Physics revision | GCSE and A Level Physics Revision ...



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|Detail lifted from the Syllabus |Page No. |

| |[pic] |2 |

|Electric current as the rate of flow of charge; | | |

|Potential difference as work done per unit charge. |[pic] |3 |

|Resistance is defined by |[pic] |3 |

|Current / voltage characteristics for an ohmic conductor, a semiconductor |Candidates should have experience of the use of a |6 |

|diode and a filament lamp; |current sensor and a voltage sensor with a data |17 |

| |logger to capture data from which to determine V / I | |

| |curves. | |

|Ohm’s law as a special case where current is proportional to potential |[pic] |6 |

|difference | | |

|Resistivity |[pic] |3-4 |

| | |14-15 |

|Description of the qualitative effect of temperature on the resistance of |Applications (e.g. temperature sensors). |6 & 7 |

|metal conductors and thermistors. | | |

|Superconductivity as a property of certain materials which have zero |Applications (e.g. very strong electromagnets, power |Research project |

|resistivity at and below a critical temperature which depends on the |cables). | |

|material. | | |

|Resistors in series - the relationships between currents, voltages and |[pic] |9 |

|resistances - | | |

|Resistors in parallel - the relationships between currents, voltages and |[pic] |9 |

|resistances | | |

|Energy - application, e.g. Understanding of high current requirement for a |[pic] |10 |

|starter motor in a motor car. | | |

|Conservation of charge and energy in simple dc circuits. |Questions will not be |2-3 |

| |set which require the use of simultaneous equations | |

| |to calculate currents or | |

| |potential differences. | |

|Cells in series and identical cells in parallel. | |22 |

|The potential divider used to supply variable p.d. e.g. application as an |The use of the potentiometer as a measuring |8 |

|audio ‘volume’ control. Examples should include the use of variable |instrument is not required. | |

|resistors, thermistors and L.D.R.’s. | | |

|Electromotive force and internal resistance - Applications; e.g. low |[pic] |22 |

|internal resistance for a car battery. | | |

|Alternating currents - Sinusoidal voltages and currents only; root mean |[pic] |21 |

|square, peak and peak-to-peak values for sinusoidal waveforms only. | | |

|Application to calculation of mains electricity peak and peak-to-peak | | |

|voltage values. | | |

|Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals |No details of the structure of the |18 |

|and frequencies and to display ac waveforms. |instrument is required but familiarity with the | |

| |operation of the controls is expected. | |

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|[pic] |

|one second (t). | |

|It is measured with an ammeter[pic]. 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. | |

|[pic] | |

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|When components are connected in series: |

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|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 the p.d. from the power supply. |

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|When components are connected in parallel: |

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|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|Voltage (V) is a measure of the |[pic] |

|of energy is required to move a |electric potential difference – a | |

|coulomb of charge is moved across a|difference in the electric field. | |

|potential difference of one volt. |That is what makes the charge | |

|(A joule is a coulomb volt!) or a |move. It is measured by a | |

|joule of energy is released |voltmeter. If you want to find the| |

|(changed into another form) when a |potential difference across a | |

|coulomb of charge moves across a |component, you place a voltmeter | |

|potential difference of one volt. |in parallel with the component. | |

|[pic] |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 (Ω). 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 ΔV/ΔI!! |

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| |

|[pic] |

|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 is proportional 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 is inversely proportional to cross-sectional-area. The bigger the cross |Physicists like to get straight line relationships if they can.... can |

|sectional area of the wire, the greater the number of electrons that experience the |you think of a way of getting a straight line graph through the origin? |

|'electric slope' from the potential difference. As the length of the wire does not |What would you have to plot? |

|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. | |

Resistance depends 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.

Resistance increases 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!

