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# Part 1: Electrical Current

Sections:

### 1.1 The Atom And Electrical Current

All matter is made of atoms. Atoms are very small and when placed in a straight line about 8 million will fit into 1mm. Atoms themselves are made up from three particles: electron, proton and neutrons. Electrons and protons have equal but opposite charges; the electron has a negative charge and the proton has a positive charge. The neutron has no charge. Charges behave like magnetic poles in that alike charges repel and unalike charges attract.

The protons and neutrons make up the nucleus which is at the centre of the atom and the electrons reside around the outside (figure 1.1). Normally an atom will have equal numbers of electrons and protons so that as a whole the atom has no overall charge.

In solid materials that are conductors the electrons are free to move between atoms. The movement may be random in all directions throughout the conductor however, if the electrons move predominantly in one direction an electric current flows. Since the protons are at the centre of the atom they can not break free, therefore electricity is the flow of negative charge and not the flow of positive charge. Because of these phenomena any region of negative charge is formed by an excess of electrons gathering and a region of positive charge is due to electrons moving away, leaving a deficit. Solid materials, where the electrons are not able to move are insulators and such materials do not conduct electricity. Materials that conduct electricity under certain conditions are called semiconductors.

In a piece of metal, a wire for instance, electrons are free to move in any direction. However, as soon as a battery is connected to both ends of the wire the electrons will move towards the positive battery terminal. For every electron that leaves the wire through this terminal, another enters the other end of the wire from the negative terminal; thus the total number of electrons in the wire remains the constant.

This flow of electrons from a negative terminal, through the wire, to the positive terminal is called an electric current. For historic reasons, in most circuits electricity is considered to flow from the positive terminal to the negative terminal; in fact for most circuits it does not matter which direction you consider the electricity to flow.

When a current flows in a conductor two important things happen:

1. heat is generated,
2. a magnetic field is set up around the conductor.

### 1.2 Unit Of Charge And Current

Each electron carries the same amount of negative charge and we could use the charge on a single electron as the unit of charge. However, the charge on an electron is tiny and electric currents contain many electrons flowing through a wire. The unit of charge is thus the coulomb (C) and one coulomb is approximately equal to the total charge of six million million million electrons (to be more exact the charge on one electron is 1.6×10-19, therefore 1C comprises the charge of 6.25×1018 electrons).

If electrons flow past a point on a wire so that 1 coulomb of charge passes every second, a current of one ampere (A) is said to flow. Therefore, electrical current is the rate at which charge passes through a wire. Mathematically we can say: $\mathbf{I=\dfrac{Q}{t}}\quad \text {and}\quad \mathbf{Q=It}$

Where:
Q = the charge transferred in coulombs (C)
I = the current in amperes (A)
t = time during which the current flows in seconds (s)

### 1.3 Energy, Work and Power

Generally speaking energy can either be useful or wasted. For example energy can be used to lift a weight but energy can be lost as heat because of friction. The useful bit of energy is called work and if we lift a weight we are said to have ‘done work’. Work is linked to force by the following equation: $\text {work done (J)\ =\ distance moved (m)}\times \text {froce for movement (N)}$

In this equation force is measured in newtons (N), distance is measured in meters (m) and the work done is measured in joules (J), which is the unit normally used for any energy. To lift an object you need to over come the force of gravity with an equal force acting is in the opposite direction. For this reason the ‘force for movement’ will be equal but opposite to the force opposing the movement.

It is important to note the difference between mass and weight. An object’s mass is due to the amount of matter it contains and has the units of kilograms (kg). Weight is the force that an object exerts downwards towards the ground and is measured in newtons (N). The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity which is 9.8 meters per second per second (often rounded up to 10 m/s2).

