Physics 2007
Sample assessment instrument and indicative responses
Extended experimental investigation:
Electricity
This sample is intended to inform the design of assessment instruments in the senior phase of
learning. It highlights the qualities of student work and the match to the syllabus standards.
Criteria assessed
• Knowledge and conceptual understanding
• Investigative processes
• Evaluating and concluding
Assessment instrument
The response presented in this sample is in response to an assessment task.
The assessment instrument and annotated response featured in this sample have been altered to
better demonstrate to a state-wide audience the features of the assessment technique: extended
experimental investigation. The response has been altered to be indicative of student work that would
typically match with the syllabus Standard A descriptors.
Extended experimental investigation on the topic of electricity.
A brief summary of the task provided by the school is presented below. The task sheet has not been
included. Refer to the syllabus 7.4.1 for requirements.
•
Carry out research on the topic.
•
Write your hypothesis for the investigation.
•
Decide on a method for the investigation.
•
Order materials and fill in the Materials Requisition Form and Risk Assessment Form.
•
Begin the investigation. Record all observations. Modify your experiment if necessary. Gather,
record and process data.
•
Write a scientific report under the headings provided.
The journals used by the students have not been included as this is not a requirement of the syllabus.
The student response contained appendices. These have not been included. One appendix has been
included in the document to show sample calculations from the student appendix.
Instrument-specific criteria and standards
Indicative responses have been matched to instrument-specific criteria and standards; those
which best describe the work in this sample are shown below. For more information about the
syllabus dimensions and standards descriptors, see www.qsa.qld.edu.au/1964.html.
Knowledge and
conceptual
understanding
Investigative
processes
Evaluating and
concluding
2 | Physics 2007
Standard A
Standard C
The student work has the following
characteristics:
The student work has the following
characteristics:
•
reproduction and interpretation of complex
and challenging concepts, theories and
principles
•
reproduction of concepts,
theories and principles
•
comparison and explanation of complex
concepts, processes and phenomena
•
explanation of simple
processes and phenomena
•
linking and application of algorithms,
concepts, principles, theories and schema to
find solutions in complex and challenging
situations
•
application of algorithms,
principles, theories and schema
to find solutions in simple
situations
The student work has the following
characteristics:
The student work has the following
characteristics:
•
formulation of justified significant
questions/hypotheses which inform effective
and efficient design, refinement and
management of investigations
•
formulation of questions and
hypotheses to select and
manage investigation
•
assessment of risk, safe selection and
adaptation of equipment, and appropriate
application of technology to gather, record
and process valid data
•
assessment of risk, safe
selection of equipment, and
appropriate application of
technology to gather and record
data
•
systematic analysis of primary and
secondary data to identify relationships
between patterns, trends, errors and
anomalies
•
analysis of primary and
secondary data to identify
obvious patterns, trends, errors
and anomalies
The student work has the following
characteristics:
The student work has the following
characteristics:
•
analysis and evaluation of complex scientific
interrelationships
•
description of scientific
interrelationships
•
exploration of scenarios and possible
outcomes with justification of conclusions/
recommendations
•
description of scenarios and
possible outcomes with
statements of conclusion/
recommendation
•
discriminating selection, use and
presentation of scientific data and ideas to
make meaning accessible to intended
audiences through innovative use of range of
formats
•
selection, use and presentation
of scientific data and ideas to
make meaning accessible in
range of formats
Sample assessment instrument and indicative responses
Indicative response — Standard A
The annotations show the match to the instrument-specific standards.
Comments
Introduction
It is proposed that there are factors that influence the extent to which metal
wires carry electrical current in circuits i.e. the length of the wire, the crosssectional area of the wire and the type of material in the wire.
Several expressions link the factors together. Resistance measured in ohms (Ω)
is found by Ohm’s law, R=V/I. V represents voltage, a measure of electrical
potential energy and I represents current, a measure of electrons that flow
through a circuit. (Wisegeek Organisation 2000).
reproduction and
interpretation of
complex and
challenging concepts,
theories and
principles
linking and
application of
algorithms, concepts,
principles, theories
and schema to find
solutions in complex
and challenging
situations
The student has
linked together the
expressions related
to the investigation.
