AQA AS Physics

Topic Questions

5.2 Resistance & Resistivity

1a4 marks

A student wishes to investigate what factors affect the resistance of a conducting wire. 

Complete Table 1 by placing a tick in the correct column to show whether each of the quantities affects or does not affect the resistance of a conducting wire. 

Table 1 

Quantity

Affects Resistance

Does Not Affect Resistance

Length

 

 

Cross-sectional area

 

 

Mass

 

 

Volume

 

 

1b2 marks

State, in words, how resistance depends on the properties identified in part (a).  

1c3 marks

The student designs an experiment to investigate the resistivity of the conducting wire. 

They measure the resistance in the wire R for varying lengths l , and plot a graph, as shown in Figure 1:

 Figure 1

5-2-s-q--q1c-easy-aqa-a-level-physics

Use Figure 1 to: 

   (i)   Calculate the gradient of the line 

   (ii)   State an appropriate unit for the gradient

1d4 marks

The notes in the student’s lab are shown in Figure 2: 

Figure 2

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The student records the cross-sectional area of the wire A = 3.8 × 10–7 m2.   

(i)
Suggest the measuring instrument the student likely used to measure the diameter of the wire 
(ii)
By referring to the gradient of the line in Figure 1, state and explain whether the student’s method to calculate the resistivity is correct

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2a4 marks

Typical models of electrical resistance describe a ‘sea’ of free-flowing electrons moving through a lattice of metal ions, as shown in Figure 1: 

Figure 1

5-2-s-q--q2a-easy-aqa-a-level-physics

(i)
Label an electron and a metal ion on Figure 1
(ii)
Describe what happens between electrons and metal ions when a current flows through a metal wire

2b1 mark

Figure 2 shows a selection of words that are used in the context of electric current: 

Figure 2

 

Attraction

Opposition

Voltage

Repulsion

Battery

Select one of the words in Figure 2 that best completes the following sentence: 

Electrical resistance is an ________________ to the flow of charge in a circuit.

2c3 marks

Resistivity is related to resistance, but unlike resistance, it does not depend on the ‘bulk’ properties of a metal wire, like its length or its cross-sectional area. 

Resistivity of metal wires do, however, depend on external conditions. 

   (i)      State the standard international (SI) units of resistivity 

   (ii)     Describe how external conditions can affect the resistivity of a metal wire

2d4 marks

Other electrical components, like NTC thermistors, also depend on external conditions. 

Figure 3 is a characteristic graph for how NTC thermistors depend on external conditions. 

Figure 3

5-2-s-q--q2d-easy-aqa-a-level-physics

(i)         Describe how an NTC thermistor depends on external conditions 

(ii)        Label the axes on the graph shown in Figure 3

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3a2 marks

Define the term ‘superconductor’.

3b3 marks

Figure 1shows how the resistivity of a superconductor varies with temperature. 

Figure 1

5-2-s-q--q3b-easy-aqa-a-level-physics

Superconductors are unique materials because at certain critical temperatures. T subscript C , their resistivity falls to zero. 

(i)
Label  T subscript C on the temperature axis for the superconductor shown in Figure 1 
(ii)
State the standard international (SI) units for resistivity and for temperature

3c2 marks

State two useful properties of superconductors. 

3d3 marks

Room temperature is typically much higher than critical temperatures of superconducting material. 

Calculate the resistivity of copper wire at room temperature. 

Use the following information: 

  • Length of copper wire = 0.50 km
  • Resistance of 0.50 km of copper wire = 1.6 Ω
  • Cross-sectional area of the copper wire = 4.4 × 10-5 m2 

Give your answer to an appropriate number of significant figures.

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4a3 marks

A cylindrical conductor X has a resistance R, which is related to its resistivity ρ by the equation: 

         R =  ρl over A

where l is its length and A is its cross-sectional area. 

A 1.0 m length of this cylindrical conductor has a resistance of 10 kΩ. Engineers consider various ways to alter the resistance of conductor X. 

State and explain what the resistance of X would become if its length is doubled to 2.0 m.

4b3 marks

Instead of doubling the length of the conductor X, an engineer suggests slicing it exactly in half through its cross-section, such that the new cross-sectional area is half of the original, as shown in Figure 1.

Figure 1

5-2-s-q--q4b-easy-aqa-a-level-physics

State and explain what the resistance of conductor X would become if its cross-sectional area halves, as shown in Figure 2.

4c2 marks

Hence, state and explain which engineering method is most suitable for changing the resistance of a cylindrical conductor.

