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AS91524 : Demonstrate understanding of electrical systems
Level 3 Credits 6
This achievement standard involves demonstrating understanding of electrical systems.
Achievement Achievement with Merit Achievement with Excellence
Demonstrate understanding of electrical systems.
Demonstrate in-depth understanding of electrical systems.
Demonstrate comprehensive understanding of electrical systems.
Assessment is limited to a selection from the following:
Resistors in DC Circuits Internal resistance; simple application of Kirchhoff’s Laws.
Capacitors in DC Circuits Parallel plate capacitor; capacitance; dielectrics; series and parallel capacitors; charge/time, voltage/time and current/time graphs for a capacitor; time constant; energy stored in a capacitor.
Inductors in DC Circuits Magnetic flux; magnetic flux density; Faraday’s Law; Lenz’s Law; the inductor; voltage/time and current/time graphs for an inductor; time constant; self inductance; energy stored in an inductor; the transformer.
AC Circuits The comparison of the energy dissipation in a resistor carrying direct current and alternating current; peak and rms voltage and current; voltage and current and their phase relationship in LR and CR series circuits; phasor diagrams; reactance and impedance and their frequency dependence in a series circuit; resonance in LCR circuits.
Relationships:
E = 21 QV Q = CV d
A
C o^ r ε ε = CT = C 1 + C 2 + τ= RC
1 2
CT C C
φ = BA t
L
ε =− ∆ t
∆φ ε=−
s
p s
p V
V
N
N
E = L Ι
R
L
τ =
Ι =Ι MAX sin ω t V = VMAX sin ω t Ι (^) MAX = 2 Ι rms
VMAX = 2 V rms C
X C
X L = ω L V =Ι Z^ ω^ = 2^ π f
This achievement standard replaced unit standard 6389, unit standard 6390, and AS90523.
Basic Electricity
Stuff you should know from Level 2 (or lower)
Materials that will conduct electricity are called electrical CONDUCTORS. Those that won't are called INSULATORS.
Solids that will conduct electricity (by using batteries alone): all metals (they contain a lot of free electrons) and carbon
Materials that have a very high resistance are called INSULATORS and those that have a low resistance are called CONDUCTORS. A piece of wire is made of millions of atoms and each one of these has its own cloud of electrons. However in a metal there is a large number of electrons that are not held around particular nuclei but are free to move at high speed and in a random way through the metal. These are known are free electrons and in a metal there are always large numbers of these. It is when these free electrons are all made to move in a certain direction by the application of a voltage across the metal that we have an electric current.
The difference between a metal (a large and constant number of free electrons), a semiconductor (a few free electrons, the number of which varies with temperature) and an insulator (which has no free electrons):
Charge and current
As a charge moves round a circuit from the positive to the negative it loses energy. There is a problem here. As you know an electric current is a flow of negatively charged electrons and these flow away from the negative terminal of a supply, round the circuit and back to the positive terminal. However the “conventional” view of current flow is from positive to negative and we will take that view when looking at the energy of electrical charge.
Each electron has only a very small amount of electric charge, and it is more convenient to use a larger unit when measuring practical units of charge. This unit is the coulomb. The charge on one electron is -1.6 x 10-19^ C(usually written as e ) You would need about 5 x 10^18 electrons to have a charge of one coulomb.
Series and Parallel Circuits
If you have a battery and two bulbs they can be connected in series or parallel.
If the batteries and bulbs in both circuits are the same then: (a) the bulbs in the parallel circuit will be brighter than those in the series circuit (b) the battery in the parallel circuit will run down quicker than the one in the series circuit
Connecting an ammeter and a voltmeter
The diagram shows the correct connections for an ammeter and a voltmeter. The ammeter is connected in series with the load and the voltmeter is connected in parallel with the load.
Ohm’s Law
This result was first discovered by a man named Ohm and so it is called Ohm's Law.
Ohm's Law states that:
You can write this in an equation as:
Resistance is measured in units called Ohms (Ω).If you plot a graph of current through a piece of wire against the voltage applied you should get a result like the one shown in the diagram below (the temperature of the wire must not change).
Resistance and heating
When an electric current flows through a wire the wire heats up. This is because the electrons collide with the atoms of the metal as they move and the atoms absorb some of their energy. This makes the atoms vibrate more strongly and so the wire heats up.
The filament in an electric light bulb is very thin and has a high resistance. The heating effect of the electric current flowing through the filament is so great (the temperature of the filament may reach over 1500oC) that the wire glows – this is how electrical energy is converted to light energy.
It is possible to have two wires carrying the same current but one with much more energy than the other.
