as and a level physics a and physics b (advancing physics...

AS and A level PHYSICS A and PHYSICS B (Advancing Physics) Uncertainties

Lesson Element uncertainties.

This brief guide is produced to give teachers and candidates a better idea of how uncertainties could be treated in experimental Physics, specifically as it relates to the OCR Physics A and B specification for first teaching from 2015. This is not intended to be a guide on how the PAGs should be carried out for the practical endorsement but rather, just provides the context for the example.

The following sets out an example from PAG 3.1

Investigation to determine the resistivity of a Metal

Fig. 1

The following shows some sample data and the subsequent treating of the uncertainties. This is not prescriptive in that you have to follow this exact model for every experiment, it merely points out a possible approach bearing in mind that any of this manipulation can come up on the question papers

The student used a voltmeter with a resolution of 0.01V and an ammeter with a resolution of 0.01A. The length of wire was varied at 10cm intervals and the rheostat adjusted so that a

R

A

V

S

L

+

metal wire


current of 0.35A was maintained throughout the investigation. The length of nichrome wire was mounted on to a metre rule.

The following data was collected and the experiment was not repeated.

The variables in the data are linked by the equation

A

I

l

V

Where V is the voltage across the wire

I is the current through the wire

l is the length of wire

A is the cross sectional area of the wire

is the resistivity of the wire

In order to find a value for resistivity ρ, all of the uncertainties in the equation have to be considered

Current 0.35A

Absolute uncertainties were as follows

Uncertainty in voltmeter 0.01v

Uncertainty in ammeter 0.01A

Uncertainty in the cross sectional area of wire- The wire was measured three times along its length with a digital micrometer and a mean taken. The readings were as follows

d1/mm d2/mm d3/mm dmean/mm

l/m pd/V

0.100 0.68

0.200 1.30

0.300 1.75

0.400 2.39

0.500 2.80

0.600 3.65

0.700 4.00

0.800 4.67

0.900 5.52


0.248 0.252 0.254 0.251

Uncertainty in a range of readings is half the range of the spread of results so

2

minmax

mm003.02

248.0254.0

This is the absolute uncertainty in the diameter of the wire ±0.003mm. We need the diameter in the area and the area is

so radius is 0.000251/2 = 4.95x10-8 m2

-because the radius is squared we have to take the uncertainty into account twice. However, we can’t just add absolute uncertainties; rather, we have to add the percentage uncertainties.

%4.22%2.1100251.0

003.0 xx

Therefore the uncertainty in the cross sectional area of the wire is ±2.4%

The uncertainty in length presents a couple of challenges. The mm ruler has an analogue scale, therefore, the uncertainty in the instrument is ± half the smallest division 0.5mm. If we were just measuring the length of the wire, then the uncertainty would be ± 1mm as we have the uncertainty in the measurement at each end. However, because there is an element of judgement due to the difficulty in measuring where the crocodile clip is in contact with the wire, we have to use our judgement and increase the uncertainty. In this case it could be logical to say it is anything between 2-4mm. Therefore we will call the uncertainty in the length of wire ±3mm.

Now that we have considered the uncertainties, we now process the data to determine the resistivity of the wire and quote its uncertainty.

Below is the graphed data.


Applying the equation to the data then, we have plotted V/l therefore the equation from above becomes

A

I

l

V

So is the gradient of the line = l

V

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20

pd/V

Length/m


Gradient 00.6)20.000.1(

)20.100.6(

l

V= gradient =

A

I

Therefore:

I

gradientxA

78

1049.835.0

1095.400.6

xxx

Ω m

The experimental value for resistivity then, is 8.49 x 10-7 Ω m

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20

pd/V

Length/m


We now have to compare this value to the book value given in some textbooks as 1.00x10-6

Ω m

Comparing this to our value of 8.49 x 10-7 Ω m and calculating the percentage difference between the two

%151001000.1

1049.81000.16

76

xx

xx

That means there is a 15% difference between the experimental value and the accepted book value. We now have to process our uncertainties to see if ‘within the uncertainties’ our value is in agreement

Uncertainties in our data

We used this equationto calculate our experimental value; therefore we need to consider the uncertainties in each quantity and add the percentage uncertainties to calculate the total uncertainty in the resistivity

length

reagradientxa

We calculated the uncertainty in area before and determined it was 2.4%

The uncertainty in the current was 0.01A so percentage uncertainty is 0.01/0.35 x 100 = 2.9%

The uncertainty in the gradient is calculated as follows. A line of worst fit is drawn on the extremes of the data, that is, the worst possible line of fit you can draw as shown by the dotted line below. Calculate the gradient of that line and calculate the percentage difference between the best and worst fit. This is the percentage uncertainty in the gradient.


Worst fit gradient )08.096.0(

00.6

=6.82

Percentage difference in the gradient

00.6

00.682.6 X 100 = 13.7%

Therefore:

% uncertainty in current = 2.9%

% uncertainty in area =2.4%

% uncertainty in gradient =13.7%

Total uncertainty in our experimental value = ±19%

The percentage difference between the book value and our experimental value was 15%

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20

pd/V

Length/m


We can say then, that our experimental value lies within the experimental uncertainties and the two values are in agreement.