[pic] (α (alpha) is the thermal resistance coefficient)

The nature of the material and the temperature is included in the resistivity (ρ) 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 |The negative sign indicates it is an attractive force. |

|‘r’ apart is given by the equation: |G is the gravitational constant – that is on your data sheet. |

|[pic] | |

|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... |You can |

|In the ‘gravitational’ world the differences in gravitational potential |measure the difference in physical height with a ruler; you can measure |

|depend on differences in height; in the ‘electrical’ world the difference|the difference in electric potential with a voltmeter. |

|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. | |

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. [pic] |

| |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 | The diagram on the left shows a typical experimental set up. The circuit should be set up as |

|plot a characteristic curve. |shown in the diagram. In this case the bulb used was marked '24W 12V' therefore the potential |

|[pic] |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. |

|[pic] |[pic] |

|You should know this curve and be able to 'interpret' this characteristic |[pic]is the symbol for a diode |

|that means explain how it shows that: |You should be able to draw this from memory. |

|The current through a diode effectively only flows in one direction only. |If there are arrows coming out of it, it is called a 'light emitting diode' or |

|It's resistance is very low when connected in forward bias as long as it |LED. This is the type of diode that lights up when it is conducting |

|has a potential difference of more than 0.6 volts (this varies but is |electricity. |

|usually about 0.6 to 0.7 volts) across it. |This is a semiconductor device – understanding why it behaves as it does |

|The diode has a very high resistance when it is connected in 'reverse bias'|requires understanding of a section of physics that we do not have to study any|

|- the opposite direction - therefore only a tiny current flows when this is|more – so don’t worry about it! |

|the case. |You need to be able to interpret the graph and read resistance at different |

| You should note that: |voltages off it. |

|At 0V no current flows. | |

|At +0.6V the forward current starts to rise sharply. | |

|At -ve voltage there is a tiny current. | |

|[pic] |When connected into a circuit in forward bias the diode is simply like a |

|Like a resistor, the diode has only two connectors. One is called the anode|conductor wire - it has such a low resistance that it hardly affects current |

|(it is connected to the positive terminal of the power supply), and the |flow. |

|other is called the cathode (it is connected to the negative terminal of |The p.d. across the diode in a circuit is about 0.6V (it's operating voltage - |

|the power supply). The diagram below shows drawings of different types of |sometimes the question will state that it is 0.65V or 0.7V). So when analysing |

|diodes and their electronic symbol. |circuits you have to remember this. Sometimes the examiner will give you a |

|Notice how the cathode side is marked with a ring or band the ordinary |graph to read the operating voltage from. |

|diodes and a flat side and/or short lead because it is important that the |When connected in reverse bias the diode acts like an open switch in the |

|diode is connected the correct way round. |circuit (it has a very high resistance) so all of the components on that strand|

|AC Supply and the Diode |will have a negligible current flowing through them - bulbs will effectively be|

|When alternating voltage is applied across a diode, it will convert the |'off' because so little current will flow that they will not light up. |

|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 it rectifies the current. It only allows half of the | |

|current signal to get though. |[pic] |

|A capacitor can then be used to smooth the signal - but that is beyond the | |

|realms of AS! | |

[pic]

Simple Circuit Analysis

Basic ideas to grasp before you look at circuit diagrams:

Voltage (V ) is an electric potential difference. It is measured in volts (V) with a voltmeter connected in parallel across the points in the circuit you wish to compare. If there is a potential difference across two points in the circuit current will flow between them. How big that current is will depend on the resistance between the two points.

Charges ‘fall’ from high electric potential to low electric potential. A power supply therefore provides a ‘slope’ or potential gradient down which the charged objects (electrons or ions) will flow.

Current (I ) is the rate of flow of charge (Q ) through a component – how much charge moves in a given time. It is measured in amps (A) using an ammeter in series with the component you are interested in.

• The charged objects that move in a wire are electrons. They have negative charge. They are the electrons that are loosely held by the atoms that make up the wire.

• The total amount of charge moving in a given time (current) depends on how many electrons move and how fast they move. The same current could be obtained by having double the number of charges moving at half the speed.

Resistance (R) is a measure of the reluctance of the conductor to allow the charges to move through it. It is measured in ohms ([pic]).

Good conductors have loosely held outer shell electrons that they are 'happy' to allow to move away from the parent atom - they have low resistivity making their resistance lower than that of an insulator of the same dimensions. Insulators hold on tightly to their electrons and do not let them wander therefore there are no free electrons to carry the charge and the resistivity of the material is high. The structure of the atom the material is made of therefore has a big effect on the resistance of the material.

A ‘wider’ wire – NEVER call it that in an answer (a wire of bigger diameter – cross section) has more electrons moving down the potential gradient provided by the power supply; therefore a wire of bigger diameter will allow a bigger current to flow through it if a given voltage is put across it. This makes its resistance smaller. The average drift velocity of the electrons does not change (the ‘slope’ is still the same steepness) – it is the increase in number moving that alters the current.

