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Date November 2014 Marks available 2 Reference code 14N.2.SL.TZ0.1
Level Standard level Paper Paper 2 Time zone Time zone 0
Command term Draw Question number 1 Adapted from N/A

Question

Data analysis question.

A student sets up a circuit to study the variation of resistance R of a negative temperature coefficient (NTC) thermistor with temperature T. The data are shown plotted on the graph.

N14/4/PHYSI/SP2/ENG/TZ0/01

The electric current through the thermistor for T=283 K is 0.78 mA. The uncertainty in the electric current is 0.01 mA.

Draw the best-fit line for the data points.

[1]
a.

Calculate the gradient of the graph when T=291 K.

[3]
b.i.

State the unit for your answer to (b)(i).

[1]
b.ii.

The uncertainty in the resistance value is 5%. The uncertainty in the temperature is negligible. On the graph, draw error bars for the data point at T=283 K and for the data point at T=319 K.

[2]
c.

Calculate the power dissipated by the thermistor at T=283 K.

[1]
d.i.

Determine the uncertainty in the power dissipated by the thermistor at T=283 K.

[3]
d.ii.

Markscheme

smooth curve that passes within ±0.5 squares of all data points;

a.

a tangent drawn at [291, 5.2] and selection of two extreme points on the tangent that use ΔR>3.5 Ω; } (judge by eye)

gradient magnitude determined as 0.20±0.02;

negative value given;

b.i.

Ω K1;

b.ii.

correct error bar for 283 K (total length of bar 3–5 squares, centred on point);

correct error bar for 319 K (total length of bar 0.5–2 squares, centred on point);

c.

substituting I2R=([0.78×103]2×7.5)=4.5×106 Wor4.6×106 W;

d.i.

fractional uncertainty in I2=2×0.010.78 (= 0.026or2.6%);

uncertainty in power (=[0.026+0.05]×4.6×106)=0.34×106 W to 0.35×106 W;

answer rounded to 1 significant figure;

or

uncertainty in I2=2×1.3%/0.026;

total uncertainty in P=7.6%/0.076;

answer rounded to 1 significant figure;

d.ii.

Examiners report

[N/A]
a.

Very poorly executed. Few SL candidates knew how to draw an acceptable tangent.

b.i.
[N/A]
b.ii.
[N/A]
c.
[N/A]
d.i.
[N/A]
d.ii.

Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.2 – Uncertainties and errors
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