The low voltage bulb has a current of 1 A flowing through it, it runs on 5 V and gives out energy as heat and light. However the mains bulb runs on 240 V and also has a current of 1 A flowing through it. It gives out a lot more energy and so is much brighter.
Potential and Potential Difference
We define the amount of electrical potential energy that a unit charge has as:
The diagram shows how the potential varies round a basic circuit. (The energy lost in the connecting wires is negligible). This means that the energy of the charge at one end of a connecting wire is the same as that at the other end. The bigger the energy change the bigger the difference in potential. We call the difference in electrical potential between two points in the circuit the potential difference between those two places.
The potential difference between two points is defined as:
The units for potential difference are therefore Joules per coulomb, or volts. (1 volt = 1 Joule/coulomb).
Electromotive force and internal resistance
When current flows round a circuit energy is transformed in both the external resistor but also in the cell itself. All cells have a resistance of their own and we call this the internal resistance of the cell.
The voltage produced by the cell is called the electromotive force or E.M.F for short and this produces a p.d across the cell and across the external resistor.
The E.M.F of the cell can be defined as the maximum p.d that the cell can produce across its terminals, or the open circuit p.d since when no current flows from the cell no electrical energy can be lost within it.
If the E.M.F of the cell is E and the internal resistance is r and the cell is connected to an external resistance R then:
The quantity of useful electrical energy available outside the cell is IR and Ir is the energy transformed to other forms within the cell itself.
We usually require the internal resistance of a cell to be small to reduce the energy transformed within the cell; however it is sometimes helpful to have a rather larger internal resistance to prevent large currents from flowing if the cell terminals are shorted.
Maximum power transfer theorem
The external resistance will affect the current drawn from a source of E.M.F, and therefore the energy lost within it since the same current will also flow through the internal resistance. It is possible to find the value of this external resistance R that will give the greatest power output.
E = IR + Ir
r = R for maximum power output and so the resistance of the load should be equal to the internal resistance of the supply.
This is the case for an amplifier and loudspeaker; the output impedance of the amplifier should be matched to that of the speaker. In other words if the output impedance of the amplifier is 15Ω the resistance of the speaker should also be 15Ω.
(However this condition is not necessarily the most efficient operating state of the system)
Kirchoff's Rules
These two important rules apply to all electrical circuits and are particularly helpful when dealing with branched circuits:
- The algebraic sum of the currents at a junction is zero. In other words there is no build up of charge at a junction
- The sum of the changes in potential round a closed circuit must be zero.
Rule 1 is about charge conservation while rule 2 is about energy conservation.
We can see how these rules work by considering the circuit shown in Figure 1.
Rule 1 At the point B there is a junction Current flowing from the cell (I) = Current in R 1 (I 1 ) + current in R 2 (I 2 )
Rule 2 Round loop A,B,C,D,E: p.d across cell = - p.d across R 1 This represents a gain of potential in the cell but a loss in R 1
Round loop B,C,D,B: p.d across R 1 = - pd across R 2 In this equation there is a minus because we are moving 'against' the current in R 2
Figure 1
A E
C B (^) R 1 D
R 2
I 1
I 2
I
Example problem Consider the circuit shown in Figure 2. Calculate the current shown in each resistor.
The directions of current have been chosen arbitrarily. When we have finished the calculation it may be that we have chosen them incorrectly. If so we can simply reverse them on the diagram.
(a) Rule 1 Apply rule 1 to junction A I 2 = I 1 + I 3 (1)
(b) Rule 2 (i) Choose the loop ABC The sum of the e.m.f.s round this loop is the sum of the (IR) products in the loop. 1.5 – 3 = 20 I 1 + 15 I 2 Therefore: - 1.5 = 20 I 1 + 15 I 2 (2)
(ii) Now consider the loop ADC The sum of the e.m.f.s round this loop is the sum of the (IR) products in the loop. 1.5 – 6 = 10 I 3 + 15 I 2 Therefore: - 4.5 = 10 I 3 + 15 I 2 (3)
Using equations 1 and 2: - 1.5 = 20 I 2 - 20 I 3 + 15 I 2 = 35 I 2 - 20 I 3 (4) Now using equations 3 and 4: - 9 = 20 I 3 + 30 I 2 Solving these gives: I 1 = 0.046 A, I 2 = - 0.162 A, I 3 = - 0.208 A
3 V^20 Ω
6 V
1.5 V
I 1
I 1
I 1
I 1
I 2
I 3
I 2
I 3
I 3 I 3
A C
D
B
Figure 2
The action of a dielectric
When a dielectric material is placed between the plates of a parallel-plate (or other) capacitor the capacitance increases.
