3.1.3 AS Level – Current Electricity Notes – LJ (2010)
Electric current as the rate of flow of charge; / / 2
Potential difference as work done per unit charge. / / 3
Resistance is defined by / / 3
Current / voltage characteristics for an ohmic conductor, a semiconductor diode and a filament lamp; / Candidates should have experience of the use of a current sensor and a voltage sensor with a data logger to capture data from which to determine V /Icurves. / 6
17
Ohm’s law as a special case where current is proportional to potential difference / / 6
Resistivity / / 3-4
14-15
Description of the qualitative effect of temperature on the resistance of metal conductors and thermistors. / Applications (e.g. temperature sensors). / 6 & 7
Superconductivity as a property of certain materials which have zero resistivity at and below a critical temperature which depends on the material. / Applications (e.g. very strong electromagnets, power cables). / Research project
Resistors in series - the relationships between currents, voltages and resistances - / / 9
Resistors in parallel - the relationships between currents, voltages and resistances / / 9
Energy - application, e.g. Understanding of high current requirement for a starter motor in a motor car. / / 10
Conservation of charge and energy in simple dc circuits. / Questions will not be
set which require the use of simultaneous equations to calculate currents or
potential differences. / 2-3
Cells in series and identical cells in parallel. / 22
The potential divider used to supply variable p.d. e.g. application as an audio‘volume’ control. Examples should include the use of variable resistors, thermistors and L.D.R.’s. / The use of the potentiometer as a measuring instrument is not required. / 8
Electromotive force and internal resistance - Applications; e.g. low internal resistance for a car battery. / / 22
Alternating currents - Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only.
Application to calculation of mains electricity peak and peak-to-peak voltage values. / / 21
Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals and frequencies and to display ac waveforms. / No details of the structure of the
instrument is required but familiarity with the operation of the controls is expected. / 18
You are expected to know all of the electricity work you did at GCSE for the A Level SYLLABUS. These notes are designed to lift your knowledge and understanding to AS level.
What is electricity?
Electricity is all to do with the movement of charge. The symbol for charge is Q – it is measured in coulombs (C). Current electricity is to do with the movement of electrons. Each electron has a charge of 1.6 x 10-19C.
There are two parts to ‘electricity’ – current and voltage.
Current (I) is the measurement of the movement of charge – how much charge (Q) moves in one second (t).It is measured with an ammeter. If you want to find the current passing through a component in the circuit, you place an ammeter in series with that component. Current is measured in amps (A). It does not matter where on the strand you place the ammeter.
/
When components are connected in series:
- the potential difference is shared across all of the components according to their resistance;
- the current through each component is the same.
- the total p.d. across the circuit adds up to thep.d. from the power supply.
- there is the same potential difference across each component;
- the current through each component depends on its resistance; the greater the resistance of the component, the smaller the current;
- the total current through the whole circuit is the sum of the currents through the separate components - this follows from Kirchhoff's First Law - see diagram above.
W is ‘work done’ or energy. A joule of energy is required to move a coulomb of charge is moved across a potential difference of one volt. (A joule is a coulomb volt!) or a joule of energy is released (changed into another form) when a coulomb of charge moves across a potential difference of one volt. / Voltage (V) is a measure of the electric potential difference – a difference in the electric field. That is what makes the charge move. It is measured by a voltmeter. If you want to find the potential difference across a component, you place a voltmeter in parallel with the component.
At ‘A-Level’ voltage should be called potential difference – but the symbol for it is still ‘V’. Do NOT call it ‘Pd’ /
Resistance (R) is a measure of how resistant a medium is to an electric current passing through it. It is the ratio of voltage to current - It is measured in ohms (). You never take the gradient of a characteristic curve to find the gradient – you simply find the ratio of the two values. It is V/I not V/I!!
There must be a complete circuit for a current to flow. If there is a gap in the circuit then the whole strand that the gap is in will not have current flow through it. The resistance of an open switch is very high – it takes on the full p.d. from the battery as its resistance is so much higher than the other components in the strand – that is a way you can find a break in a circuit – look for the p.d. across the break!
