, the circuit must first be broken.
 The ammeter is connected in series into the circuit.
 The current to be measured flows through the meter.

Click on the figure below to interact with the model.

 Figure 2.  Connecting an ammeter.

Click on the lamp and move it slightly. This will break the circuit. Drag the
ammeter
An ammeter measures current. Ammeters are connected in series in a circuit and must have a low resistance.
ammeter
into position then rewire the circuit to make it complete. Your finished circuit should look like the one shown in Fig.3.

Click on the figure below to interact with the model.

 Figure 3.  Current flows through the ammeter.

The ammeter shows a reading of 90 mA. Check that the arrows showing the flow of current appear when the switch is on and disappear when the switch is off.

In the ideal case, the addition of the ammeter should not affect the behaviour of the circuit. Real ammeters do change circuits, but usually the changes are too small to be significant.

The simulation adjusts the ammeter automatically to read in the most convenient units, A, mA, or μA. With the switch off, the ammeter reads in μA and, since the circuit is incomplete, the reading is 0.00 μA. Once the switch is closed, the meter automatically reads in mA. This is called autoranging. Real meters can also be
autoranging
An autoranging multimeter adjusts its measurement range automatically to give an appropriate reading.
autoranging
, as you will discover from the practical work in Using a Multimeter.
Select the words which best complete each sentence.

• To measure current, an is used. The circuit is and the meter is connected in . The current to be measured flows the meter.
Understanding voltage
How can you change the amount of current flowing in a simple circuit? One answer is to change the
voltage
Potential difference, or voltage V is a measure of the difference in energy between two points in a circuit. Charges gain energy in the battery and lose energy as they flow round the rest of the circuit.
voltage
of the power supply.

To start with, it is easiest to think of voltage as the 'push' supplied by the battery which causes the current to flow. Charges gain energy as they pass through the battery and lose energy as they pass around the rest of the circuit.
Where in the torch circuit will charges lose most energy?

The charges lose almost all the energy gained as they pass through the lamp. You can see this release of energy in the lamp filament because electrical energy is converted into heat and light. Only a small amount of energy is used as charges move around the connecting wires which make up the rest of the circuit.

 Your physics teacher will tell you that charge is measured in coulombs, C, and that energy is measured in joules, J.
 One volt is defined as one joule per coulomb.
 In other words, one coulomb of charge flowing through a 1 V cell gains 1 joule of energy.
 The voltage of the power supply determines how much energy charges will gain.
 Charges passing through a 10 V power supply gain twice as much energy as they do passing through a 5 V power supply.

How much energy is gained when 0.5 C of charge flow through a 6 V power supply?
If 2 C of charge gains 10 J of energy passing through a power supply, what is the voltage of the power supply?

You can investigate the effect of a change in power supply voltage using the simulation in Fig.4.

Click on the figure below to interact with the model.

 Figure 4.  Changing power supply voltage.

With the power supply voltage set to 4.5 V in Fig.4, the ammeter reads 45 mA. The current has decreased to half its original value.

Click the battery symbol and edit the voltage to 3 V and then to 6 V.
How much current flows when the battery voltage is 3 V?
• mA
How much current flows when the battery voltage is 6 V?
• mA

From investigations like this, you can conclude that:

The current flowing is proportional to the voltage applied.

In other words, if the voltage increases, the current flowing increases by a corresponding amount.

 The voltage across any component can be measured precisely using a voltmeter.
 This applies equally to power supply voltages in which charges gain energy, and to other components, in which energy is lost.
 Voltmeters are connected in parallel with the circuit.
 There is no need to delete any links or to change the circuit in any way, other than adding the voltmeters.

The simulation of Fig.5 shows how voltmeters are connected to a circuit.

Click on the figure below to interact with the model.

 Figure 5.  Connecting voltmeters.

Experiment with different values of power supply voltage in Fig.5. You can drag the voltmeters away from the circuit and replace them without affecting the behaviour of the circuit as a whole.

You can think of the
voltmeter
A voltmeter measures the voltage, or difference in energy, between two points in a circuit. Voltmeters are connected in parallel and must have a high resistance.
voltmeter
across the battery as measuring energy gain, while the voltmeter across the lamp measures energy loss. The energy gained by the charges flowing through the battery is equal to the amount of energy lost in the external circuit.

Decide whether the following statements are true or false.
•  A voltmeter is used to measure voltage. False True Connecting a voltmeter to a circuit causes a change in the circuit. False True Voltmeters are connected in parallel with the circuit. False True
Resistance
Resistance
Resistance R limits current flow.
Resistance
is the property of components that limits current flow.

In the circuits above, the resistance of the lamp limits current flow. A real lamp has an extremely thin wire filament, which heats up and glows white-hot as current flows through it.