I can be expressed in the derived version of Ohm’s Law (Fig 2). Figure 2 links
the relationship between material conductivity (σ), electric field (E) and current
density (J) in a basic expression,
J=σE
(1)
Resistivity is a fundamental parameter of a material that describes how easily it
can transmit an electrical current. High values of resistivity imply that the
material is resistant to the flow of electricity and low values of resistivity imply
electrical current is transmitted easily. The derived formula comes from the
formula for Resistance, R=V/I, incorporating resistance (R), resistivity (ρ), crosssectional area (A) and length (L).
R = L/Aσ
= L ρ/A
(2)
Where ρ = σ
Figure 1 Derived formula
Length and cross-sectional form a fundamental part of this formula indicating
the influential effect it has on resistance (Virtual Institute of Applied Science).
The relationship between length (L) and resistance (R) is shown in Figure 2.
R α L or R = k L
Where k1 = ρ/A
(3)
(4)
Figure 2 Formula linking resistance and length of a conductor
Figure 3 shows the inverse relationship present between resistance (R) and
cross-sectional area (A) of a wire.
R α 1/A or R = k/A
(5)
(6)
Where k2 = L ρ
formulation of
justified significant
questions/hypotheses
The initial trial was
done to ascertain
whether the full
investigation was
feasible.
Figure 3 Formula linking resistance and area of a conductor
An initial trial was conducted using a length of copper wire to see the
relationship between length and resistance. Copper wire of nominal diameter
1.15mm was used to establish the practicality of using the material, and to test
the likely range of resistances. Lengths of 20 cm, 40 cm, 60 cm and 80 cm were
used.
Queensland Studies Authority September 2012 | 3
Comments
Materials
Copper wire (1.15mm, nominal), Ohmmeter, crocodile clips, ruler, micrometre screw
gauge, sticky tape
Assessment of risk and safety management
assessment of
risk
The ohmmeter was a risk since it produced a small electric current. Holding or touching
the length of wire being measured was avoided. Rubber soled shoes were worn at all
times in order to minimise the risk of electrocution. Water and other conductive metals
not associated with the experiment were kept away (A Risk Assessment was
completed in the original student work).
Method
effective and
efficient
design and
management
of the
investigation.
In this
response, the
results of the
initial trials
were recorded
in the journal.
1. The ohmmeter was configured. The wires and crocodile clips were assembled. The
room had a constant temperature.
2. A 20 cm length of copper wire was spread out and measured using a ruler.
3. The length of wire was held taut and flat and crocodile clips were attached to the
ends of the wire.
4. An appropriate ohm value on the ohmmeter was set. The reading of resistance on
the ohmmeter was then recorded. The setting was 100mA–250Ω.
5. Steps 2–4 were repeated with variable lengths of 40 cm, 60 cm and 80 cm.
Results
Length +/– 1 mm
Resistance +/– 0.1 Ohms
Copper Diam (1.15+/– 0.01)mm
200
400
600
800
3.200
6.300
9.400
12.20
Table 1. Measured resistance (on 100mA–250Ω scale) and resistivity values
application of
technology to
gather, record
and process
data
Calculations
were done to
decide if the
data was
valid.
4 | Physics 2007
The data in Table 1 was used to create Graph 1. The graphical representations show
that the data can be fitted with a straight line, to a correlation factor of 0.9996 for the
copper wire. The equation for the best-fitted straight line for the nichrome wire shows
an intercept on the vertical axis of 20.6 Ohms, and a slope of 15 Ohms/m. No wires
less than 20 cm in length were used.
Resistivity values
The resistivity values (ohm.m) of the materials used:
Copper
Nichrome
Aluminium
Steel
–8
1.68 x 10
–6
–6
–6
1.1 x 10 to 1.5 x 10 (value of 1.0 x 10 taken in this investigation)
–8
2.83 x 10
values vary due to composition
Sample assessment instrument and indicative responses
Comments
The trial data has
been presented to
make meaning
accessible to the
intended audience
Resistance (milli ohms)
Resistance vs. length
14
12
10
8
6
4
2
0
y = 15.05x + 0.25
R² = 0.9994
Copper wire
1.15mm
Linear (Copper
wire 1.15mm)
0
0.5
Length of wire (m)
1
Linear (Copper
wire 1.15mm)
Graph 1 Resistance values for Copper 1.15 mm
Discussion
effective and
efficient design,
refinement and
management of
investigations
An initial problem was the meters were supplied with probes that could not be
easily attached to the lengths of wire. Pieces of wire with an alligator clip on each
end were available. These could be clipped from the probes to the end of the
copper wire. The copper wire was insulated with a clear covering. When the
alligator clips were attached to the wire, there was no reading on the meter. The
ends of the wire were rubbed with a small file and then with sand-paper so as to
give a clean metal surface to ensure a good contact with the clips. These wires of
the probes and alligator clips have a resistance, and would need to be subtracted
from the measurement of the total resistance to give the resistance of the copper
wire that was to be measured.