There are four factors that affect resistance:
Resistance isproportional to length. If you take a wire of different lengths and give each a particular potential difference across its ends. The longer the wire the less volts each centimetre of it will get. This means that the 'electric slope' that makes the electrons move gets less steep as the wire gets longer, and the average drift velocity of electrons decreases. The correct term for this 'electric slope' is the potential gradient. A smaller potential gradient (less volts per metre) means current decreases with increased length and resistance increases. /
Resistance isinversely proportional to cross-sectional-area. The bigger the cross sectional area of the wire, the greater the number of electrons that experience the 'electric slope' from the potential difference. As the length of the wire does not change each cm still gets the same number of volts across it - the potential gradient does not change and so the average drift velocity of individual electrons does not change. Although they do not move any faster there are more of them moving so the total charge movement in a given time is greater and current flow increases. This means resistance decreases. This does not give rise to a straight line graph as cross sectional area is inversely proportional to resistance not directly proportional to it. / Physicists like to get straight line relationships if they can.... can you think of a way of getting a straight line graph through the origin? What would you have to plot?
Resistancedepends on the material the wire is made of. The more tightly an atom holds on to its outermost electrons the harder it will be to make a current flow. The electronic configuration of an atom determines how willing the atom will be to allow an electron to leave and wander through the lattice. If a shell is almost full the atom is reluctant to let its electrons wander and the material it is in is an insulator. If the outermost shell (or sub-shell with transition metals) is less than half full then the atom is willing to let those electrons wander and the material is a conductor.
A graph for this would be a bar chart not a line graph.
Resistanceincreases with the temperature of the wire. The hotter wire has a larger resistance because of increased vibration of the atomic lattice. When a material gets hotter the atoms in the lattice vibrate more. This makes it difficult for the electrons to move without interaction with an atom and increases resistance. The relationship between resistance and temperature is not a simple one – it is no longer on the syllabus!
( (alpha)is the thermal resistance coefficient)
The nature of the material and the temperature is included in the resistivity() of the material – it has a big effect on resistance.
/ Metals have low resistance. That is because they have lots of free electrons - the metallic structure is a 3-D lattice of ions surrounded by a sea of delocalised electrons.In a piece of metal that is not connected to a power supply the delocalised electrons move in random directions (no preferred direction) producing no net charge and no net current flow.
When the metal has a potential difference applied across it the electrons (negative) are attracted to the positive terminal as opposite charges attract. They do not just experience a pull from the positive terminal – they are also pulled by the ions in the lattice – therefore there is not simply a flow of electrons in one direction – they are pulled in all directions – just more in one direction than another. Therefore a general drift of electrons occurs – a drift of electrons that is superimposed on the random movement of electrons that normally occurs in the metal.
The bigger the potential difference the stronger the pull on the electrons – the faster the electrons move and the greater the drift velocity.
Electric potential difference makes current flow.
/ If a ball is placed on a surface it will roll to the point of lowest gravitational energy. It is easy for us to envisage the changes in gravitational potential around us – the topography of the surface is visible – the undulation of the surface and the gradient of the slopes are easily visible to us. We know that steep slopes will cause the ball to accelerate faster than gentle slopes, and that a zero gradient will not cause acceleration at all.
Gravity makes masses accelerate – it provides a force between masses that we can relate to because our own mass experiences the force of attraction between it and the mass of the planet Earth.
The force of gravity experienced between two masses m1 and m2 a distance ‘r’ apart is given by the equation:/ The negative sign indicates it is an attractive force.
G is the gravitational constant – that is on your data sheet.
We find it harder to ‘see’ an electric landscape as we are not naturally aware of the electric dimension around us. But if we were ‘charged beings’ perhaps we would see ‘electric ups and downs’ in the same way as we can see physical slopes around us in this dimension.
Imagine you are a positive charge. The area around another positive charge would appear like a hill to you – you would have to do work to get nearer to it; you would automatically be pushed away by it (see the diagram on the right). The area around a negative charge would appear like a dip to you – you would naturally fall deeper into it – accelerating towards the opposite charge – you would be attracted to it. /
Let’s take this model a little bit further...
In the ‘gravitational’ world the differences in gravitational potential depend on differences in height; in the ‘electrical’ world the difference in electrical potential depends on differences in voltage – called electric potential difference OR just potential difference.
The gradient of a slope is given by the difference in height divided by the horizontal distance it changes over; the ‘electric slope’ called the electric potential gradient is the difference in voltage divided by the distance over which that voltage difference acts. / You can
measure the difference in physical height with a ruler; you can measure the difference in electric potential with a voltmeter.