4d3 marks

Another cylindrical conductor Y is made of the same metal but has a much larger cross-sectional area, three times as great as conductor X. This is shown in Figure 2.

Figure 2

5-2-s-q--q4d-easy-aqa-a-level-physics

State and explain which cylindrical conductor, X or Y, is the better conductor of electric current. 

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5a5 marks

At room temperature a superconducting metal has resistivity of 4.5 × 10–7 Ω m. 

A wire made from this superconducting metal has a radius of 0.70 mm.

(i)
Calculate the cross-sectional area of the wire.
(ii)
Hence, calculate the resistance of a 3.0 m length of the wire at room temperature
5b2 marks

The critical temperature of the superconducting metal described in part (a) is –265.3 ºC. 

State and explain what happens to the resistance of the metal if the temperature reaches absolute zero.

5c2 marks

Give two applications of superconducting metals in industry.

5d3 marks

A thermistor is made of a type of metal called a semiconductor. 

Figure 1 shows a thermistor connected in series with a resistor R and an ammeter. 

Figure 1

5-2-s-q--q5d-easy-aqa-a-level-physics

The ammeter reads the total current flowing through the circuit. 

State and explain how the reading on the ammeter changes if the temperature of the thermistor increases.

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1a2 marks

Shareen is an aspiring electrical engineer who sets out to investigate the resistivity of a metal wire. The material of the wire is unknown.

Figure 1 shows the micrometer screw gauge she uses to measure the diameter of the wire.

Figure 1

5-2-s-q--q1a-hard-aqa-a-level-physics

Determine the resolution of the main scale and the micrometer scale as shown in Figure 1

1b3 marks

Shareen measures the diameter of the wire using the micrometer screw gauge and takes a reading from the main scale and micrometer scale, which is shown in Figure 2.

Figure 2

5-2-s-q--q2a-hard-aqa-a-level-physics

Determine the cross-sectional area of Shareen’s wire.  

1c5 marks

Shareen then uses an ohmmeter to measure the resistance R for different lengths L of the wire. Her measurements are shown in Table 1 below: 

Table 1

Length L / cm

Resistance R / Ω

 

80.0

7.94

 

70.0

6.99

 

60.0

5.89

 

50.0

4.93

 

40.0

4.27

 

 

Determine the resistivity of the wire, including an appropriate unit. 

Use the additional column in Table 1 to show how you arrived at your answer.

1d4 marks

Suggest and explain two improvements to Shareen’s experimental method that would reduce the uncertainty in the final value of resistivity.

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2a3 marks

Thin films of carbon are sometimes used in electronic systems. 

Typical dimensions of such a film are shown in Figure 1: 

Figure 1

WYi3oQ4L_5-2-s-q--q2a-hard-aqa-a-level-physics

Calculate the current which passes through the carbon film in Figure 1 for an applied voltage of 2.5 mV. 

The resistivity of carbon = 4.0 × 10–5 Ω m

2b4 marks

The applied voltage is kept constant, but the current is now directed through the carbon film as shown in Figure 2: 

Figure 2

5-2-s-q--q2b-hard-aqa-a-level-physics

Show that the current is approximately a million times larger if it is directed through the carbon film as shown in Figure 2

2c4 marks

A tensile force is applied to the carbon film as shown in Figure 2, in a plane that is normal to the current. 

Without performing any calculations, discuss how the resistance of the carbon film changes as a result of the applied tensile force.  

State any assumptions you make in your answer.

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3a3 marks

At room temperature a metal has a resistivity of 3.0 × 10–7 Ω m. 

A 2.5 m length of wire made from this metal has a cross-sectional area of 0.50 mm2. 

Calculate the power dissipated in this length of wire when it carries a current of 10 mA.

3b2 marks

Explain the assumption that is necessary for calculating the answer to part (a).

3c3 marks

The wire is cooled from room temperature θr and becomes superconducting. 

Sketch a graph on the axes provided in Figure 1 below to show how the wire’s resistivity would vary with temperature as it is cooled from room temperature θr. 

Include any appropriate labels on your sketch. 

Figure 1

5-2-s-q--q3c-fig-1-hard-aqa-a-level-physics

3d2 marks

Explain why the efficiency of electrical power transmission is improved when conventional copper wires are replaced with metal wires that are superconducting. 

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4a5 marks

Cables used in high-voltage power transmission typically consist of multiple wires. 

A cross-section of such a cable is shown in Figure 1: 

Figure 1

5-2-s-q--q4a-hard-aqa-a-level-physics

This cable consists of seven wires, each of diameter 7.4 mm. The central steel wire has a resistance per metre of 3.3 × 10–3 Ω m–1 and the surrounding aluminium wires each have a resistance per metre of 1.1 × 10–3 Ω m–1. 