The alligator clips were clipped together, so that the resistance of the wires of the
probes and alligator connections could be measured. However the result was not
reliable nor consistent. Moving the wires of the circuit, and trying to hold the clips
hard together gave results which varied from 45 Ohms to less than 1 Ohm.
However, when the ends of the copper wire were clipped to the meter, the meter
gave a steady display. The resistance for each of the various lengths of copper
wire and of the nichrome wire was measured, so that a graph could be produced
to see if the result was linear.
formulation of
justified significant
questions/hypothes
es which inform
effective and
efficient design,
refinement and
management of
investigations
From the results, clear trends and relationships were apparent.
The value of the correlation factor close to Unity shows that with a high degree of
statistical significance, the data is linear. The trends in the data thus support the
hypothesis that resistance varies linearly with length, for any metal. From
Equation 3, k1 is the slope of the graph of R vs. L. Further experiments with
different metal wires were considered.
Data for resistance found in the initial trials was used in further trials. The wires
used were considered to be of a consistent diameter throughout the length.
Queensland Studies Authority September 2012 | 5
Comments
Hypothesis
If the length of a wire is increased then its resistance will increase if its cross-sectional
area and temperature remains constant. If the cross-sectional area increases then the
resistance of a conductor will decrease if its length and temperature remain constant.
effective and
efficient
design,
refinement
and
management
of
investigations
Method
Wire lengths (independent variable) of 20 cm, 40 cm, 60 cm and 80 cm were used
across four different wires (copper, nichrome, aluminium and steel) in recording
resistance (dependent variable), due to their prevalence and common use. The longer
lengths of wire were measured before the shorter lengths.
Results
Measured resistance
(on 100mA–250Ω scale)
Material
appropriate
application of
technology to
gather,
record and
process valid
data
Diameter
(mm)
Crosssectional area
2
(mm )
20 cm length
40 cm
length
60 cm
length
80 cm
length
copper
0.49
0.1886
15.3
29.3
43.0
59.3
copper
1.15
1.0387
3.20
6.30
9.36
12.2
nichrome
0.3
0.0707
1882
3756
5630
7575
nichrome
0.43
0.1452
1320
2660
4016
5133
nichrome
0.65
0.3318
577.0
1115
1649
2220
nichrome
0.87
0.5945
300.0
611.1
887.0
1170
aluminium
1.05
0.8659
9.45
19.7
30.9
40.6
steel
1.1
0.9503
22.4
47.0
74.3
99.4
Table 2 Measured resistance (on 100mA–250Ω scale) and resistivity values
(The values for nichrome and steel have been shaded for ease of reference.)
Length (cm) and Unit of reading
20
Theoretical resistance
linking and
application of
algorithms,
concepts,
principles,
theories and
schema to
find solutions
in complex
and
challenging
situations
6 | Physics 2007
3.2348x10
40
–7
6.4696x10
60
–7
9.7045x10
80
–7
1.2039x10
–7
Ω
Measured resistance
3.20
6.30
9.36
12.2
0.58
2.68
3.69
6.07
100mA–250Ω
% error
–8
Table 3 Values for Copper (resistivity =1.68x10 ), 1.15 mm diameter, cross-sectional
2
area =1.038689m (These values were chosen as they give a value for the resistivity of
copper from experimental data that is close to the theoretical value.)
