11 mark
Which of the following is a correct unit for resistivity, ρ?
Ω
Ω m–1
Ω m–2
Ω m
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5.2 Resistance & Resistivity
21 mark
Which of the following statements about resistivity is false?
The resistivity of a metal wire depends on temperature
The resistivity of a metal wire depends on length
Resistivity is measured in Ω m
Resistivity is a measure of a wire’s resistance to electric current
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31 mark
A student carries out an experiment to determine the resistivity of a metal wire.
She determines resistance from measurements of potential difference and the corresponding current, and measures the length of a wire with a metre rule and the diameter of the wire.
Which of the following is the most appropriate piece of equipment to measure the diameter of a metal wire?
A metre rule
An ammeter
A micrometer
A ruler
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41 mark
Which of the following statements about superconductors is true?
Superconductors are highly conducting plastic materials
The resistance of a superconductor is zero below a critical temperature
Superconductors have very low resistance at extremely high temperatures
The resistance of a superconductor is near zero below its critical temperature
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51 mark
Which of the following is not a possible application of superconducting material?
Electrical transformers
MRI scanners
Tyres for electric vehicles
Maglev trains
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61 mark
A metal wire of length 2.5 m and cross-sectional area 7.1 × 10–9 m2 has a resistivity of 2.8 × 10–7 Ω m.
What is the resistance of the wire?
9.9 Ω
99 Ω
1 Ω
1000 Ω
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71 mark
When the temperature of nickel wire increases, its ability to conduct electricity:
remains the same
decreases
remains the same at first, then decreases
increases
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81 mark
Which graph shows how the resistance R of an NTC thermistor varies with temperature, T?
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91 mark
Which graph shows how the resistance varies with temperature for a superconducting material around its critical temperature, 
?
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101 mark
A nichrome wire of length 4.2 m and cross-sectional area 6.0 × 10–10 m2 has a resistance of 1 kΩ.
What is the resistivity of the nichrome wire?
1.4 × 10–10 Ω m
1.4 × 10–7 Ω
1.4 × 10–10 Ω
1.4 × 10–7 Ω m
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11 mark
Two wires, P and Q, each of the same length and the same material, are connected in parallel to a battery.
The diameter of P is half that of Q.
What fraction of the total current passes through P?
0.10
0.20
0.50
0.25
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21 mark
An NTC thermistor suspended in a water bath and the temperature is gradually increased.
Which of the following graphs best represents how the current I in the thermistor varies with the potential difference V across it?
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31 mark
A conducting liquid fills a cylindrical metal case to a depth 
as shown in the diagram.
The resistance R between the case and the metal rod is correctly described by which of the following statements?
R ∝
R ∝
2R ∝
R ∝
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41 mark
A wire of uniform cross-sectional area A has a resistance R.
The wire is stretched until its length increases by 15%.
Assuming the new wire has the same volume as before, by how much has the resistance of the wire increased?
30%
32%
33%
35%
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51 mark
A strain gauge consists of a length of wire with uniform cross-sectional area A and resistance 3.00 kΩ. It is attached to large pipe, such that when the pipe expands, the strain gauge changes in dimensions.
During one particular expansion, the length increases by 5% and the diameter reduces by 10%.
What is the new resistance of the strain gauge?
3.89 kΩ
3.88 kΩ
3.87 kΩ
3.86 kΩ
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61 mark
A composite wire is made using four uniform wires of the same material but varying diameters as shown:
Which graph correctly shows the variation of resistance R with distance d from the point X?
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71 mark
A wire of resistivity 1.5 × 10–8 Ω m has a radius of 0.25 mm and a length that is able to be wound in circles 50 times round a plastic rod of radius 1.25 cm.
What is the resistance of the wire?
4.15 Ω
3.50 Ω
3.14 Ω
0.3 Ω
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81 mark
In an experiment to investigate how the potential difference V varies with length 
of a copper wire of uniform cross-sectional area A, a student measures the potential difference across the wire at equal intervals of length and plots a graph.
What are the correct dimensions of the gradient of the graph?
J m–2 s–1 A–1
J m–1 s–1 A–1
J m–1 s–2 A–1
J m–1 s–1 A–2
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91 mark
The graph shows the variation with length l of resistance R for two wires X and Y made from the same material.
Which of the following statements is correctly concluded from the graph?
cross-sectional area of X = 2 x cross-sectional area of Y
resistivity of X = 2 x resistivity of Y
when equal lengths of X and Y are connected in series to a battery, power in X = 2 x power in Y
when equal lengths of X and Y are connected in parallel to a battery, current in X = 2 x current in Y
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101 mark
In a fire alarm system, a negative temperature coefficient thermistor T has a resistance of 2 kΩ at room temperature and is connected in a circuit as shown:
The alarm is triggered when the potential difference between X and Y reaches 4.5 V.
From room temperature, what is the percentage reduction of resistance required for the alarm to be triggered?
12.5%
25%
66%
87.5%
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11 mark
Which statement about superconductors is correct?
The temperature at which a material becomes a superconductor is called the critical temperature
When a material becomes a superconductor, its resistivity is almost zero
Copper is a superconductor at room temperature
When current passes through a superconductor, the potential difference across it becomes a maximum
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21 mark
Which graph shows the variation of the resistance with temperature for an NTC thermistor?
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31 mark
Two wires P and Q made of the same material are connected to the same electrical supply.
P has twice the length of Q and one-third of the diameter of Q, as shown in the diagram .
What is the ratio 
?
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41 mark
Two electrically-conducting cylinders X and Y are made from the same material.
Their dimensions are as shown.
The resistance between the ends of each cylinder is measured.
What is the ratio 
?
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51 mark
Tensile strain may be measured by the change in electrical resistance of a strain gauge.
A strain gauge consists of folded fine metal wire mounted on a flexible insulating backing sheet.
The strain gauge is firmly attached to the specimen, so that the strain in the metal wire is always identical to that in the specimen.
When the strain in the specimen is increased, what happens to the resistance of the wire?
it decreases, because the length decreases and the cross-sectional area increases
it decreases, because the length decreases and the cross-sectional area increases
it increases, because the length decreases and the cross-sectional area increases
it increases, because the length increases and the cross-sectional area decreases
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61 mark
A researcher has two pieces of copper of the same volume. All of the first piece is made into a cylindrical resistor P of length x.
All of the second piece is made into uniform wires each of the same length x which he connects between two bars of negligible resistance to form a resistor Q.
How do the electrical resistances of P and Q compare?
P has a larger resistance than Q
Q has a larger resistance than P
P and Q have equal resistance
Q may have a larger or smaller resistance than P, depending on the number of wires made
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71 mark
Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10–8 Ω m, and wire Y is made of a metal of resistivity 5.6 × 10–8 Ω m.
The diameter of wire X is 0.315 mm.
What is the diameter of wire Y?
0.17 mm
0.33 mm
0.57 mm
1.0 mm
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81 mark
A metal wire has a length and a cross-sectional area A.
The wire is connected to a cell of emf ϵ, with no internal resistance, such that a current I flows in the wire.
Which expression gives the resistivity of the wire?
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91 mark
Which graph shows how the resistance per unit length r of a wire varies with radius of the wire?
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101 mark
A student carries out an experiment to determine the resistivity of a metal wire.
She determines resistance from measurements of potential difference and the corresponding current and measures the length of a wire with a metre rule and the diameter of the wire with a micrometer.
Each measurement is made with an uncertainty of 2 %.
Which quantity contributes the largest uncertainty in the calculated value of resistivity?
Cross-sectional area, A
Length,
Potential difference, V
Current, I
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