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Date May 2017 Marks available 4 Reference code 17M.2.SL.TZ1.4
Level Standard level Paper Paper 2 Time zone Time zone 1
Command term Determine Question number 4 Adapted from N/A

Question

A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable.

The following data are available:

Length of cable = 10 m
Cross-sectional area of cable = 6.0 mm2
Resistivity of copper = 1.7 × 10–8 Ω m

Calculate the current in the copper cable.

[1]
a.i.

Calculate the resistance of the cable.

[2]
a.ii.

Explain, in terms of electrons, what happens to the resistance of the cable as the temperature of the cable increases.

[3]
b.

The heater changes the temperature of the water by 35 K. The specific heat capacity of water is 4200 J kg–1 K–1.

Determine the rate at which water flows through the shower. State an appropriate unit for your answer.

[4]
c.

Markscheme

I «=\(\frac{{8.5 \times {{10}^3}}}{{240}}\)» =35«A»

 

 

a.i.

= \(\frac{{1.7 \times {{10}^{ - 8}} \times 10}}{{6.0 \times {{10}^{ - 6}}}}\)

= 0.028 «Ω»

 

Allow missed powers of 10 for MP1.

a.ii.

«as temperature increases» there is greater vibration of the metal atoms/lattice/lattice ions

OR

increased collisions of electrons

 

drift velocity decreases «so current decreases»

«as V constant so» R increases

 

Award [0] for suggestions that the speed of electrons increases so resistance decreases.

b.

recognition that power = flow rate × cΔT

flow rate «\( = \frac{{{\text{power}}}}{{c\Delta T}}\)» \( = \frac{{8.5 \times {{10}^3}}}{{4200 \times 35}}\)

= 0.058 «kg s–1»

kg s−1 / g s−1 / l s−1 / ml s−1 / m3 s−1

 

Allow MP4 if a bald flow rate unit is stated. Do not allow imperial units.

c.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[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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