By comparing the resistivity of aluminium and steel, show that about 5% of the total current flowing through the cable flows through the central steel wire. 

You should assume that each wire in the cable is connected to the same voltage supply.

4b4 marks

The potential difference across a length of 1.0 km of the cable is 80 V. 

Calculate the total power loss for a 1.0 km length of cable.

4c2 marks

A mechanical engineering student suggests the following: 

“The central steel wire should be replaced with another aluminium wire because aluminium has a lower resistivity. Hence, more current can be transmitted across long distances.” 

Comment on the student’s suggestion by comparing the properties of the steel and aluminium wires.

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1a4 marks

State what is meant by a superconducting material. Explain, therefore, why this material would be useful in improving the efficiency of power stations and hence reduce carbon dioxide emissions.

1b2 marks

With the aid of a sketch graph, explain the term transition temperature.

1c3 marks

Niobium has the highest transition temperature of any superconductor. 

Sketch on the axes in Figure 1 the variation of resistance with temperature for Niobium that becomes superconducting at 9.2 K. 

Figure 1

5-2-s-q--q1c-medium-aqa-a-level-physics

1d3 marks

Explain why superconductors are useful for applications which require strong magnetic fields and name two such applications.

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2a2 marks

A cable consists of seven straight strands of copper wire each of radius 30 µm as shown in Figure 1. 

Figure 1

5-2-s-q--q2a-medium-aqa-a-level-physics

The cable is 1.5 m in length and has a resistance of 1.3 Ω. 

Calculate the resistance of one strand of copper wire.

2b4 marks

Calculate the resistivity of copper and state an appropriate unit in your answer.

2c2 marks

One strand of the wire is now stretched to three times its original length by a process that keeps its volume constant. 

If the resistivity of the copper wire remains constant, show that the resistance increases by 9R.

2d1 mark

State one advantage of using a stranded cable rather than a solid core cable with copper of the same total cross-sectional area.

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3a2 marks

Explain the required conditions for a material to become superconducting.

3b3 marks

Figure 1 shows the cross-sectional area of a cable consisting of parallel filaments that can be made superconducting, embedded in a cylinder of copper.

 Figure 1

5-2-s-q--q3b-medium-aqa-a-level-physics

The diameter of the copper in the cable is 0.48 mm. 

Calculate the resistance of 2.2 m length of the cable. 

            Resistivity of copper = 1.7 × 10–8 Ωm

3c2 marks

Explain, with a calculation, how the resistance would change for a copper wire in the cable with a diameter twice as wide as that in part (b).

3d3 marks

State and explain what happens to the resistance of the cable when the embedded filaments of wire are made to be superconducting.

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4a3 marks

A thermistor is a type of sensory resistor commonly used in thermostats to control the central heating in houses. 

State how the resistance of a negative temperature coefficient (ntc) thermistor changes with temperature and explain why this occurs.

4b4 marks

Figure 1 shows part of a miniature electronic circuit with two small resistors connected in parallel. 

The material from which each resistor is made has a resistivity of 2.6 × 105 Ω m and both resistors have dimensions of 15 mm by 2.3 mm by 1.3 mm. 

Figure 1

5-2-s-q--q4b-medium-aqa-a-level-physics

Calculate the total resistance of the electronic circuit in MΩ.

4c2 marks

The designer increases the size of the circuit including the base by making every dimension larger by a factor of 10. The potential difference across the resistors is unchanged. 

Show this increase in dimensions results in the resistance of each resistor decreasing by a factor of 10.

4d1 mark

The resistors are replaced with wires with a circular cross-sectional area with diameter d and a resistance per unit length r. 

Sketch a graph of how the resistance per unit length r varies with diameter d of one of the wires.

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5a4 marks

An electrical heating element, made from uniform nichrome wire, is required to dissipate 600 W when connected to the 230 V mains supply. 

The radius of the wire is 0.16 mm. 

Calculate the length of nichrome wire required. 

            Resistivity of nichrome = 1.1 × 10–6 Ω m

5b2 marks

Suggest two properties that the nichrome wire must have to make it suitable as an electrical heating element.

5c3 marks

Explain why the resistivity of the nichrome wire changes with temperature.

5d3 marks

An engineer wants to use the same uniform nichrome wire to use in another identical electrical heating element which is also required to dissipate 600 W when connected to the 230 V mains supply. 

The only nichrome wire they have available has a radius of 0.08 mm. 

Calculate the length needed for this new nichrome wire to produce the same current through the heating element.

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