Introduction

Many scientists in the eighteenth century believed that there was only one type of mobile electrical charge: positive electricity. They proposed that materials became positively charged when electrical particles were added to them while materials having fewer electrical particles were negatively charged.

These scientists were correct in thinking that objects were charged by the movement of electrical charges. However modern experiments have shown that objects are generally charged by the movement of negatively charged electrons. The properties of conductors, insulators, and even semiconductors can be explained by considering the movement of electrons.

Many scientists in the eighteenth century believed that there was only one type of mobile electrical charge: positive electricity. They proposed that materials became positively charged when electrical particles were added to them while materials having fewer electrical particles were negatively charged.

These scientists were correct in thinking that objects were charged by the movement of electrical charges. However modern experiments have shown that objects are generally charged by the movement of negatively charged electrons. The properties of conductors, insulators, and even semiconductors can be explained by considering the movement of electrons.

Charges on the move

Press the button in Fig.1 below to start the experiment. You should notice that when the ping-pong ball, coated with metallic
paint, is touched against the negatively charged plate it begins shuttling to and fro between the charged plates.Use the slider to alter the distance between the plates and note that the

**current**The

**unbalanced force***rate*at which the ball transfers small quantities of charge from one terminal of the power supply to the other across the gap.

Moving the plates closer together makes the ball shuttle more frequently between the plates and so the total quantity of charge transferred per second increases. This is shown as a higher reading on the ammeter.

Push the switch in the circuit in Fig.2 to connect the power supply and ammeter to a lamp.

Click on the figure below to interact with the model.

Pushing the switch in Fig.2 means that the lamp lights up and the ammeter registers a current.

From the shuttling ball experiment in Fig.1 we saw that when the ball transferred charges, the ammeter detected a current. In the circuit in Fig.2 we see that when we pushed the switch to connect the power supply, the ammeter again detected a current. From these two observations we can conclude that a current is a flow of individual charges from one terminal of a power supply to the other.

Charge and current

Quantities of charge are measured in coulombs (C). One

**coulomb**^{18}electrons.coulomb is approximately equivalent to the charge carried by 6.25 × 10

^{18}electrons.

Current is defined as the rate of flow of charge. This means that the size of a steady current is the quantity of charge flowing past a particular point in a circuit in 1 second. The base unit for current is the

**ampere**The precise definition of 1 ampere is stated in terms of the magnetic effect of a current passing through a conductor; however, as a working definition we can say that there is a current of 1 A in a circuit when 1 C of charge passes any point in 1 second. In symbols, the current in a circuit

*I*is defined as:

where

*Q*is the quantity of charge, in coulombs, moving between the ends of a conductor in a time of

*t*seconds.

Our definition states that a current is the flow of charge per second. A current of 5 A indicates that charge is flowing in a circuit at a rate of 5 coulombs per second (Cs

^{−1}). Therefore we can say that 5 A is equivalent to 5 coulombs per second (5 Cs

^{−1}). By rearranging the equation above we can also see that a charge of 500 C could be written as 500 amp seconds (500 As).

Current in a series circuit

When the switch is closed in the circuit in Fig.3 the ammeters show the currents before and after each of the components
in the simple **series**circuit.

Click on the

**voltage**Click on the figure below to interact with the model.

When components are joined in series the current at all points in the

**series circuit**Any alteration to the supply voltage will alter the size of the current at

*all*points in a series circuit.

Current in a parallel circuit

The circuit in Fig.4 shows a lamp and buzzer connected in **parallel**. Ammeters are used to measure the current at various parts of the circuit. When the switch is closed, two of the ammeters show the currents in the branches of the

**parallel circuit**Click on the battery in Fig.4 and enter any value for the battery voltage in the range 0 to 20 V. Pay particular attention to the readings on the ammeters.

Click on the figure below to interact with the model.

Compare the three current readings you have taken.

Change the battery voltage and see if the relationship is still true.

You should have found that when components are joined in parallel, the total current taken from the battery is equal to the sum of the currents in the parallel branches.

This can be expressed mathematically as:

This equation can also be described by saying that the sum of the currents entering a junction in a circuit is equal to the sum of the currents leaving the junction. This is known as

**Kirchhoff's First Law**Kirchhoff's First Law

Kirchhoff's First Law is a consequence of the fact that there is no build-up of charge at any point in a simple circuit so
charges must flow into and out of any junction in a circuit at the same rate.
Voltage

When the switch in Fig.7 is held closed some chemical

**energy**Click on the figure below to interact with the model.

Push the switch in Fig.7 to complete the circuit. As charges pass through the buzzer some of their electrical energy is converted into sound. Since energy is given out by the buzzer, the charges leaving the buzzer have less energy than those entering. This electrical energy difference across the buzzer is maintained by the battery. Each coulomb of charge moving from the high-energy side of the battery to the low-energy side carries a certain quantity of energy from the battery to the buzzer.

