3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
Detail lifted from the Syllabus
Page No.
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Electric current as the rate of flow of charge;
Potential difference as work done per unit charge.
3
Resistance is defined by
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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 / I curves.
Ohm’s law as a special case where current is proportional to
potential difference
Resistivity
Description of the qualitative effect of temperature on the
resistance of metal conductors and thermistors.
Superconductivity as a property of certain materials which
have zero resistivity at and below a critical temperature
which depends on the material.
Resistors in series - the relationships between currents,
voltages and resistances Resistors in parallel - the relationships between currents,
voltages and resistances
Energy - application, e.g. Understanding of high current
requirement for a starter motor in a motor car.
Conservation of charge and energy in simple dc circuits.
6
17
6
3-4
14-15
Applications (e.g. temperature sensors).
6&7
Applications (e.g. very strong
electromagnets, power cables).
Research
project
9
9
10
Questions will not be
set which require the use of simultaneous
equations to calculate currents or
potential differences.
Cells in series and identical cells in parallel.
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.
2-3
22
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.
Use of an oscilloscope as a dc and ac voltmeter, to measure
time intervals and frequencies and to display ac waveforms.
21
2
No details of the structure of the
instrument is required but familiarity with
the operation of the controls is expected.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
the p.d. from the power supply.
When components are connected in parallel:



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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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:
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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 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?
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!
( (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
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
You should know this curve and be able to 'interpret' this
characteristic that means explain how it shows that:



is the symbol for a diode
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.

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.
You should note that:


You should be able to draw this from memory.
At 0V no current flows.
At +0.6V the forward current starts to rise sharply.
At -ve voltage there is a tiny current.
When connected into a circuit in 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.
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.
When connected 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.
Notice how the cathode side is marked with a ring or band
the ordinary diodes and a flat side and/or short lead
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
it rectifies the 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!
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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 ( ).
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
each other the resistance of the whole arrangement is R/ N
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in parallel with
3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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.
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
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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 and it is positioned on a strand of a circuit with a 420m resistor and a potential difference of 9.0 V is provided
by a power supply.
Total resistance of the strand is 420m
plus 6.3 m as the resistor and the ammeter are in series.
Therefore the total resistance of the strand = 0.420
+ 0.000 006 3
= 0.420 006 3 .
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
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
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
, 5.0
and 20 ) – calculate the equivalent resistance.
1
/R TOTAL = 1/2 + 1/5 + 1/20 = 0.75
So, R TOTAL = 1/0.75 = 1.3 ( or 4/ 3)
(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
resistance of the arrangement:
1
to the arrangement let us look at the effect it has on the value of the
/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
(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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
resistor
5.0
resistor
V = IR
V=IR
I= V /
I=V/
20
resistor
3000
voltmeter
V = IR
V =IR
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
R
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 W
and the voltmeter has a resistance of 3000 .
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 resistors would have a resistance of 15 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 then we would have a very different situation. The parallel arrangement would then
be of three 3000 resistors (equivalent to 1000 ) 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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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:
where
 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 m 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 m in Kaye and Laby. All resistivities of metals are usually quoted
in terms of X 10-8 m 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 .
----------------------------------------------We can manipulate the equation to get R on the left
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
This equation is of the form Y=mx; it forms a straight line that goes through the origin.
 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 /A as A is kept constant to give a fair test
- If your variable 'x' is 1/A then m (the gradient) becomes l 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
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.
as
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).
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
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


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!
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
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!
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)






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.
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
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!
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!
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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'
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!
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.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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.
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!
is on your data sheet.
You can use equations like V=IR and P=IV to work out RMS or peak values.
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
Ohm’s Law applied to the full circuit
The electromotive force (EMF)  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.
 = 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:
 = V + lost volts = IR + Ir = I(R + r)
Dashed line – encloses the battery – the cells and the internal resistance – remember you cannot see the ‘resistor’ of
the battery
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Open switch – called being on open circuit – the voltmeter reads the EMF of the battery - .
Close the switch – external p.d. is the reading on the voltmeter - V.
Difference between the two is the lost volts  - 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
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3.1.3 AS Level – Current Electricity Notes – LJ (2010)
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
connection between two crossing wires
two crossing wires that are not connected to each other
switch (open)
switch (closed)
signal lamp
filament lamp
cell
battery
power supply
fuse
resistor
diode
variable resistor
thermistor
ammeter
voltmeter
L.D.R. (light dependant resistor)
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