A longer wire has fewer volts per metre as the volts are shared out across more wire – the potential gradient is therefore not as steep and the average drift velocity of the electrons will be less making the current smaller. This means that a longer wire has a bigger resistance. The number moving in a given length of the wire is the same – it is the change in their drift velocity that changes the current.

| |When components are connected in series their resistances are added to give a sum total. |

| |A useful fact - when components are connected in parallel the resistance of the whole parallel |

| |arrangement is always smaller than the resistance of the lowest value strand of the arrangement. |

| |A useful shortcut - if you have N identical resistors of value R [pic] in parallel with each other |

| |the resistance of the whole arrangement is R/ N [pic] |

Ammeters have very low resistances. (They are made by connecting a low resistance shunt in parallel with a galvanometer to give them a very low resistance). They can therefore be connected in series with a component in a circuit without changing the resistance on that strand of the circuit by very much at all.

Voltmeters have a very high resistance, (They are made by connecting a high resistance shunt in series with a galvanometer to give them that very high resistance). They can therefore be connected in parallel with a component in a circuit without changing the resistance of the circuit by very much at all.

Step 1: Split it into strands

A ‘strand’ is a route to/from the power supply that does not branch off midway. Therefore if you have parallel components in series with other components you have to simplify that arrangement before you can do this step.

In the above example:

Strand 1 has two resistors in series they will therefore share the voltage drop from the supply.

Strand 2 only has one resistor it will therefore get the entire voltage drop from the supply.

Strand 3 poses a problem. The equivalent resistance of the two in parallel has to be found first. Once this has been done the strand will be like strand 1 – two in series.

is equivalent to a single resistor of R / 2 (see the ‘tip’ above) we can therefore re-sketch the circuit or (to save time in an exam!) mark on it in such a way as to indicate this.

 

[pic]

Step 2: Share out the voltages

Pure parallel components can be split into separate routes back to the power supply; therefore they each become strands of the circuit. You need to simplify resistor arrangements until you have a simple parallel circuit.

Each strand has access to the full potential difference provided by the power supply. Whatever a voltmeter around the power supply reads is what a voltmeter around the components on that strand will read. We say that the potential or voltage drop across the components is the same as the potential drop across the power supply.

That means that the whole of strand 1 (the one with R 1 in it) will have the same voltage across it as the battery does – the reading on the voltmeter. The ammeter and resistor together share the potential drop from the battery.

The same is true for each of the three strands in our circuit (from above).

Rather than draw in lots of voltmeters get into the habit of putting arrows across each strand to show how the voltage is distributed. It is a good idea to have a marker pen (not green or red!) with you in the exam to do this when you have circuit diagrams to deal with.

Strand 1 is easy – two equal resistors so they get half each.

Strand 2 is easy too, as the entire potential drop is across one resistor.

Strand 3 is a bit trickier. V is shared across 1.5R, therefore each R gets V / 1.5 = 2 / 3V . That makes R get 2 / 3V and R / 2 get 1 / 3V

Why ammeter voltage drops can be ignored

The resistance of an ammeter is negligible. Therefore the voltage share that it gets when it is in a strand is negligible also and generally we can ignore the voltage drop that an ammeter would get and assume that for all intents and purposes it is zero.

This is not really the case. It does have a resistance and therefore does take some of the voltage drop but if your voltmeter can only be read to three or four significant figures (which is usually the case) it will not record that difference and read zero when placed in a circuit.

Let’s do a calculation to work out what that voltage value would be. Suppose an ammeter has a resistance of 6.3 m[pic] and it is positioned on a strand of a circuit with a 420m[pic] resistor and a potential difference of 9.0 V is provided by a power supply.

 Total resistance of the strand is 420m[pic] plus 6.3 m[pic] as the resistor and the ammeter are in series.

Therefore the total resistance of the strand = 0.420 [pic] + 0.000 006 3 [pic] = 0.420 006 3 [pic].

The voltage is shared out across the strand according to the resistance values… each ohm gets the same voltage drop.

