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Date May 2015 Marks available 7 Reference code 15M.2.HL.TZ1.3
Level Higher level Paper Paper 2 Time zone Time zone 1
Command term Determine, Explain, and State Question number 3 Adapted from N/A

Question

This question is about a thermistor circuit.

The circuit shows a negative temperature coefficient (NTC) thermistor X and a 100 kΩ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Define electromotive force (emf).

[1]
a.

The graph below shows the variation with temperature T of the resistance RX of the thermistor.

(i) Determine the temperature of X when the potential difference across R is 4.5 V.

(ii) State the range of temperatures for which the change in the resistance of the thermistor is most sensitive to changes in temperature.

(iii) State and explain the effect of a decrease in temperature on the ratio \(\frac{{{\rm{voltage across X}}}}{{{\rm{voltage across R}}}}\).

[7]
b.

Markscheme

the work done per unit charge in moving a quantity of charge completely around a circuit / the power delivered per unit current / work done per unit charge made available by a source;

a.
(i) VX = 7.5 (V);
\(I\left( { = \frac{{4.5}}{{100 \times {{10}^3}}}} \right) = 4.5 \times {10^{ - 5}}{\rm{A}}\) or \(\frac{{{V_X}}}{{{V_R}}} = \frac{{{R_X}}}{{{R_R}}}\);
\({R_X}\left( { = \frac{{7.5}}{{4.5 \times {{10}^{ - 5}}}}} \right) = 1.67 \times {10^5}\Omega \) or \({R_X}\left( { = \frac{{7.5}}{{4.5}} \times 100 \times {{10}^3}} \right) = 1.67 \times {10^5}\Omega \);
\(T =  - 37\) or \( - 38\) °C
(ii) 50 to (up to) 30 °C / at low temperatures;
(iii) as the temperature decreases Rx increases; same current through R and X so the ratio increases or VX increases and VR decreases so the ratio increases;
b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Core » Topic 5: Electricity and magnetism » 5.3 – Electric cells
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