| Date | May 2013 | Marks available | 2 | Reference code | 13M.2.SL.TZ1.1 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Outline | Question number | 1 | Adapted from | N/A |
Question
Data analysis question.
A particular semiconductor device generates an emf, which varies with light intensity. The diagram shows the experimental arrangement which a student used to investigate the variation with distance d of the emf ε. The power output of the lamp was constant. (The power
supply for the lamp is not shown.)
The table shows how ε varied with d.
Outline why the student has recorded the ε values to different numbers of significant digits but the same number of decimal places.
On looking at the results the student suggests that ε could be inversely proportional to d. He proceeds to multiply each d value by the corresponding value of ε.
(i) Explain why this procedure can be used to disprove the student’s suggestion but it cannot prove it.
(ii) Using the data for d values of 19.1 cm, 16.0 cm and 10.0 cm discuss whether or not ε is inversely proportional to d.
The graph shows some of the data points with the uncertainty in the d values.
On the graph
(i) draw the data point corresponding to the value of d=19.1 cm.
(ii) assuming that there is a constant absolute uncertainty in measuring all values of d, draw the error bar for the data point in (c)(i).
(iii) sketch the line of best-fit for all the plotted points.
All values of ε have a percentage uncertainty of ±3%. Calculate the percentage uncertainty in the product dε for the value of d=18.0cm.
Markscheme
reference to meter/instrument;
reference to constant accuracy/precision;
Award [2] for “voltmeter measures to 0.1 V”.
clear deviation means not/unlikely to be valid;
close to constant only means possibility of validity;
third value correct;
products so far apart clearly not inversely proportional;
or
attempts to show that \(\frac{{{d_1}}}{{{\varepsilon _2}}} \ne \frac{{{d_2}}}{{{\varepsilon _1}}}\) or \(\frac{{{d_1}}}{{{d_2}}} \ne \frac{{{\varepsilon _2}}}{{{\varepsilon _1}}}\) for two pairs of values;
third pair of values used;
ratios so far apart clearly not inversely proportional;
(i) point plotted ±½ small square;
See graph for position.
1.5 small squares down +5.5 small squares across from previous plotted point.
(ii) symmetrical error bar, 1 small square in each direction ±½ small square;
(iii) single smooth curve within each error bar;
Do not condone multiple, hairy or unduly thick lines.
% uncertainty in d value \(\left( {{\rm{ = }}\frac{{{\rm{0.2cm}}}}{{{\rm{18cm}}}}} \right)\)=1/1.1%;
% uncertainty in dε product=4/4.1%;
Allow ECF from wrong absolute error in d.
Examiners report
Many candidates failed to recognise that the number of decimal places is a reflection of the precision of a piece of equipment – it this case the millivoltmeter. Using different number of significant figures simply indicates that the reading is larger or smaller but it will be to the same precision. A sizeable proportion of candidates believed the number of decimal places was something that they could choose in an arbitrary manner.
(i) Most candidates failed to realise that the result of multiplying a series of corresponding values of ε and d only needed to show different values for the equation to be disproved but that all possible values would need to be taken prove it (clearly an impossibility).
(ii) By performing the task in (i) most candidates showed that there was too large a discrepancy between the three sets of products to suggest that the equation was viable.
(i) Most candidates were able to correctly plot the data point despite there being a relatively difficult scale division.
(ii) The majority of candidates drew an appropriate error bar.
(iii) Many failed to take sufficient care when sketching the line of best fit. Lines of best fit are not always straight and it is important that candidates practise drawing curves in preparation for examinations. It was common to see multiple lines, some of which did not pass through the horizontal part of the error bar (the vertical edges being irrelevant and of arbitrary length).
Most candidates were able to find the percentage uncertainty in the d value or correctly added the two percentage values; many were unable to do both.