So, 0.420 006 3 [pic] share 9V

therefore each ohm gets 9 / 0.420 006 3 V

and the ammeter gets 0.000 006 3 x 9 / 0.420 006 3 V = 0.000 14 V

This value is so low it would not show up on the multimeters we use in class. The voltmeter would read zero and we can therefore ignore the ammeters in the circuit.

Step 3: Calculate the current or 'heat dissipation' (power output as heat) in a component

Now that we have the value of each resistance and the p.d. across each one it is easy to work out the current passing through a component. We just use V =I R.

To calculate the heat dissipated in a component

Whenever a current passes through a component electrical energy is changed into heat energy. The dissipation of energy as heat is calculated using P = IV where P is power (energy in unit time – W - watts (J/s - joules per second).

Using V =I R we can substitute into this equation:

 P = IV but V =I R

so, P = I(IR) = I 2 R

Also I = V/R

so, P = (V/R) V = V 2/R

So, P = IV = I2 R = V 2/R

When to ignore the current through a voltmeter

The total current that flows through a parallel arrangement depends on the voltage drop across it. Voltmeters have very high resistance. They make very little difference to the total resistance of the arrangement.

Let us demonstrate this with a calculation:

Three resistors in parallel (2.0 [pic] , 5.0 [pic] and 20 [pic]) – calculate the equivalent resistance.

[pic]

1 /R TOTAL = 1/2 + 1/5 + 1/20 = 0.75

So, R TOTAL = 1/0.75 = 1.3 ( or 4/ 3) [pic]

(2 s.f. because the resistances were given to that standard)

(Note that this is smaller than the smallest one in the arrangement! This is always the case – useful tip!!)

If we now add a voltmeter of resistance 3 000 [pic] to the arrangement let us look at the effect it has on the value of the resistance of the arrangement:

[pic]

1 /R TOTAL = 1/2 + 1/5 + 1/20 + 1/3000 = 0.75033

(Working to so many figures purely to illustrate the point!)

So, R TOTAL = 1/0.75033 = 1.3 [pic] (the same value)

The voltmeter does not interfere in a measurable manner with the resistance of the arrangement. You would need very sensitive meters to notice the difference. The higher the resistance of the voltmeter the less it interferes with the circuit it is measuring potential differences in.

 The current that passes through the arrangement will be greatest in the resistor of lowest value. Let us suppose that a voltage of 6.0 V was applied across our arrangement. We can work out the current through the whole arrangement using V = IR

V = IR

I = V / R

= 6.0 / 1.33

(Here a calculated value is put in at one more sig fig than we must quote to – necessary for accuracy – always work to one more figure!)_

= 4.5 A

This current is split into the four branches of the circuit. Using the values of each of the resistors in turn with the p.d. across them we can work out how much current goes into each strand.

|2.0 [pic] resistor |5.0 [pic] resistor |20 [pic] resistor |3000 [pic] voltmeter |

|V = IR |V = I R |V = IR |V =IR |

|I= V / R |I = V / R |I= V / R |I = V / R |

|= 6.0 / 2.0 |= 6.0 / 5.0 |= 6.0 / 20 |= 6.0 / 3000 |

|= 3.0 A |= 1.2 A |= 0.30 A |= 0.002 A |

Sum of currents = 0.002 A + 0.30A + 1.2 A + 3.0 A = 4.502 A

= 4.5 A (2 sig figs) – we can ignore the current draw by the voltmeter as it is so small

The only time a voltmeter will interfere with a circuit is if it is used with resistors of large values similar to that of its own resistance. You should then find out how much current it does draw from the power source as it will be similar to that of the resistors and it will interfere with the resistance of the resistor within the circuit.

Always read the question carefully. If it says a ‘high resistance voltmeter…’ it means ignore the current drawn by it and assume it does not affect the resistance of the circuit. BUT if it gives you the resistance you need to do calculations with that resistance to find out what it reads.

In this circuit let us suppose the value of V is 9 volts, the value of R is 30[pic]W and the voltmeter has a resistance of 3000 [pic].

Because the resistance of the voltmeter is ‘high’ (compared to the resistances in the circuit) we can ignore it and confidently say that the reading on it will be 3.0V. The two parallel 30 [pic]resistors would have a resistance of 15 [pic] in that arrangement, forming only a third of the resistance in the strand. The voltmeter would therefore read 3V.