The voltage

*V*across the buzzer is defined by the equation:

where

*W*is the electrical energy transferred by

*Q*coulombs of charge passing through the buzzer. With this definition we are able to describe the voltage as the energy transformed per coulomb. A 6 V battery will transfer 6 joules of energy to each coulomb of charge leaving the battery.

Electrical energy is classified as one type of potential energy. Since the energy of the charges entering and leaving the buzzer is different, we can say that there is an 'electrical energy difference' across the buzzer. This is more commonly referred to as a

**potential difference**or

**p.d.**The size of the voltage across any component in a circuit is numerically the same as the potential difference. When describing electrical circuits the terms 'voltage' and 'p.d.' are often used interchangeably.

As well as having different voltages, batteries are available in a range of different physical sizes.

Voltage

*V*is measured in units of volts (V) if the energy

*W*is measured in joules (J) and the charge

*Q*is measured in coulombs (C). One volt is the electrical energy difference between two points if one

**joule**Voltage in series circuits

In Fig.9 the

**LED**Click on the battery in Fig.9 and enter a value for the battery voltage in the range 0 to 20 V. Pay particular attention to the readings on the voltmeters.

Click on the figure below to interact with the model.

When components are joined in series with a battery, the battery voltage is the

*sum*of the voltages across the individual components. This can be expressed mathematically as:

If the supply voltage changes the voltages across

*each*component changes but their sum always equals the supply voltage.

Voltage in parallel circuits

In Fig.10, the lamp and buzzer are connected in parallel and voltmeters are used to measure the p.d.s across various parts
of the circuit. When the switch is closed, two of the voltmeters show the p.d.s across the components connected in parallel.
The other voltmeter shows the total supplied by the battery. Click on the battery and enter any value for the battery voltage in the range 0 to 20 V.

Click on the figure below to interact with the model.

When components are joined in parallel the voltage across

*each*of the branches in the parallel circuit is the same. This can be summarized mathematically as:

Altering the supply voltage alters the voltage but the voltage across each component is always the same.

EMF and potential difference

The idea of electric current that we have considered so far is based on energized charges flowing from a battery and delivering
their energy to components such as buzzers and lamps. The charges then return to the battery to be re-energized.
The chemical reaction in the battery has the capacity to provide energy to the charges. The

*total*energy provided by any power supply, such as a battery, to each coulomb of charge is called the

**EMF**. The letters

**EMF****electromotive force**. As a result you might think that this is a type of force, and that it should be measured in units of newtons. However, this is not the case!

The EMF is the energy supplied to each coulomb of charge leaving the battery and its units are therefore JC

^{−1}. These are exactly the same units as voltage, so EMF values can also be quoted in volts (V).

Click on the figure below to interact with the model.

In each of the cases in Fig.11 you should have noticed that the sum of the supply EMFs equals the sum of the p.d.s across the components.

The behaviour of the circuit in Fig.11 can be summarized mathematically in the equation:

Electrical power

We can combine two of our existing equations to derive an expression for the electrical energy transformed per second (

**electrical power** and |

Combining these two equations gives |

Rearranging this gives |

The term W/t is the energy transferred per second. This is called the electrical power P which is measured in units of watts. |

Therefore |

The energy transferred per second to an electrical component is called the electrical

**power***P*) and is measured in units of watts. Mathematically, electrical power is calculated from the equation:

Summary

Electrical current is the result of charges moving in a circuit. The magnitude of the current is defined as the rate of flow of charge and can be calculated using the equation below:

The current through all components connected in series is equal. In parallel circuits, the total current is the sum of the currents in the individual branches.

The EMF (electromotive force) of a battery is a measurement of its capacity to provide energy to the charges.

The magnitude of a voltage is defined as the energy supplied to each coulomb of charge. The voltage can be calculated using the equation:

The p.d.s across components connected in parallel are the same.

The total p.d. across components in series is equal to the sum of the p.d.s across the individual components.

The rate at which electrical energy is transferred to a component is called the electrical power. Power is calculated by multiplying the p.d. across by the current through the component:

Electrical current is the result of charges moving in a circuit. The magnitude of the current is defined as the rate of flow of charge and can be calculated using the equation below:

The current through all components connected in series is equal. In parallel circuits, the total current is the sum of the currents in the individual branches.

The EMF (electromotive force) of a battery is a measurement of its capacity to provide energy to the charges.

The magnitude of a voltage is defined as the energy supplied to each coulomb of charge. The voltage can be calculated using the equation:

The p.d.s across components connected in parallel are the same.

The total p.d. across components in series is equal to the sum of the p.d.s across the individual components.

The rate at which electrical energy is transferred to a component is called the electrical power. Power is calculated by multiplying the p.d. across by the current through the component:

Well done!

Try again!