The charges on the plates of the capacitor induce opposite charges on the two surfaces of the dielectric. This has the effect of reducing the potential difference across the capacitor. The capacitance of a parallel-plate capacitor with a material of relative permittivity εr filling the space between the plates is
where εr is the ratio of the capacitances when the space between the plates is a vacuum or a dielectric.
Practical forms of capacitor
Most capacitors are of the parallel-plate type, either as two flat plates or as a 'swiss roll' arrangement, with the plates and dielectric rolled into a cylinder.
The air capacitor has the advantage of being simple to make and having a precisely known capacitance with almost perfect properties at all frequencies. The tuner in a radio is a variable air capacitor, consisting of two sets or plates in air overlapping each other. The overlap of the plates and hence the capacitance may be varied by moving one set of plates into the other.
Paper capacitors are thin metal sheets, with a paper dielectric of relative permittivity of about 5 between them. They are then rolled into a cylinder. The whole arrangement is packed in a cylinder of metal or plastic. Such capacitors are not very stable but they are cheap to make.
Electrolytic capacitors are made by passing an electric current through a solution of aluminium borate using aluminium electrodes. When this happens a very thin layer of oxide forms on the anode. The thickness of this layer depends on the applied potential difference and on the time for which the current is passed. This oxide film is used as the dielectric in electrolytic capacitors. It may be very thin, less than 10 -7m but it has very high insulation strength of some 10^9 V m- 1
Breakdown potential for a capacitor
Every capacitor has a working voltage, this is the maximum potential that should be applied between the plates. Any more than this and the dielectric material between the plates will break down and become conducting and the capacitor will be destroyed, usually resulting in a small bang as the material breaks down. Warning: Some badly made power supplies have a capacitor connected across their outputs and so remain live even after the power supply has been switched off. Always be careful when handling apparatus containing capacitors.
Capacitor networks
In practical circuits capacitors are often joined together. We will consider the cases of two capacitors, first in parallel and then in series.
(a) If two capacitors are connected in parallel.
The potential across both capacitors is the same (V) and let the charges on the capacitors be Q 1 and Q 2 respectively.
Now Q = CV, and so Q = C 1 V and Q = C 2 V. But the total charge stored Q = Q 1 + Q 2 , therefore
Q = Q 1 + Q 2 = V(C 1 + C 2 )
Giving:
(b) If two capacitors are connected in series.
The charge stored by each capacitor is the same. If V 1 and V 2 are the potentials across C 1 and C 2 respectively then: V 1 = Q/C 1 and V 2 = Q/C 2. Therefore: V = V 1 + V 2 = Q(1/C 1 + 1/C 2 )
(Notice that they are the "reverse" of the formulae for two resistors in series and parallel)
The charge distribution on series and parallel capacitors
When two capacitors are joined tighter in a circuit and then connected to a voltage supply charge will move onto the plates. The actual distribution of charge for a series and parallel circuit is shown below:
Discharging a capacitor
When t = RC, V = Vo/e = 0.37 Vo and the product RC is known as the time constant for the circuit. The bigger the value of RC the slower the rate at which the capacitor discharges.
The value of C can be found from this discharge curve if R is known.
Charging a capacitor
As the capacitor charges the charging current decreases since the potential across the resistance decreases as the potential across the capacitor increases.
The area below the current-time curve in both charging and discharging represents the total charge held by the capacitor.
The energy stored in capacitor
The energy stored in a capacitor is given by the equation:
Since the energy supplied by a power source is E = QV this means that capacitors store half the energy supplied to them (the rest is lost as heat in the wires and the power source).
Basic Magnetism
Magnetic fields have a large number of uses in the modern world in, for instance, particle accelerators, plasma bottles, lifting magnets, linear induction motors, hard drive heads and many other applications. Knowledge of those fields has also helped in the studies of the Physics of the van Allen radiation belts, quasars and aurorae.
Flux and flux density
To understand the meaning of magnetic flux (Ф) and magnetic flux density (B) think first about an ordinary bar magnet.
Around the magnet there is a magnetic field and this gives a ‘flow of magnetic energy’ around the magnet. It is this flow of energy that we call magnetic flux ( Ф ). Magnetic flux flows from the north pole of a magnet round to its south pole as shown by the arrows on the lines in the diagram.
Magnetic flux is given the symbol Ф and is measured in units called Webers (Wb).
The amount of magnetic flux flowing through a given area will change from one point to another around the magnet.