BUT if the value of R was 3000 [pic] then we would have a very different situation. The parallel arrangement would then be of three 3000 [pic] resistors (equivalent to 1000 [pic] ) and the voltmeter would only read a quarter of the terminal voltage 2.25V (2.3V on the dial). If the voltmeter was replaced with a very high resistance (sometimes called high impedance) electronic meter (like a multimeter) then the reading on it would be 3V as before – its resistance would not have to be included in the calculation.

As a rule of thumb: if the resistance of the meter is more than 100 times that of the resistors then ignore its affect on the circuit. If it is less than that do a calculation.

Resistivity

We know that there are three factors that affect the resistance of a wire at constant temperature:-

• Resistance is proportional to length

• Resistance is inversely proportional to cross-sectional-area

• Resistance depends on the material the wire is made of

We put these into an equation:

[pic]

where

ρ is the resistivity of the material

R is the resistance of the wire (the ratio of the potential difference across its end to the current that flows through it)

l is the length of the wire

A is the cross sectional area of the wire (if circular this will be pr2 = pd2/4)

Unit of resistivity

We can discover the unit for resistivity from this equation

The unit of resistance multiplied by the unit for CSA divided by the unit for length

That gives us Ωm as the unit for resistivity.

What is resistivity?

The electrical resistivity, or specific resistance, is the resistance between the opposite faces of a metre cube of a material.

We are used to thinking of resistance in wires. So, it would be the resistance of a metre of wire with a cross sectional area of 1 m2

Imagine a wire like that! Wow! What dimensions, hardly a wire at all - more like a metal cylinder!

You would expect the resistivity of such a wire to be very small as the cross sectional area is so great.... and the values for resistivity of metals are very small.

Nichrome is quoted to have a resistivity of 103 X 10-8 Ωm in Kaye and Laby. All resistivities of metals are usually quoted in terms of X 10-8 Ωm so that comparisons between them can easily be made, but it has to be remembered that Most numbers are probably reasonably accurate to 2 significant figures were quoted but it is clear that you should expect values to depend upon your particular sample.

Values are affected by impurities. Values given in different sources vary considerably. Resistivity is temperature dependent.

The reciprocal of the electrical resistivity is the electrical conductivity σ.

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We can manipulate the equation to get R on the left

[pic]

This equation is of the form Y=mx; it forms a straight line that goes through the origin.

ρ is a constant for a particular material

R is the Y variable and what m is depends upon what you choose 'x' to be.

- If your variable 'x' is the length then m (the gradient) becomes€ρ/A as A is kept constant to give a fair test

- If your variable 'x' is 1/A then m (the gradient) becomes ρl as l is kept constant to give a fair test

The potential difference provided by cells connected in series is the sum of the potential difference of each cell separately (bearing in mind the direction in which they are connected). A cell's potential difference between its terminals has a chemical source and that this can 'run down' with use or incorrect storage providing less of an electrical gradient for the current (i.e. the voltage stamped on a battery might not be correct). 

|Data logging |

|A data logger (also called datalogger or data recorder) is an electronic device that records data  and stores it for you. It can be set to record at | |

|regular time intervals or upon the pressing of a key or button. | |

|Sensors  are usually electrical transducers - things that change a physical quantity such as the loudness of sound into an electrical signal). They | |

|detect the physical quantity being monitored (e.g. light level or voltage, current etc) .They are usually  designed to feed the information to a digital| |

|processor (or computer). They generally are small, battery powered, portable, and equipped with a microprocessor, internal memory for data storage, and | |

|sensors. | |

|Some data loggers interface with a personal computer and utilize software to activate the data logger and view and analyze the collected data, while | |

|others have a local interface device (keypad, LCD) and can be used as a stand-alone device. | |

|Sample rate is the rate at which measurements are taken e.g. a sample rate of 50 Hz would be a reading taken every 0.02s (50 in a second). | |

| | |

|Using a data logger in an electrical circuit. | |

|To plot a characteristic curve you would need a current sensor and a voltage sensor. Each of these would have to go to separate 'channels' in the data | |

|logger. It is not usual to have the response 'sampled' as you need to physically change the voltage from the supply and then take a reading. It is | |

|therefore usually manually sampled by the pressing of a button. | |

|I would not even have this example on here if an exam board did not have this 'experiment' on their syllabus! Data loggers are best for long tedious | |