Electrons have a charge of 1.6 x 10-19C. Metals have a structure that is composed of a lattice of ions surrounded by a sea of electrons. Those electrons move randomly within the metal, their kinetic energy being related to the temperature of the metal. When the electrons in a metal are made to move in a general direction we get a net flow of charge – that is called a current. To get this net flow we have to provide an ‘electric slope’ for the charges to move down – the potential difference.
A battery supplies an ‘electric slope’ for charges in the circuit. One side of the circuit is ‘electrically higher up’ than the other side. The steeper the ‘slope’ the harder the push that the charges will get – therefore the faster they will move. The bigger the potential difference, the bigger the current that flows.
Resistance of a conductor increases with temperature. That is because the lattice of the metal vibrates more as the temperature increases – that increases the interaction of the electrons with the lattice. Increased interaction impedes the movement of the electrons, thereby increasing the resistance of the metal.
Resistance of a thermistor decreases with temperature. More electrons that carry the current are released as it gets warmer – more charge carriers, therefore more current.
/ If the resistance of the wire is constant this relationship is described by this equation:V = IR
Double the ‘slope’ and you double the rate the charge moves... and therefore current doubles too.
If resistance is constant I is directly proportional to V for a given resistance.
This is a special case – it is called Ohm’s Law – and a graph of the results give us the characteristic for an ‘ohmic conductor’.
Ohm’s Law states that for a conductor of constant resistance (a conductor at fixed temperature) the current that flows through the conductor is directly proportional to the potential difference applied across its ends.
To investigate the properties of a component we plot a characteristic curve.
/ The diagram on the left shows a typical experimental set up. The circuit should be set up as shown in the diagram. In this case the bulb used was marked '24W 12V' therefore the potential difference across the bulb was varied from 0V to 12V and voltmeter and ammeter readings and observations were recorded in a table. The experiment was repeated to spot anomalies. Mean values were calculated – anomalies repeated and a graph could then be plotted.
If a wire you investigated was changing temperature you would get a characteristic similar to the characteristic of a filament lamp – because in that the wire is getting hotter as the current flowing though it increases – and that increases the resistance of the wire. Ohm’s Law is NOT obeyed by a filament lamp.
You should know this curve and be able to 'interpret' this characteristic that means explain how it shows that:
- The current through a diode effectively only flows in one direction only.
- It's resistance is very low when connected in forward bias as long as it has a potential difference of more than 0.6 volts (this varies but is usually about 0.6 to 0.7 volts) across it.
- The diode has a very high resistance when it is connected in 'reverse bias' - the opposite direction - therefore only a tiny current flows when this is the case.
- At 0V no current flows.
- At +0.6V the forward current starts to rise sharply.
- At -ve voltage there is a tiny current.
is the symbol for a diode
You should be able to draw this from memory.
If there are arrows coming out of it, it is called a 'light emitting diode' or LED. This is the type of diode that lights up when it is conducting electricity.
This is a semiconductor device – understanding why it behaves as it does requires understanding of a section of physics that we do not have to study any more – so don’t worry about it!
You need to be able to interpret the graph and read resistance at different voltages off it.
Like a resistor, the diode has only two connectors. One is called the anode (it is connected to the positive terminal of the power supply), and the other is called the cathode (it is connected to the negative terminal of the power supply). The diagram below shows drawings of different types of diodes and their electronic symbol.
Notice how the cathode side is marked with a ring or band the ordinary diodes and a flat side and/or short lead because it is important that the diode is connected the correct way round.
AC Supply and the Diode
When alternating voltage is applied across a diode, it will convert the alternating current (AC), which flows back and forth, to direct current (DC), which flows only in one direction - but it only does that for half of the cycle - we say itrectifiesthe current. It only allows half of the current signal to get though.
A capacitor can then be used to smooth the signal - but that is beyond the realms of AS! / When connected into a circuitin forward bias the diode is simply like a conductor wire- it has such a low resistance that it hardly affects current flow.
The p.d. across the diode in a circuit is about 0.6V (it's operating voltage - sometimes the question will state that it is 0.65V or 0.7V). So when analysing circuits you have to remember this. Sometimes the examiner will give you a graph to read the operating voltage from.
Whenconnected in reverse bias the diode acts like an open switch in the circuit(it has a very high resistance) so all of the components on that strand will have a negligible current flowing through them - bulbs will effectively be 'off' because so little current will flow that they will not light up.