Download Slide 1

2.2 Resistance
G482 Electricity, Waves & Photons
2.2.2 EMF
Mr Powell 2012
Index
2.2.4 Resistivity
Assessable learning outcomes
There are opportunities for discussion of the factors that
determine resistance including temperature, leading to
superconductivity in some materials.
Candidates should be able to:
(a) define resistivity of a material;
(b) select and use the equation.....
(c) describe how the resistivity's of metals and
semiconductors are affected by temperature;
(d) describe how the resistance of a pure metal wire and
of a negative temperature coefficient (NTC) thermistor is
affected by temperature.
RA

L
RT  R1  R2 ......
1
1
1
1
 

RT R1 R2 R3
Mr Powell 2012
Index
GCSE Background
From GCSE physics we already know that;
V = IR
So simply in this circuit the resistance of the bulb is 12.
This is a measure of how much the bulb resists the flow
of electrons.

But where does R and rho  come from and how are
they linked?

To understand this topic clearly we need to delve into
the structure of materials and their electronic
configurations.

We must think about the chemistry behind things and
the physical dimensions of materials…
Mr Powell 2012
Index
Resistance 1
Ohm’s law:
The pd across a metallic conductor is proportional to the current through it,
provided the physical conditions do not change
Q. For the resistor opposite calculate:
a) the resistance at this current
b) the new pd when the current
is 50 A
2mA
R ohm
12V
a) R = V =
I
b) V = I R =
12
2.0 x 10-3
50x10-6 x 6000
= 6000
= 0.3 V
http://phet.colorado.edu/simulations/index.php?cat=Physics
http://www.batesville.k12.in.us/physics/PhyNet/e&m/current/ECurrent_Notes.htm
Mr Powell 2012
Index
Resistance 2
Measurement of resistance:
r
Record the pd across R for
increasing values of current.
R
A
( change r to change the
circuit current ()
V
The ammeter has a
very low resistance ( 0.2 ohm)
The voltmeter has a
very high resistance ( 20,000 ohm)
Pd / V
Gradient =
V
I
Gradient = resistance
Why?
I/A
Mr Powell 2012
Index
Spark Version – m = Resistance!
Voltage /V
Current /A
Mr Powell 2012
Index
Conductors
• Metals are generally known as conductors.
• Copper electricity cables is an example and
what we mean is that they conduct
electrons very well.
• Metals are conductors rather than
insulators as they have a unique "property".
• This "property " is that the outermost
electron on the atom is relatively loosely
held and can hop from atom to atom when
pushed!
Mr Powell 2012
Index
Ionisation Energies

The table below shows how much energy it takes to remove a whole mole of electrons
from their respective atoms.

The blue shaded regions show which are the easy ones.

It is a similar type of thing that is happening in a conductor….
Energy in J/mol
Metal
n=1
n=2
n=3
Free Electrons
Li
520
7298
11815
1
K
419
3051
4412
1
Cu
746
1958
3554
1 or 2
Zn
906
1733
3833
2
NB: Don’t need to learn these energies just be aware of the idea of the stripping away!
Mr Powell 2012
Index
Modelling

So what we are talking about is an electron being ripped from its atom (home)
and then moving through the structure of the other adjacent atoms in a form of
drift or current.

This is an interesting motion where each electron gains some KE from the e.m.f.
Jumps to another adjacent atom losing the KE and then repeats the process over
and over….

Here is a simple example of how the process might work with boron
e-
e-
e-
e-
NB: Boron was picked due to simple structure – it is not a good conductor!
Mr Powell 2012
Index
Modelling II
 Lets examine this rod of an elemental material
 You can manipulate the rod and see how many atoms might look.
 Then imagine how the electrons would move as on the previous slide
 The harder it is to strip away that “free electron” the higher the
resistance!
Mr Powell 2012
Index
Other physical factors…
e-

At any temperature above 0K atoms will jiggle
around and impede any flow of electrons

Only the electrons move as they are about 2000
times lighter than the atoms they are attached
to and pick up the e.m.f

In a Copper wire with 1 x
electron carriers
per m3 you would have to accelerate 1 x10-26kg's
of electrons.

This is quite a mass of electrons and the more
you have the more push you have to use overall
to get them moving!