|experiments like light level changes in a room over a week or very rapid sampling like the flicker of an electric light bulb when lit by an a.c. voltage| |

|supply. Using them for this seems ludicrous as you do not use the sampling facility and might as well just take readings!. | |

|You could I suppose set it up and then steadily increase the voltage supply, allowing sampling to occur. To do this you would have to select the same | |

|sampling speed for each sensor and the same starting time for each and then select a voltage/current display for the same time intervals after the | |

|sampling was complete. | |

|To draw this on a circuit diagram you would simply draw a box with the words 'data logger' in it and connect that to the sensors. The sensors would have| |

|to be placed into a circuit appropriately. For example a current sensor is effectively an ammeter so it would be put in series with the component you | |

|wished to measure the current through. Similarly a voltage sensor would have to be put in parallel with the component you were monitoring with the data | |

|logger. | |

|I suggest that you use the symbols for ammeter and voltmeter in your diagram but label them as sensors. Make sure you put them correctly into your | |

|circuit diagram - current sensor in series and voltage sensor in parallel. | |

|Remember | |

|Dataloggers are no more or less accurate than regular meters | |

|Sometimes the software gives an impressive number of significant figures in the data list - but this may not be representative of the accuracy - just | |

|the whim of the programmer! | |

|Datalogger probes and sensors can have faults that lead to false data being collected. | |

|For a simple experiment they do not save time as they can take a lot of time to set up - but for vast numbers of readings over a long time they are a | |

|very valuable tool! | |

| | |

| |

An oscilloscope is basically a voltmeter that shows you how voltage varies with time... it plots a voltage against time graph on the screen.

It is connected in parallel to the component you are looking at (like a voltmeter).

 Instead of getting a digital readout (as on a multimeter) it gives you a graph.

• The y-axis is voltage (so you can see how many volts are across the component).

• The x-axis is time (so you can see whether the voltage is steady (D.C.) or varying (A.C.))

This is most useful when you look at AC voltages.

 You can switch the x-axis on or off using the timebase control dial – and change the scale of the ‘graph’ too using this dial.

You can change the y-axis scale using the voltage gain dial.

When you change the settings the graph looks different but you haven’t changed the supply voltage – just what the graph of it looks like.

You should be able to work out the frequency from the period by using f = 1/T

 [pic]

You do not have to learn the structure of an oscilloscope – I just want you to understand how it works so you can use it properly!

• A heated electrode gives off electrons (thermionic emission).

• If these are accelerated across a vacuum (must be a vacuum otherwise they would just ionize the air!)

• by a potential difference (they would be pulled towards a positive plate).

• They can be directed at a fluorescent screen and where they hit it will light up - photons of visible light emitted

• If the electron beam has the voltage you are investigating put across it (on the Y plates) it will be pulled towards the +ve one (bigger the voltage the bigger the pull!... so the further up the screen the beam will move)

• Across the screen a sawtooth wave pulls the spot from left to right steadily (at a speed shown on the timebase dial) and then flips it back to the left again to start again.

|[pic] |If the timebase is off you just get a spot - you can vary its size using the focus and |

| |intensity controls - you shouldn't leav it on like this for a long time as it will 'burn |

| |out the screen'  - affect the zinc suphide coating |

|[pic] |If the timebase is on at a good speed you get a line because the fluorescence doesn't have|

| |time to die away before the screen is hit again! |

|[pic] |If a DC voltage is applied across the Y-plates when the timebase is off then the steady |

| |voltage makes the spot be a fixed distance higher than its rest position and you get |

| |a spot (above or below) the no signal spot. |

| |You can measure the voltage by working out how much it has 'jumped up' and converting the |

| |divisions on the screen to volts. |

| |It is good practice to make it jump up - measure the voltage and then switch the contacts |

| |round - making it jump down - and measure the voltage again - you should get the same |

| |result! |

|[pic] |If a DC voltage is applied across the Y-plates when the timebase is on then the steady |

| |voltage makes the line be a fixed distance higher than its rest position and you get |

| |a horizontal line (above or below) the no signal line. |

| |You measure the voltage in the same way as you would using the 'spot' |

|[pic] |If an AC voltage is applied across the Y-plates when thetimebase is off then the |