Example

How much energy (or how much work) is needed to lift a 70kg man off the floor to a height of 3m (using the acceleration due to gravity = 10 m/s2). $\text {mass weight}=70\times 10=700 N$ $\text{work done}=\text{distance moved}\times \text{opposing force}=3\time 700=2100J$

Power is the rate of using energy or doing work. Lifting the man in the previous example to 3m will always require the same amount of work but the quicker you do it, the more power is needed. $\text{power}=\dfrac{\text{work or energy}}{\text{time}}=\dfrac {\text{joules}}{\text{seconds}}$ $\mathbf{P=\dfrac{W}{t}}$

The unit of power is the watt (W, not to be confused with the symbol for work). One watt is the power used supplying one joule per second. The symbol W is also used for energy used or work done, so be careful not to get confused with W used as the units of power.

### 1.4 Electromotive Force, Potential Difference And Voltage

Moving electrons through a conductor as an electrical current requires energy because, as the electrons move they constantly dissipates energy (as heat). This energy can be supplied by many means including batteries or generators. In the case of a battery chemical energy is converted into electrical energy, whereas a generator converts chemical energy to mechanical energy (through combustion) before turning it into electrical energy. For historical reasons the amount of energy needed to move one coulomb of charge around a circuit is called the electromotive force or EMF (E). The unit of EMF is the volt (V) and one volt is one joule per coulomb, thus: $\text{EMF (V)}\ =\ \dfrac{\text{Energy (J)}}{\text{Charge (C)}}$ $\mathbf{E=\dfrac{W}{Q}}$

Example

A battery with an EMF of 6V can supply a current of 5A round a circuit for five minutes. How much energy is provided?

The total charge transferred in 5 minutes: $Q=It\times 5\times 5\times 60=1500C$

The total energy supplied to do this: $\text{energy}=E\times Q=6\times 1500=9000J$

When you lift a ball to a height of two meters above the ground you give it potential energy. When the ball is dropped this potential energy is converted to kinetic energy until, at the point when it hits the ground, there is no potential energy left. A coulomb of charge travelling around a circuit behaves in a similar way.

Each coulomb of charge leaving from a battery with an EMF of 6V has six joules of potential energy. By the time the charge reaches the battery again, having travelled around the circuit, it will have dissipated all six joules and posses no potential energy. The amount of energy expended by one coulomb of charge when travelling between any two points in a circuit is known as the potential difference (PD) between those points. Since the potential difference is a number of joules per coulomb the unit of PD is the volt (i.e. the same unit used for EMF). The PD between two points is thus called the voltage drop and has the symbol U (the symbol V used to be used). Therefore, from the previous equation we can say: $\mathbf{U=\dfrac{W}{Q}}$

Example

How much electrical energy is converted into heat each minute by an immersion heater which takes 13A from a 240V supply?

Quantity of charge flowing per minute: $Q=It=13\times 60=780C$

Energy converted in one minute: $W=U\times Q=240\times 780=187\ 200=187.5kJ$

### 1.5 Electrical Circuits, Voltmeters And Ammeters

The path around a circuit must be unbroken for an EMF to push electrons around it, such a circuit is said to be closed. If a switch is included in the circuit it can be used to break the path and produce an open circuit where no electrons can flow (figure 1.2a and 1.2b). Figure 1.2: (a) a closed circuit where current (I) can flow; (b) an open circuit where no current can flow.

In a high voltage circuit, current may arc across a small gap causing considerable damage. Most switches will arc briefly when opened however, as long as the current doesn’t jump the gap for too long, it is not a problem.

Voltmeters measure a potential difference between two points and so must be connected in parallel. If you take a voltage reading across a supply in a open circuit you will be measuring the supply’s EMF, you can only measure voltage drops across a load (e.g. a piece of equipment) if a current is flowing. Figure 1.3 shows the placement of voltmeters in a circuit. Ammeters measure the current flowing through a point in a circuit, therefore they are connected in series. Figure 1.3: The placement of voltmeters in parallel. V1 measures the voltage drop across Load 1, V2 measures the voltage drop across Load 1 and Load 2 (which will equal VS if the resistance of the wires is negligible) and VS that measures the supply voltage.

Figure 1.4 shows the placement of a voltmeter in series.