Area and length must also effect such a problem
e-
eee-
1028
Mr Powell 2012
Index
Resistance or Resistivity
 The formulae used to take into account how the physical
factors of a wire effect resistance is chicken or egg as
you can either consider using it from the R or the 
perspective.
l 
R   
 A
RA

l
 The way I remember is resistivity = RAL and of course remember to
put the L underneath to make the units correct!
NB: when A = 1m2 and l = 1m  = R
Mr Powell 2012
Index
Resistivity Formula
There are two main principles at play here;
 The resistance is proportional to length i.e. the
longer the wire the more resistance there is
 The resistance is inversely proportional to the area
of the wire i.e. the bigger the area the smaller the
resistance.
l 
R   
 A
Rl
1
R
A
where
R = Resistance in ohms 
 = Resistivity in ohm metres m
A = Cross sectional area in metres squared m2
l = length in metres m
NB:  is the taken as the value of the Resistivity at room temperature 20C
Mr Powell 2012
Index
Facts and Figures
 This table shows some examples you should be familiar
with.
 Quite simply they mean that for each substance the
resistivity will be …… m (at 20C) as its constant
Type
Metal
Material
Resistivity in m
Copper
1.7 x 10-8
Gold
2.4 x 10-8
Aluminium
2.6 x 10-8
Germanium (pure)
0.6
Silicon (pure)
1.7 x 103
Glass
1.7 x 1012
Perspex
1.7 x 1013
Polyethylene
1.7 x 1014
Sulphur
1.7 x 1015
Semiconductors
Insulators
Mr Powell 2012
Index
Simple Example…
Mr Powell 2012
Index
Simple Example…
Mr Powell 2012
Index
Simple Application….

Robert Oppenheimer was making a complex atomic bomb called “Fat Man”. He
needed to use a certain type of wire in his detonator circuits to connect to the primary
so that the overall resistance in that part of the microcircuit was exactly 0.0008 .
Then his timing would be just right to produce the maximum number of neutrons
possible and thus kill as many Japanese civilians in Hiroshima as possible. He had a
choice of copper, gold or aluminium wire to use in the circuit. However, each wire was
of a different thickness and length.

Without cutting the wires work out which one he could use…you need to do three
separate calculations using the following data;
Material
 Resistivity in
m
Thickness
cm
Length
cm
Copper
1.7 x 10-8
0.1
20
Gold
2.4 x 10-8
0.2
10
Aluminium
2.6 x 10-8
0.4
12
Hint: tabulate your data or write it out for each question with conversions in full
Mr Powell 2012
Index
Electrical Resistance Data SWG - Standard Wire Gauge
Mr Powell 2012
Index
Material
Resistivity at 20°C
silver
copper
gold
aluminium
magnesium
nickel
iron
chromium
manganese
carbon (graphite)
Manganin
Ω·m
1.6 × 10-8
1.7 × 10-8
2.2 × 10-8
2.7 × 10-8
4.2 × 10-8
6.9 × 10-8
10.1 × 10-8
13.2 × 10-8
160 × 10-8
3 000 × 10-8
44 × 10-8
µΩ·cm
1.6
1.7
2.2
2.7
4.2
6.9
10.1
13.2
160
3 000
44
Constantan (Eureka)
49 × 10-8
49
Nichrome
110 × 10-8
110
Mr Powell 2012
Index
Superconductivity
This is the property of a material which is at or below a
critical temperature Tc where it has zero resistivity .
Implications:
Tc
• Zero resistance
• no pd exists across a superconductor with a current
flowing
• the current has no heating effects
temp
Properties of a superconductor:
 material loses the effect above the critical temperature
Tc.
 If Tc is above 77K ( -196 C)
superconductor
it’s a high temperature
 The highest Tc max = 150 K - 123C
Mr Powell 2012
Index
Finding the Resistivity of a Wire
 This new formulae has a simple characteristic which again would fit the;
y = mx + c principle
 One way of working out a resistivity of any material is to set up a circuit with a
sample of the substance. Measure the area of the wire several times and take
the average. Then measure the current flow through and potential difference
across the wire. This enables you to work out R. Then repeat the experiment
for several different lengths.

grad   
 A

R   l
 A
R
l
NB:  is the taken as the value of the Resistivity at room temperature 20C
Mr Powell 2012
Index
Resitivity?

