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Resistivity Question

Q6. A wire probe is used to measure the rate of corrosion in a pipe carrying a corrosive liquid.

The probe is made from the same metal as the pipe so the rate of corrosion of the wire in the probe is the same as in the pipe.

The diagram below shows the probe.

(a) The wire in an unused probe has a resistance of 0.070 Ω and a length of 0.50 m.

Given that the resistivity of metal in the wire is 9.7 × 10–8 Ω m, calculate the diameter of the wire.

[3 marks]

(b) In order to measure the resistance of a used working probe, it is connected in the circuit shown below.

When R3 is adjusted to a particular value the current in the cell is 0.66 A.

(i) Calculate the total resistance of the circuit.

You may assume that the cell has a negligible internal resistance.

[1 mark]

(ii) The resistance of R2 is 22 Ω and the resistance of R3 is 1.2 Ω.

Calculate the current in R3.

[1 mark]

(iii) Calculate the resistance of the probe when the resistance of R1 is 2.4 Ω.

[3 marks]

(iv) Calculate the percentage change in the diameter of the probe when its resistance increases by 1.6 %.

[2 marks]

(v) A voltmeter is connected between points A and B in the circuit and R3 stays at 1.2 Ω.

Explain, without calculation, why the reading on the voltmeter does not change when the cell in the circuit is replaced with another cell of the same emf but a significant internal resistance.

[2 marks]

(Total 12 marks)