Sample assessment instrument and indicative responses
Comments
Resistance vs. length
y = 73.265x + 0.005
R² = 0.9987
60
50
40
Cu 0.49mm
30
Cu 1.15mm
y = 15.006x + 0.266
R² = 0.9996
20
10
Linear (Cu 0.49mm)
Linear (Cu 1.15mm)
0
0
0.5
Length (m)
1
Graph 2 Resistance versus length for Copper wire
Resistance vs. length
8000
y = 9476.5x - 27.5
R² = 0.9999
7000
Resistance (milli ohms)
discriminating
selection, use
and
presentation
of scientific
data and
ideas to
make
meaning
accessible to
intended
audiences
through
innovative
use of graphs
Resistance (milli ohms)
70
nichrome 0.3mm
nichrome 0.43mm
6000
y = 6397.5x + 83.5
R² = 0.9981
5000
nichrome 0.65mm
nichrome 0.87mm
4000
y = 2731.5x + 24.5
R² = 0.9998
3000
2000
Linear (nichrome
0.3mm)
Linear (nichrome
0.43mm)
1000
0
0
0.2
y = 1443x + 20.5
R² = 0.9993
0.4
0.6
0.8
1
Length (m)
Linear (nichrome
0.65mm)
Linear (nichrome
0.87mm)
Graph 3 Resistance versus length for Nichrome wire.
Queensland Studies Authority September 2012 | 7
Comments
discriminating
selection, use
and
presentation
of scientific
data
The data for
copper has
been used as
an example
here as the
recorded
results are
very close to
theoretical
results
Diameter of wire
(mm)
Cross-sectional area
2
(mm )
Slope of line
Calculated
resistivity (ohm.m x
10)
0.3
0.0707
9476.5
0.6698
0.43
0.1452
6397.5
0.9288
0.65
0.3318
2731.5
0.9060
0.87
0.5945
1443
0.8577
Table 4 Calculated values of resistivity of Nichrome wire.
Resistance vs. crosssectional area
comparison
and
explanation
of complex
concepts,
processes
and
phenomena
Resistance (milli ohms)
6000
5000
4000
nichrome 20cm
3000
nichrome 40cm
2000
nichrome 60cm
1000
nichrome 80cm
0
0
0.2
0.4
0.6
0.8
Cross-sectional area (mm2)
Graph 4 Resistance versus cross-sectional area for nichrome wires.
8 | Physics 2007
Sample assessment instrument and indicative responses
Comments
6000
Resistance vs. 1/Cross-sectional
area
Resistance (milli ohms)
y = 764.06x - 125.48
R² = 0.9996
5000
nichrome 20cm
nichrome40cm
4000
y = 607.31x - 173.89
R² = 1
nichrome 60cm
3000
nichrome 80cm
y = 397.39x - 80.869
R² = 1
2000
Linear (nichrome
20cm)
1000
0
0
y = 196.25x - 29.601
R² = 0.9993
2
4
6
8
1/Cross-sectional area (106 m-2)
Linear
(nichrome40cm)
Linear (nichrome
60cm)
Graph 5 Resistance versus 1/Area for nichrome wires
comparison
and
explanation of
complex
concepts,
processes
and
phenomena
Discussion
Clear trends and relationships were apparent. The data in Graphs 2 and 3 shows a
linear relationship with a high confidence level by the correlation factor of greater than
0.999 in each case. It is evident from Graph 3 that as length increased so did
resistance. This is shown by a 20 cm length of nichrome wire (0.87mm) that had a
resistance of 300.0 100mA–250Ω. When the length is increased by 60 cm a
resistance of 1170 100mA–250Ω was recorded. This value was nearly four times
larger than the original value. The other wires yielded a similar relationship.
The value of resistance was found to be directly proportional to length. This means
the shorter the length of wire, the smaller the resistance. The formula R = 1443L +
20.5 (Graph 3) was found for the nichrome (diameter 0.87mm) wire for example.
The value of the constant in the linear function of R = f (L) does vary for each sample
metal. The results about resistance and resistivity cannot be interpreted when
comparing different metals and different alloys when the materials used vary so
greatly in resistivity as shown in Table 2.
Queensland Studies Authority September 2012 | 9
Comments
Table 2 data has several inconsistencies. The calculated resistivity for copper
(0.49mm) is not close to the value calculated for the copper of 1.15 mm diameter.
The resistivity values for the 1.15 mm copper are close to the theoretical value at
0
room temperature (20 C). Table 4 shows the resistivity values for nichrome
calculated from the values in Graph 3.The calculated values for resistivity for
nichrome show variation. The values for the 0.3 mm wire are below the theoretical
–6
value of 1.0 x 10 ohm.m. The values for the other three lengths are within normal
experimental accepted errors.