Use the graphing technique to find
out the resistivity of a sample wire
which is 0.26cm thick. What metal
is the wire made from?

grad   
 A
R
l
NB:  calculated at 20C
Length in m
Resistance in m
0.10
0.18
0.20
3.70
0.30
5.50
0.40
7.10
0.50
9.20
0.60
11.00
0.70
13.00
0.80
14.50
0.90
14.60
1.00
18.00
Mr Powell 2012
Index
Looks like Gold to me!
Graph to show resistance against length
20
18
Resistance in milli ohms
16
14
y = 18.253x
12
10
8
6
1.32739x10-6m2 x 18.253x10-3 m-1 =2.42 x 10-8m
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
Length of wire in meters m
Mr Powell 2012
Index
d) Thermistor
The resistance of a thermistor decreases as the temperature increases so if we
look at it from the VI perspective it is the opposite of a bulb!
Mr Powell 2012
Index
d) How do they work?
The exact conduction mechanisms are not fully understood but metal oxide NTC
thermistors behave like semiconductors, as shown in the decrease in resistance
as temperature increases. The physical models of electrical conduction in the
major NTC thermistor materials are generally based on this theory;
A model of conduction called "hopping" is relevant for some materials. It is a form
of ionic conductivity where ions (oxygen ions) "hop" between point defect sites
in the crystal structure.
The probability of point defects in the crystal lattice increases as temperature
increases, hence the "hopping" is more likely to occur and so material
resistivity decreases as temperature increases.
Only need the
outcome in red for
AS Physics
Mr Powell 2012
Index
d) Temperature Sensors?
They are inexpensive, rugged and reliable. They
respond quickly to changes and are easy to
manufacture in different shapes.
An example could be made from a combination of
Fe3O4 + MgCr2O4 (metallic oxides)
A NTC thermistor is one in which the resistance
decreases with an increase in temperature.
The circuit shows how you can use the thermistor as
a potential divider. As the temperature changes
the division of voltage or energy will change. You
need the 5k resistor or the voltage would be that
of the cell a constant 3V.
A common use is the glass heat sensor in a car or
the temperature sensor in a conventional oven.
Mr Powell 2012
Index
LDR
The resistance of a lightdependent resistor (LDR)
decreases as light intensity
increases. This is a similar
process to a thermistor
lux (symbol: lx) is the SI unit of illuminance and luminous emittance
measuring luminous power per area
Mr Powell 2012
Index
Mini Resistivity Question….
A metal wire of length 1.4 m has a
uniform cross-sectional area = 7.8 ×
10–7 m2.
Calculate the resistance, R, of the
wire.
The wire is now stretched to twice its
original length by a process that keeps its
volume constant.
If the resistivity of the metal of the wire
remains constant, show that the resistance
increases to 4R.
Resistivity of the metal is = 1.7 × 10–8
Wm
Basic
iSlice
Mr Powell 2012
Index
Mini Resistivity Question….
A metal wire of length 1.4 m has a
uniform cross-sectional area = 7.8 ×
10–7 m2.
Calculate the resistance, R, of the
wire.
The wire is now stretched to twice its
original length by a process that keeps its
volume constant.
If the resistivity of the metal of the wire
remains constant, show that the resistance
increases to 4R.
Resistivity of the metal is = 1.7 × 10–8
Wm
Basic
iSlices
Mr Powell 2012
Index
Connection
•
•
•
Connect your learning to the
content of the lesson
Share the process by which the
learning will actually take place
Explore the outcomes of the
learning, emphasising why this will
be beneficial for the learner
Demonstration
• Use formative feedback – Assessment for
Learning
• Vary the groupings within the classroom
for the purpose of learning – individual;
pair; group/team; friendship; teacher
selected; single sex; mixed sex
• Offer different ways for the students to
demonstrate their understanding
• Allow the students to “show off” their
learning
Activation
Consolidation
• Construct problem-solving
challenges for the students
• Use a multi-sensory approach – VAK
• Promote a language of learning to
enable the students to talk about
their progress or obstacles to it
• Learning as an active process, so the
students aren’t passive receptors
• Structure active reflection on the lesson
content and the process of learning
• Seek transfer between “subjects”
• Review the learning from this lesson and
preview the learning for the next
• Promote ways in which the students will
remember
• A “news broadcast” approach to learning
Mr Powell 2012
Index