In position B there are a smaller number of magnetic field lines passing through the loop than there is when it is in position A so the magnetic field is stronger at A. The amount of flux passing through a unit area at right angles to the magnetic field lines the flux density (B) at that point.
Flux density is measured in Tesla (T) where 1 T = 1 Wbm-
If we now use more than one loop of wire, in others words a coil of N turns as shown in position C the flux flowing through the N turns is simply N times that flowing through the single loop. The quantity N Ф is called the flux linkage for the coil at that point.
When an electric current flows in an anti- clockwise direction in a current- carrying coil, the end of the coil behaves likes the North pole of a magnet as predicted by:
When an electric current flows in an clockwise direction in a current- carrying coil, the end of the coil behaves likes the South pole of a magnet as predicted by:
Electromagnetic Induction: Induction (magnetism makes current)
Fleming's right-hand rule
Fleming proposed a simple rule for giving the direction of the induced current to explain Faraday's experiments:
The right hand slap rule shows the direction of the induced current where the thumbs indicates the direction of the movement and the fingers pointing at 90o^ point in the direction of the magnetic field.
Electromagnetic induction is used in most modern devices.
Electromagnetic induction may sound rather complicated but all it means is a way of generating electricity by using moving wires, moving magnets or changing the voltages in one coil to make electrical energy in another.
A voltage (E.M.F) can be induced in a wire or a coil if the wire is in a region where the magnetic field is changing. This can be done by: (a) moving the wire through a fixed field (b) moving a fixed field (a permanent magnet) relative to the wire or (c) varying the field by using A.C. in a coil
When a coil is moved into a magnetic field, the current induced in the wire can be predicted by the right hand slap rule.
Current cannot be made when the coil is completely in or out of the magnet field as the two currents cancel each other out (the current flowing around the coil is a consequence only of the current induced between Z and Y). The graph below shows the induced current as a coil passes through a magnet field.
However, you can create a resultant current in a constant magnetic field if you rotate the wires.
This effect is used in electrical generators (the one shown is an A.C. generator).
As the coil rotates it cuts through the lines of magnetic flux producing an induced E.M.F
In generators where the output current may be very large, as in a power station, it is the magnet that rotates while the coil remains at rest.
In modern alternators installed in a power station the E.M.F generated will be some 25 kV and the current produced over 1000 A!
Effect of changing the speed of rotation of the coil on the induced E.M.F. If the speed of rotation of the coil is changed two things happen
(a) since the rate of cutting of magnetic flux is increased the output E.M.F will be increased also in line with Faraday’s law
(b) the frequency of the output E.M.F will be increased as well since the coil makes a revolution in a shorter time
Induced E.M.F
When the magnetic flux through a coil changes, the E.M.F generated in the coil can be expressed as:
This change of flux ø can be produced by either: (a) moving the wire or coil through the field or (b) changing the intensity of the magnetic field
If we think of a conductor moving through a constant magnetic field then the E.M.F (E) generated between the two ends of the conductor at any moment is given by the equation:
where N is the number of conductors cutting the flux (If there is only one wire cutting the field N = 1).
For an electrical generator this can be made into the equation:
Lenz's law
The direction of the induced E.M.F was explained by Lenz who proposed the following law in 1835:
We can explain this law by considering the energy changes that occur when a magnet is moved towards a coil. Assume that the magnet is moved towards the coil with its north pole facing towards the coil. Now by Lenz's law this should induce a current in the coil such that the right-hand end of the coil (B) nearest the magnet is also a north pole. If this is true then it should repel the magnet and work must be done on the magnet to move it in against this repulsion.
The energy used goes to produce the induced E.M.F in the coil.
Since the E.M.F generated opposes the changes that produce it, it is known as a back E.M.F. This effect is particularly important in electric motors.
Self-inductance
If the current through a coil is altered then the flux through that coil also changes, and this will induce an E.M.F in the coil itself. This effect is known self-induction and the property of the coil is the self-inductance (L) of the coil, usually abbreviated as the inductance.
An air-cored inductor is connected in series with a d.c. supply and a 12 V bulb.
The resistance of the solenoid will be low so that it barely affects the light emitted by the bulb, and placing an iron core inside the inductor will make no difference to the bulb's brightness.
If the experiment is repeated using a.c. with an air core, the inductance will probably prevent the lamp from reaching its full brightness. If an iron core is placed inside the solenoid, however, its inductance is increased considerably and the lamp goes out due to the increased self-inductance and resulting back E.M.F in the coil. The coil and iron rod are called a choke.
A single wire connected to a cell and doubled back on itself has no net magnetic field - the field produced by the current in one direction cancels that produced by the current in the other. This is known as non-inductive winding.