The measurement unit for resistance is the
ohm
Resistance is measured in ohms, Ω, kilohms, kΩ (thousands of ohms), and megohms, MΩ (millions of ohms).
ohm
, Ω. A resistance of 1 Ω limits the current flowing to 1 A if a voltage of 1 V is applied. Other commonly used units are kilohms (kΩ), thousands of ohms, and megohms (MΩ), millions of ohms.

 Resistance is measured using an ohmmeter.
 The component is removed from the circuit altogether so that it can be connected to the meter separately.
 An ohmmeter contains its own power supply and a circuit is completed which allows the resistance to be measured.

 Figure 6. Measuring resistance.

You can find out how to measure the resistance of real components from the practical work in Using a Multimeter.

Simulated circuits do not include ohmmeters because you can't use these devices to measure the resistance of a component when it is part of a circuit.

In equations, current is represented by the symbol I, voltage is represented by V, and resistance by R. These properties are linked by the following equations:

As explained in Introducing Circuits, these equations are called Ohm's equations, named after Georg Ohm who first understood the relationships between current, voltage, and resistance.

Check the equations by rearranging the interactive version.

Click on the figure below to interact with the model.

 Figure 7.  Torch circuit.

 The voltage across the lamp in Fig.7 is 4.5 V.
 The current through the lamp is 45 mA.
 Therefore, the resistance of the lamp filament is

It is important to think about the units used for R, V, and I. Equations and formulae always work with fundamental units, that is, with R in ohms, V in volts, and I in amps. Before substituting a value for I in the equation above, the ammeter reading, 45 mA, was converted into A: 45 mA = 0.045 A.

In electronic circuits, it is often more convenient to think about current in mA. If a value for I is substituted in mA, then the resistance will be given in kΩ, as shown below:

Which type of meter is used to measure each of the following?
•  Current Ammeter Ohmmeter Voltmeter Voltage Ammeter Ohmmeter Voltmeter Resistance Ammeter Ohmmeter Voltmeter
How should these meters be connected?
•  Ammeter In parallel In series Voltmeter In parallel In series
 Figure 8. Using an ohmmeter?
Which diagram in Fig. 8 shows the correct way of using an
ohmmeter
An ohmmeter measures resistance. To find its resistance, the component to be tested must be removed from any circuit and connected to the ohmmeter separately.
ohmmeter
to measure the resistance of a lamp?
Series circuits
Components are connected in
series
Components are connected in series when they are joined end to end in a circuit, so that the same current flows through each.
series
when they are joined end-to-end so that the same current flows through each.

Before operating the switches in Fig.9, answer the questions comparing the series circuit with a simple circuit in which a single lamp is operated from a 9 V power supply.
In the circuit with two lamps in series, will it be easier or more difficult for current to flow?
What is the effect on the resistance around the circuit as a whole?

Click on the figure below to interact with the model.

 Figure 9.  Two lamps connected in series.

Now close the switches in the simulation. The single lamp shines with its normal brightness, but the lamps in series are dim.
How much current is flowing through the single lamp?
•  mA
How much current is flowing through the lamps connected in series?
•  mA

This is obvious. Connecting the lamps in series increases the resistance around the circuit, allowing less current to flow.
What is the voltage across the single lamp?
•  V
What is the voltage across each of the lamps in series?
•  V

In the series circuit, the charges lose half their energy in passing through each lamp.

In Fig.10, three lamps are connected in series. Answer the questions before operating the switch.
How much current will flow through each of the three lamps?
•  mA
What will be the voltage across each of the three lamps?
•  V

Click on the figure below to interact with the model.

 Figure 10.  Three lamps connected in series.

Check your answers by closing the switch in the simulation. If you can get these questions right, you are well on the way to understanding the relationships between current, voltage, and resistance.

Parallel circuits
Components are connected in
parallel
Components are connected in parallel when they are joined side by side in a circuit, so that they provide alternative pathways for current flow.
parallel
when they are joined side-by-side so as to provide alternative pathways for current flow.

In Fig.11, two lamps are connected in parallel. Before operating the switch, answer the questions comparing the parallel circuit in Fig.11 with a simple circuit with one lamp.
In the circuit with two lamps in parallel, will it be easier or more difficult for current to flow?
What is the effect on the resistance around the circuit as a whole?

Click on the figure below to interact with the model.

 Figure 11.  Two lamps connected in parallel.

Close the switch. Both lamps shine with their normal brightness.

It is easier for current to flow because there is more than one way for the charges to go. Drag the left-hand lamp out of the circuit. The current changes to 90 mA. This circuit is the same as the original circuit with one lamp. Drag the lamp back into the circuit. The current is 180 mA. Since the current has doubled, the resistance round the circuit as a whole is halved.