Inconsistent results have resulted when using the two thinnest wires, copper 0.49
mm and nichrome 0.3 mm. The assumption has been made that the wires have a
consistent diameter throughout the length but this is probably not the case. The
thinner wire may heat up more easily with current flow. The measurement of the
diameter also had to be exact.
It is difficult to ascertain if the values for steel are like the theoretical values as there
are done to compare with. The values in Table 2 for steel are however consistent.
The values jn Table 2 for aluminium are consistent but are less than half the
theoretical value above. An oxide can form on the outside of aluminium which may
have affected its conductive properties in the investigation. The resistance for the
60cm length of nichrome wire (0.65 mm) is inconsistent with the other readings for
that length and was disregarded.
systematic
analysis of
primary and
secondary
data to identify
relationships
between
patterns,
trends, errors
and anomalies
linking and
application of
algorithms,
concepts,
principles,
theories and
schema to find
solutions in
complex and
challenging
situations
10 | Physics 2007
Table 3 shows the theoretical values of resistance were calculated for the copper
wire (1.15 mm diameter). When compared with the actual measured value (by
ohmmeter) little variation was seen. When 20 cm, and other values (Sample
calculation 1) were substituted into the equation (Figure 2) a resistance of 3.235
100mA–250Ω was calculated, deviating only 0.1352 100mA–250Ω from the
measured value of 3.216 100mA–250Ω, equivalent to an error of 0.59%. This
indicated the approximate accuracy of this equation. Graph 2 showed a slight
amplification of this error over an increase in length. This variation was minimal. The
correlation between calculated and theoretical values backs up the reliability of this
data. This linear and uniform data showed no major anomalies.
Cross-sectional area was calculated by using the formula for area (sample
calculation 3) by substituting the radius of the wire. A nichrome wire with cross2
sectional area of 0.07 mm had a resistance of 1882 100mA–250Ω as opposed to a
2
nichrome wire with and area of 0.59 mm that had a resistance of 299.8 100mA–
250Ω.
Graph 2 compared the resistance values measured for the two lengths of copper. As
stated, the smaller diameter wire gave unreliable data. Graph 5 compared the
nichrome wires investigated. Graphs 4 shows that as the cross-sectional area of the
nichrome wires increased the resistance decreased. Graph 5 shows how the value of
resistance inversely affected the value of cross-sectional area over a consistent wire.
2
An R of 0.99 confirmed how this data followed linear and predictable trend.
Several factors may have affected the measured values of resistance. The variation
of electrical activity between different metals in contact also occurs in the study of
electro-chemistry (Smith 1996), and the effect of contact-potentials between different
metals could be a factor when measurements with the small currents (milli amps) of
an ohmmeter produce small voltages (milli volts) in the sensing circuit when the
contact voltages maybe of the same size. It proved difficult to compare metals and
alloys e.g. steel and copper. Steel and nichrome did not have exact theoretical
values for resistivity for comparison. The use of very narrow diameter wires did not
give reliable results as stated.
Sample assessment instrument and indicative responses
Comments
Sources of error include:
•
The limitations of the micrometre and ohmmeter instruments affecting the
precision of the recorded values.
•
Human error in measuring due to parallax readings.
•
The use of a ruler to measure in centimetres.
•
The calibration of the micrometre which was not done by a professional.
•
Measurements made within seconds of each other, causing heating of the wire,
resulting in higher readings.
Recommendations
To alleviate errors in future changes could be made in the design and methodology.
The method showed several flaws when attempting to measure small resistances.
A different method may be to pass a small current through the circuit, from a
voltage source of known size, and use a separate voltmeter to measure the
electrical potential difference (i.e. a voltage) across the ends of the wire that is
being tested, and use Ohms law to calculate the resistance. The temperature would
have to be held constant so that any heating effects of the current would be
controlled.
exploration of
scenarios and
possible
outcomes with
justification of
conclusions/
recommendations
Fully stretching out the wire and pulling it taut to decrease the number of
deformities and bends could improve the accuracy of results. If a measurement is
to taken for a 20 cm length then a 25 cm length should be cut and the crocodile
clips placed exactly at the 20 cm length. In this way the exact length is obtained.
Lengths from 20 cm to 80 cm (at 10cm intervals) could be investigated in future
investigations. The material of the clips could be investigated.