| |sinusoidally varying voltage makes the spot move up and down around its rest position and |

| |you get avertical line through and centring on the no signal spot. (From this you can work|

| |out the peak to peak voltage). |

| |Remember that the peak to peak voltage has to be halved to give you the peak voltage - and|

| |that has to be divided by root 2 to give you the RMS voltage! |

|[pic] |If an AC voltage is applied across the Y-plates when thetimebase is on then |

| |the sinusoidally varying voltage makes the spot move up and down around its rest position |

| |as it moves across the screen and you see a sine wave graph. (From this you can work out |

| |the period and hence the frequency of the signal - do it across several periods on |

| |different timebase settings to double check your readings). |

The UK mains supply is about 230 volts AC. It used to be 240V but it has been brought down in a stage in the transition to 220V (like the rest of Europe).

Mains voltage can kill if it is not used safely.

A direct current DC supply has a steady voltage across the supply terminals – one is positive (red) with respect to the other (black). Current flow is in one direction only +ve to –ve.

An alternating current AC supply has an alternating voltage across the supply terminals – one terminal changes from being positive to negative back to positive again when the other changes from negative to positive back to negative again. The potential difference across them changes in a sinusoidal way. The variation occurs in a regular way. The frequency of the supply indicates how many times the sinusoidal variation occurs each second.

You should be able to recall the frequency of UK mains supply – 50 Hz and the RMS value of mains voltage – 230 V. You should also recall the peak value (V0) as 330V – although you can work that out from the equation on your data sheet. [pic]

The RMS value is the root mean square value – you do not have to worry about the math of how this is worked out – it hasn’t been on the syllabus for an age – just use the equations as given.

BUT you do have to know what the RMS value means – it is the equivalent energy transfer of an AC supply and a DC supply. A battery of 230V would supply the same energy to a circuit that a 230V RMS AC supply would give. The AC supply does that by going through a range of values – sometimes higher and sometimes lower than the 230V.

Make sure you could sketch the graph below – including labels and values on the axes!

[pic]

[pic] is on your data sheet.

You can use equations like V=IR and P=IV to work out RMS or peak values.

Ohm’s Law applied to the full circuit

[pic]

The electromotive force (EMF) ε of a battery is the total energy per coulomb transferred into electrical energy by the battery. It is measured in volts.

Part of it is used to drive a current through the battery itself. This is called the ‘lost volts’.

The rest of the voltage is called the circuit potential difference V.

ε = V + lost volts

The current driven through the battery is the same as that in the circuit – current in a strand is the same throughout.

The symbol for the resistance of the battery is ‘r’. It is called the internal resistance.

Lost volts = Ir

For the external circuit:

V = IR

For the total circuit:

ε = V + lost volts = IR + Ir = I(R + r)

[pic]

Dashed line – encloses the battery – the cells and the internal resistance – remember you cannot see the ‘resistor’ of the battery

• Open switch – called being on open circuit – the voltmeter reads the EMF of the battery - ε.

• Close the switch – external p.d. is the reading on the voltmeter - V.

• Difference between the two is the lost volts ε - V

• Ammeter reads current - I

If the external circuit has a large resistance in comparison with the internal resistance there is a very small difference when the switch is closed – lost volts are negligible – but if it is of the same order as it the difference will be great.

Cells in series – add the internal resistances – they are in series – add the voltages

Cells in parallel - the resistances are in parallel – use the equation – n identical ones will have a battery internal resistance of r/n – the voltage of a battery of cells in parallel is the same as the voltage of a single cell

Appendix

You should be able to interpret and/or draw circuit diagrams using standard symbols. The following standard symbols should be known: 

 

|connecting wire |[pic] |

|connection between two crossing wires |[pic] |

|two crossing wires that are not connected to each other |[pic] |

|switch (open)  |[pic] |

|switch (closed) |[pic] |

|signal lamp |[pic] |

|filament lamp |[pic] |

|cell |[pic] |

|battery |[pic] |

|power supply |[pic] |

|fuse |[pic] |

|resistor |[pic] |

|diode |[pic] |

|variable resistor |[pic] |

|thermistor |[pic] |

|ammeter |[pic] |

|voltmeter |[pic] |

|L.D.R. (light dependant resistor) |[pic] |

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