The example used above doesn’t have error bars on the graph. The reason for this is that they are just too small to display, therefore the worst fit line is just drawn using judgement on the extremes of data. That is, the worst possible line you could draw considering the spread of data.

Below is an example of some data with the error bars plotted with best and worst fit lines.

It is reasonable to expect the worst fit line to extend from the top extremity of the largest data point to the lowest point on the smallest data point as shown.

The uncertainty in the gradient can be determined by the method explained earlier. We can take this a step further if you are asked for the uncertainty in the y-intercept.

In the example above, the y-intercept of the best fit line is 2.2. The uncertainty in this is the difference in y-intercepts of best and worst fit divided by the best fit intercept x 100.


So in this example: 1002.2

5.12.2

= 32% Therefore the uncertainty in the y-intercept is

±32%

AS and A level PHYSICS A and PHYSICS B (Advancing Physics) Level of response resource

AS Level Physics A

H156/02 Depth in Physics

Sample Question Paper

Question 7(a)


Candidate response 1


Candidate response 2


Commentary and marks

Candidate response 1. Level 3, 6 marks

Commentary

This response shows a clear and logical line of reasoning. The answer is structured in terms of experimental design → measurements → processing of results, and it is clear how to determine a value for the Planck constant using a graphical method. The response is clearly in level 3.

In the ‘Experiment’ section (E), the student has made an attempt at E1 and E3 but does not fully explain the potential divider arrangement. He has gained E2, E4, E5 and E6 so this is definitely a level 3 response. However, to ensure full marks, the student should talk about adjusting the potential divider to zero voltage and then increasing the voltage.

In the ‘Processing’ section (P), the student has gained P1 and P2 (via the graph), P5 and P6. This is a high level 3 response.

Overall, this response would just score the full 6 marks.

Candidate response 2. Level 2, 4 marks

Commentary

There is some structure to the response and it has a line of reasoning, but the links are not always clearly made. For example, ‘This is the minimum voltage, threshold frequency’ is too vague a statement, and ‘The wavelength value is provided, so no need to calculate it’ misses the point that 1/λ does need to be calculated in order to be able to plot the graph. In order to reach the top level, the student would need to add more experimental detail and structure the first part of the answer more carefully.

In the ‘Experiment’ section (E), the student has included E2, E5 and an attempt at E3 (‘Vary the voltage until the light starts to show’). In the ‘Processing’ section (P), he has included P1, P2, P5 and P6.

Three points from E and at least 2 from P puts this answer in level 2. It is high in the level 2 band (4 marks), but does not quite reach level 3 because the student has not included E4. To improve the answer, therefore, the student should mention repeating several times and finding an average value for Vmin each time.

Version 1 1 © OCR 2016

Useful information for OCR A Level Physics’ teachers

Contact with the OCR science team

[email protected] Practical Endorsement queries, comments or ideas for practical activities

[email protected] – the existing (and continuing) address for general queries

twitter @OCR_science OCR Community http://www.ocr.org.uk/community/ see updates from the science

team, collaborate with your colleagues and discuss education and assessments. Available from the open access qualification webpages Physics A http://ocr.org.uk/qualifications/as‐a‐level‐gce‐physics‐a‐h156‐h556‐from‐2015/ Physics B http://www.ocr.org.uk/qualifications/as‐a‐level‐gce‐physics‐b‐advancing‐physics‐h157‐h557‐from‐2015/

Full AS and A Level Specifications Qualification summary brochure Full set of AS and A Level Sample Assessment Materials (SAMs) The Scheme of Work Builder Delivery Guides Topic Exploration Packs and Transition Guides Lesson Elements Candidate exemplars (Level of Response exam questions with commentary)coming

soon Practice MCQs coming soon Links to OCR-endorsed textbooks.

Available from Interchange – password protected https://interchange.ocr.org.uk/

A full set of AS practice papers and mark schemes for Physics A and Physics B Suggested activities for each of the 12 Practical Activity Groups (PAGs) The Practical Endorsement PAG Tracker spreadsheet Physics Practical Skills Handbook Physics Maths Skills Handbook Scheme of Work support document.

Other useful OCR webpages http://www.ocr.org.uk/qualifications/by-subject/science/ The science homepage, with links to all our science qualifications, team info, newsletters, videos and more, plus a link to www.ocr.org.uk/positiveaboutpractical with videos and links explaining aspects of the Practical Endorsement. http://www.ocr.org.uk/ocr-for/teachers/ Contains links to useful information including free, termly, teacher networks (to see listings and book yourself in http://www.ocr.org.uk/ocr-for/teachers/teacher-networks/). Training www.cpdhub.ocr.org.uk Upcoming face to face courses and online webinars plus resources from CPD sessions which have previously run.

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