Waiting for the wire to cool after each ohmmeter measurement could have reduced
thermal resistance. Measuring the wire with the ruler at eye level could eliminate
parallax error. Measuring the length at 5 cm intervals or measuring more diameters
may have given a wider spread of results and improve accuracy of the graphical
equations. Wires of equal diameter could be used e.g. 1mm or larger as the results
have shown that very thin wires do not give reliable results. Wires of known
composition (metals and alloys) are best to use in future to allow comparison. A
further investigation could use the same lengths but deliberately place kinks in the
wire to see the effect on resistance values.
Conclusion
The results supported the key relationships predicted, showing that when length
increased so did resistance. When cross-sectional area increased, resistance
decreased. It was concluded that a linear relationship existed between resistance
and length and that an inverse proportional relationship existed between resistance
and cross-sectional area.
Queensland Studies Authority September 2012 | 11
Comments
Reference list
“Dependence of Resistance on Cross-sectional Area.” Virtual Institute of Applied
science Web. 26 Aug 2011. <http://www.vias.org/physics/example 4 5 04.html>
“Factors affecting Resistance, Electricity, Science Help. Online Science
TutoringITutorvista.com. “Tutorvista.com – Online Tutoring, Homework Help for math,
Science, English from best Online Tutor. Web. 18 Aug 2011.
http://www.tutorvista.com/content/science/science-ii/electricity/factors-affectingresistance.phg
“GCSE Physics: Resistance and Area.” GSCE.com Revising Revision. Web. 26 Aug
2011. http://www.gcse.com/vary4b.htm
“How is Electrical Resistance Measured?” WiseGEEK: Clear Answers for Common
Questions. 18 Aug 2011. http://www.wisegeek.com/how-is-electrical-resistancemeasured.htm.
“Physics Zone: Resistance in a Conductor.” Oswego City School District Regents
Exam Prep Center. Web. 26 Aug 2011.
<http://regentsprep.org/Regents/physics/phys03/bresist/default.htm>
“Resistance and Resistivity” Web. 26 Aug 2011. <http://hyperphysics.phyastr.qsu.edu/hbase/electric/resis.html>
“Resistance of Conductors.” Martin’s World. Web. 16 Aug 2011.
<http://www.marts100.com/resistance.htm>
“Resistance.” The Physics Classroom. Web. 26 Aug 2011.
<http://physicsclassroom.com/class/circuits/u9l3b.cfm>
“SparkNotes: SAT Physics: Resistance.” SparkNotes: Today’s Most Popular Study
Guides. Web 26 Aug 2011.
http://www.sparknotes.com/testprep/books/sat2/physics/chapter14section3.rhtml
Smith Roland, “Exploring Chemistry” (1996).
12 | Physics 2007
Sample assessment instrument and indicative responses
Comments
Appendix
Sample calculation 1 Finding theoretical resistance
R = L ρ/A
R=?
L = 0.2
ρ = 1.68 E–8
A = 1.038689m
2
R= 0.2 x 1.68 E–8 /1.038689
linking and
application of
algorithms,
concepts,
principles,
theories and
schema to find
solutions in
complex and
challenging
situations
R= 3.23485 x10 Ω
–9
Sample calculation 2 Finding percentage error
Calculated R = 3.216 x10 Ω Theoretical R = 3.23485 x10 Ω
% difference = (recorded – theoretical)/theoretical x 100
= (3.216–3.23485)/ 3.23485 x 100
= 0.5827%
–9
–9
Sample calculation 3 Finding area (Graph 6)
A = πr diameter = 0.87 mm
2
A = π(0.435)
2
A = 0.594 mm
2
radius = 0.435 mm
Sample calculation 4 Calculating inverse area (Graph 7)
2
A = 0.594 mm
R = 1/A
R = 1/0.594
–7
2
= 3.4 x10 m
Sample calculation 5
2
A = 0.14522 mm
k = 6397.5 (from graph 5)
ρ=kA
= 6397.5 x 0.14522
–6
= 0.929 x 10 ohm.m
Queensland Studies Authority September 2012 | 13
Student response — Standard C
Comments
Introduction
In this report the following question was looked at: “how do different wires and
different widths affect current and resistance in wires?” Resistance is the property
of a component which restricts the flow of electric current
(http://www.kpsec.freeuk.com/resistan.htm). An object with low resistance is called
a conductor. A conductor has free valence electrons which mean that the electrons
have free movement between each molecule. The further away from the nuclei the
valence electrons are the more movement they have causing a greater
conductance.
reproduction of
concepts,
theories and
principles
formulation of
questions and
hypotheses to
select and
manage
investigations
Figure 1 Diagram of electrons around a nucleus.