The voltage across each of the lamps in parallel is 9 V. Charges leaving the battery have gained a definite amount of energy which is not affected by the number of lamps in the external circuit. Energy loss occurs only when the charges begin to flow through the lamps.

Fig.12 shows three lamps connected in parallel. Answer the questions before closing the switch.

What will be the ammeter reading?
•  mA
How much current will flow through each of the three lamps?
•  mA
What will be the voltage across each of the three lamps?
•  V

Click on the figure below to interact with the model.

 Figure 12.  Three lamps connected in parallel.

Series–parallel combinations
To develop your understanding a little further, consider the circuit in Fig.13 with series and parallel elements:

Answer the question before operating the switches in Fig.13.
How will the ammeter reading for the series–parallel combination compare with the reading for the single lamp?

Click on the figure below to interact with the model.

 Figure 13.  Series–parallel combination.

Operate the switches in the simulation. The current is less because any pathway around the circuit passes through more than one lamp. The resistance around the circuit is increased compared with a single lamp.

Drag lamp 1 out of the circuit. The circuit is broken and all the lamps go out. Lamp 1 is in the series part of the circuit. Replace the lamp in the circuit.
How much current is flowing in lamp 1?
•  mA
How much current is flowing in lamp 2?
•  mA

The current divides equally between the two lamps in parallel so that 30 mA flows through each. This is true because the two lamps have the same resistance.

Drag lamp 2 out of the circuit. Current still flows through the parallel pathway and the remaining lamp is brighter because current is no longer being shared. On the other hand, lamp 1 is dimmer because the resistance as a whole around the circuit is increased. Replace lamp 2 in the circuit.
What is the voltage across lamp 2?
•  V

This is the voltage measured by the voltmeter.
What is the voltage across lamp 1?
•  V
 Charges leaving the battery have gained 9 joules per coulomb, charges entering the parallel part of the circuit have 3 joules per coulomb.
 Therefore, 9 − 3 = 6 joules per coulomb have been used up passing through lamp 1.
 In other words, the voltage across lamp 1 is 6 V.

Reality check
In both Introducing Circuits and the present unit, it has been assumed that the properties of lamps remain the same whatever current is flowing and that power supplies can deliver unlimited current. All of this helps in developing a fundamental understanding of circuits, but it should be made clear that the behaviour of real lamps and batteries is not quite so simple.

 Resistance in metallic conductors changes with temperature.
 As the temperature increases, it is less easy for electrons to move around. In other words, the resistance of the material increases.
 Current flowing through a lamp filament causes the filament to heat up and glow white-hot.
 Therefore, the resistance of a normally illuminated lamp is greater than the resistance of the same lamp when disconnected or only partly illuminated.

 Figure 14. White-hot lamp filament.

In real power supplies, the current provided is limited by the internal resistance of the supply. This acts in series with the power supply terminals. The internal resistance is small, less than 1 Ω for most cells and batteries. Provided the resistance in the external circuit is large compared with the internal resistance, the voltage at the power supply terminals will remain close to its rated value. You can find out more about internal resistance from Cells and batteries.

Summary

Current, I, is measured in amperes, amps, A. Other common units are milliamps, mA, thousandths of an amp, and microamps, μA, millionths of an amp.

To connect an ammeter, the circuit must be broken and the meter inserted in series so that the current to be measured flows through the meter.

Voltage, V, is measured in volts, V. This is a measure of the electrical energy gained by charges in the power supply, or lost as charges flow round the external circuit.

To connect a voltmeter, the circuit is unchanged. The voltmeter is connected in parallel across the component of interest.

Resistance, R, is measured in ohms, Ω. Other common units are kΩ, thousands of ohms, and MΩ, millions of ohms.

To connect an ohmmeter, the component must be removed from the circuit altogether and connected to the meter separately.

When components are connected in series, they are joined end to end so that the same current flows through each.

When components are connected in parallel, they are joined side by side to provide alternative pathways for current flow.

Filament lamps are not so simple as they appear.

Exercises
 Figure 15.
The three lamps in Fig.15 have the same properties and their resistance is assumed to be constant. If ammeter A3 reads 50 mA, what will be the reading on ammeter A1?
•  mA   (to the nearest whole number)
What will be the reading on ammeter A2 in Fig.15?
•  mA   (to the nearest whole number)
Calculate the resistance of lamp L3 in Fig.15.
•  Ω   (to the nearest whole number)
 Figure 16.
In Fig.16, the ammeter A1 reads 60 mA and the voltmeter V1 reads 6 V. What will be the readings on the ammeters and voltmeters in the following circuits?

• A2:  mA    V2:  V

A3:  mA    V3:  V

A4:  mA   V4:  V

A5:  mA    V5:  V
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