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Date May 2012 Marks available 5 Reference code 12M.2.SL.TZ1.9
Level Standard level Paper Paper 2 Time zone Time zone 1
Command term Calculate Question number 9 Adapted from N/A

Question

Part 2 Electric current and resistance

The graph below shows how the current I in a tungsten filament lamp varies with potential difference V across the lamp.

(i) Define the electrical resistance of a component.

(ii) Explain whether or not the filament obeys Ohm’s law.

[3]
a.

(i) Calculate the resistance of the filament lamp when the potential difference across it is 2.8 V.

(ii) The length of the filament in a lamp is 0.40 m. The resistivity of tungsten when the potential difference across it is 2.8 V is 5.8×10–7Ω m. Calculate the radius of the filament.

[5]
b.

Two identical filament lamps are connected in series with a cell of emf 6.0 V and negligible internal resistance. Using the graph on page 26, calculate the total power dissipated in the circuit.

[2]
c.

Markscheme

(i) potentialdifferenceacrossthecomponentcurrentinthecomponent;
Award [0] for simple statement of voltage divided by current

(ii) Ohm’s law states that voltage is (directly) proportional to current or
potentialdifferencecurrent /resistance is a constant;
graph not linear/gradient not constant so Ohm’s law not obeyed / calculation of VI at two points showing that they are different;
Award [0] for bald statement of Ohm’s law not obeyed.

a.

(i) (from graph, when V = 2.8 V,) I = 0.33 A; (accept answers in range 0.32 to 0.34 A)
R=VI=2.80.34=8.5Ω; (accept answers in range 8.2 to 8.8 Ω)

(ii) A=(ρlR=5.8×107×0.408.5=)2.7×108;
(accept answers in range 2.6 to 2.8×10–8)

r=Aπ seen/used;
=9.3×10-5m; (accept answers in range 9.2 to 9.5×10–5)

b.

each lamp has a potential difference of 3.0 V so current equals 0.35 A;
(accept answers in range 0.34 to 0.35 A)
2.1 W; (accept answers in range 2.0 to 2.1 W)
Award [1] for answers that use voltage 6.0 V with current 0.52 A to get P=3.1W.

c.

Examiners report

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

Syllabus sections

Core » Topic 5: Electricity and magnetism » 5.2 – Heating effect of electric currents
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