(Diagram removed due to copyright issues.)
There are a few things that affect the resistance of an object. Length affects the
resistance where the longer the electrons have to travel the higher the resistance.
Whilst the greater the cross sectional area the less resistance there is
(http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html). The temperature
affects it where the higher temperatures causes more heat which then in turn
causes the nuclei to vibrate more then it collides with the electrons more frequently.
Resistivity is defined as ‘the ability of a material to resist electrical conduction’
(http://www.glossary.oilfield.slb.com/Display.cfm?term=resistivity). Resistivity is
dependent on the material that is used. “It was found that by increasing the wires
length and width the resistance would increase, whilst at the same time the
resistance relied heavily on what properties the material had. To prove that this was
right the experiment below was designed where the different resistance at different
lengths, widths, and, materials and then compared. The idea of if the length of the
wire is increased (from 10cm) the resistance will increase, and if the material is
changed then the resistance will change depending on the metal’s properties, was
looked at in depth in this experiment. To do this the resistance had to be recorded
at different lengths, widths, and resistivity.
Hypothesis
If the length of the wire is increased (from 10cm) the resistance should increase,
and if the material is changed then the resistance should change depending on the
metals’ properties.
Method
manage
investigations
14 | Physics 2007
The wire’s width and length was measured, and was recorded. The alligator clips
were attached at two points that were specific lengths apart measured previously.
The resistance was then measured by the use of an ohmmeter and the results were
recorded. This was repeated with all the wires.
Sample assessment instrument and indicative responses
Comments
assessment of
risk
Safety
Cutting tools were used to cut the wires. To minimise the chances of students
cutting themselves the wires were cut by one student per group. The microohmmeter used 10 Amps which involved a low voltage, and it was a heavy object.
To minimise the chances of students hurting themselves by dropping the microohmmeter on their feet it was placed in one spot for the whole time the experiments
were being done.
Modifications
The insulated wires were not used because getting a proper reading could not be
done. Nickel, iron, zinc, silver, lead and graphite were dropped because it was not
available to use. Constantant and nichrome wires were added because they were
available to use. Did not read the temperature because it was too hard to do
properly. Instead of getting the results of different lengths on one wire only, the
different lengths were done on all wires.
Results
Table 1 Resistance and Resistivity values
Resistance (milli ohms)
Length (cm)
Material and
width (mm)
application of
technology to
gather, record
and process
data
application of
algorithms,
principles,
theories and
schema to find
solutions in
simple
situations
10
20
30
Calculated
Average
Resistivity
Value (ohm.m)
Theoretical
Resistivity
Value
(ohm.m)
40
–8
1.68x10
–8
–8
1.68x10
Copper
(0.58)
6.54
12.78
19.78
25.54
1.727x10
–8
1.6883x10
–8
1.7420x10
–8
1.6869x10
–8
Av =1.7111x10
Copper
(1.28)
1.33
2.49
3.66
4.96
1.710x10
–8
1.706x10
–8
1.6703x10
–8
1.6077x10
–8
Av = 1.6735 x10
Aluminium
(1.22)
2.52
5.10
6.90
9.34
2.9412x10
–8
2.9833x10
–8
2.6887x10
–8
2.7296x10
–8
Av = 2.8357 x10
Constantant 42.50
(1.2)
84.86
127.3
169.7
48.07 x 10
49x10
–8
47.98x10
–8
49.76x10
–8
47.799 x10
–8
Av = 48.4023x10
Nichrome
(0.91)
246.6
443.1
592.2
99.99x10
110x10
–8
80.189 x10
–8
96.062 x10
–8
96.289 x10
–8
Av = 93.1325x10
153.8
–8
–8
2.65x10
–8
–8
–8
–8
–8
Queensland Studies Authority September 2012 | 15
Comments
Resistance vs. length
Resistance (milli ohms)
selection, use
and
presentation of
scientific data
and ideas to
make meaning
accessible
30
y = 64x + 0.16
R² = 0.9987
25
Copper 0.58mm
20
Copper 1.28mm
15
y = 12.06x + 0.095
R² = 0.9992
10
5
Linear (Copper
0.58mm)
0
Linear (Copper
1.28mm)
0
0.2
0.4
Length (m)
0.6
Graph 1 Resistance versus length for Copper wire.
Resistance (milli ohms)
Resistance vs. length
10
y = 22.26x + 0.4
R² = 0.9958
8
6
Al 1.22mm
4
Linear (Al
1.22mm)
2
0
0
0.2
0.4
Length (m)
0.6
Graph 2 Resistance versus length for Copper wire.
Resistance (milli ohms)
Resistance vs. length
200
150
y = 424.09x + 0.065
R² = 1
100
Constanant 1.2mm
50
Linear (Constanant
1.2mm)
0
0
0.2
0.4
Length (m)
0.6
Graph 3 Resistance versus length for Constanant wire.
16 | Physics 2007
Sample assessment instrument and indicative responses
Comments
Resistance vs. length
analysis of primary
and secondary data
to identify obvious
patterns and trends
Resistance (milli ohms)
700
y = 1511.9x - 19.055
R² = 0.9834
600
500
400
Nichrome 0.91mm
300
Linear (Nichrome
0.91mm)
200
100
0
0
0.2
0.4
Length (m)
0.6
Graph 4 Resistance versus length forNichrome wire.
Discussion
reproduction of
concepts, theories
and principles
Using the following equation it can be found that the resistance is resistivity by
length divided by the cross sectional area (width).
(http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.htm)
Rearranging the equation it can be seen that resistivity is resistance by width
divided by length. To find the resistivity of the copper wire with width of 0.58cm so
a cross-area of 0.2642, length of 0.1 meters and resistance of 6.538 milli ohms
–8
which equals 1.727x10 ohms m.
According to the data it can be concluded that the width, length and resistivity
affects the resistance where the wider the wire the less resistance, the longer the
wire the more resistance and the higher the resistivity the higher the resistance.
These conclusions were made because Table 1 shows how the length and
resistivity increased the resistance whilst the area (copper 0.58 and copper 1.28)
decreased the resistance.
identify obvious
errors
While conducting this experiment some errors were made because the
measuring of the length was only done in centimetres, the width in millimetres
and the resistance in milli ohms. An anomaly was found where the average
resistivity of the two copper wires was expected to be the same but found that the
two wires with different widths had different resistivity. This could be from the fact
that even though the two wires are made out of the same materials the materials
themselves could have impurities in them changing the property. To fix this in a
future experiment the wires would have to be made sure they were pure.
Queensland Studies Authority September 2012 | 17
Comments
The Graphs 1–4 show a result that would be expected where the length increase in
a set amount each time so does the resistance in a linear form in proportion to the
amount increased and the resistivity. The calculated resistivity and the graph of
resistance vs. length with Nichrome (Graph 4) had results that were not expected.
Where the resistivity decreased greatly from 10cm to 20cm and then increased by a
considerable amount from 20cm to 30 cm and then only decreased slightly from
30cm to 40cm.
description of
scenarios and
possible
outcomes with
statements of
conclusion/
recommendation
Part of the reason for this anomaly could be because the wire was slightly bent at
certain areas even after it was straightened meaning that the length that were
measured would be slightly off which has a greater effect on the resistance when
the wire has a high resistivity such as nichrome has. The other reason is because
the resistance is so high the error is going to be greater but still within the error
range. Whilst conducting the experiment the wires were knocked sometimes
changing the resistance value. If this experiment was to be done again it is
recommended that the wires be measured in millimetres and the wires are placed
onto the table every time it is measured instead of being held. And the wires are
fully straightened and not bent in any way.
Conclusion
The aim was to find out how resistance was affected when the resistivity, length of
wire and width of wire, were change about. This aim was achieved. It was found
that when you increase either the length or resistivity the resistance increased but
increasing the width decreased the resistance of the wire. The wires should have
been placed on the bench every time and the length measured up to nearest
millimetre instead of centimetre.
Acknowledgments
The QSA acknowledges the contribution of St Joseph’s College Gregory Terrace in the
preparation of this document.
18 | Physics 2007
Sample assessment instrument and indicative responses