CIE AS Physics

Topic Questions

Syllabus Edition

First teaching 2020

Last exams 2024

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9.3 Resistivity

11 mark

The unit of resistivity, expressed in terms of base units, is given by                                            

             k g space x cubed space y to the power of negative 2 space end exponent z to the power of negative 3 end exponent         

Which base units are x, y and z ?

 

x

y

z

A

B

C

D

ampere

metre

metre

second

metre

ampere

second

ampere

second

second

ampere

metre

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21 mark

A cylindrical wire of length 10 m and diameter 2.0 mm has a resistance of 0.050 Ω.

 From which material is the wire made?

 

Material

Resistivity / Ω m

A

bronze

1.6 × 10–7

B

nichrome

1.6 ×10–6

C

silver

1.6 × 10–8

D

zinc

6.3 × 10–8

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31 mark

The resistance of one device R1 is designed to change with temperature; the resistance of another device R2 is designed to change with illumination.

 What are the names of these devices ?

 

R1

R2

A

thermistor 

light-dependent resistor

B

thermistor

potential divider

C

semiconductor diode 

light-dependent resistor

D

semiconductor diode 

potential divider

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41 mark

A light-dependent resistor (LDR) is connected in series with a resistor R and a battery.

cie-ial-images498png

The resistance of the LDR is equal to the resistance of R when no light falls on the LDR. When the light intensity falling on the LDR increases, which statement is correct?

  • the current in R decreases

  • the current through the LDR decreases

  • the p. d. across R decreases

  • the p .d. across the LDR decreases

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51 mark

A copper wire is stretched so that its diameter is reduced from 1.0 mm to a uniform 0.5 mm. The resistance of the unstretched copper wire is 0.2 Ω.

 What is the resistance of the stretched wire?

  • 0.4 Ω

  • 0.8 Ω

  • 1.6 Ω

  • 3.2 Ω

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61 mark

Which graph best represents the way in which the current I through a thermistor depends upon the potential difference V across it ?

cie-ial-physics-images-9-3-e-q6

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71 mark

A power cable has length 2000 m. The cable is made of twelve parallel strands of copper wire, each with diameter 0.51 mm.

 What is the resistance of the cable ? (resistivity of copper = 1.7 × 10–8 Ω m)

  • 0.014 Ω

  • 3.5 Ω

  • 14 Ω

  • 166 Ω

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81 mark

A circuit is set up with an LDR and a fixed resistor as shown.

 cie-ial-images504png

The voltmeter reads 4 V.

The light intensity is increased.

 What is a possible voltmeter reading?

  • 3V

  • 4V

  • 6V

  • 8V

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91 mark

A cylindrical wire 4.0 m long has a resistance of 31 Ω and is made of metal of resistivity 1.0 × 10–6 Ω m.

 What is the radius of cross-section of the wire?

  • 1.0 × 10–8 m

  • 2.0 × 10–8 m

  • 6.4 × 10–8 m

  • 2.0 × 10–4 m

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101 mark

When a thin metal wire is stretched, it becomes longer and thinner. This causes a change in the resistance of the wire. The volume of the wire remains constant.

 Which graph could represent the variation with extension x of the resistance R of the wire ?

cie-ial-physics-images-9-3-e-q10

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11 mark

A thermistor and another component are connected to a constant voltage supply. A voltmeter is connected across one of the components. The temperature of the thermistor is then reduced, but no other changes are made.

 In which circuit will the voltmeter reading increase ?

cie-ial-physics-images-9-3-h-q1

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21 mark

A copper wire is to be replaced by an aluminum alloy wire of the same length and resistance.

 Copper has half the resistivity of the alloy.

 What is the ratio  fraction numerator d i a m e t e r space o f space a l l o y space w i r e over denominator d i a m e t e r space o f space c o p p e r space w i r e end fraction  ?

  • square root of 2

  • 2

  • square root of 2

  • 4

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31 mark

The current in a block of semiconductor is 30.0 mA when there is a potential difference (p.d.) of 10.0 V across it. The dimensions of the block and the direction of the current in it are as shown.

cie-ial-images526png

The electrical meters used are accurate to ± 0.1 mA and ± 0.1 V. The dimensions of the block are accurate to ± 0.2 mm.

 What is the resistivity of the semiconductor?

  • 10.0 ± 0.2 Ω m

  • 10.0 ± 0.3 Ω m

  • 10.0 ± 0.5 Ω m

  • 10.0 ± 0.8 Ω m

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41 mark

The resistance of a metal cube is measured by placing it between two parallel plates, as shown.


cie-ial-images527png

The cube has volume V and is made of a material with resistivity ρ. The connections to the cube have negligible resistance.

Which expression gives the electrical resistance of the metal cube between X and Y? 

  • rho V to the power of 1 third end exponent

  • rho V to the power of 2 over 3 end exponent

  • rho over V to the power of 1 third end exponent

  • rho over V to the power of 2 over 3 end exponent

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51 mark

A wire PQ is made of three different materials, with resistivities ρ, 2ρ and 3ρ. There is a current I in this composite wire, as shown.

cie-ial-images528png

Which graph best shows how the potential V along the wire varies with distance x from P ?

cie-ial-images529png

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61 mark

A strain gauge consists of a length of wire with a uniform cross-sectional area. Its resistance is 2.50 kΩ. It is attached to a large pipe.

 When the pipe expands, the strain gauge changes in dimensions, such that the length increases by 4% and the diameter reduced by 1%.

 What is the new resistance of the strain gauge?

  • 2.60 kΩ

  • 2.65 kΩ

  • 2.80 kΩ

  • 3.00 kΩ

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71 mark

The variation with temperature of the resistance RT of a thermistor is shown on the graph.

cie-ial-images530png

The thermistor is connected into the circuit shown below.

The battery has an e. m .f. of 9.0 V and negligible internal resistance. The voltmeter has infinite resistance.

cie-ial-images531png

 What is the temperature of the thermistor when the reading on the voltmeter is 4.0 V?

  • 2.5 °C

  • 13.0 °C

  • 16.0 °C

  • 24.0 °C

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81 mark

A conducting liquid fills a cylinder metal case to a depth y as shown in the diagram.

cie-ial-images533png

The resistance between the case and the metal rod is

  • proportional to y

  • proportional to y2

  • inversely proportional to y

  • inversely proportional to y2

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91 mark

The following strain gauge consists of a fine metal wire, so that an applied tension on the strain gauge results in changes in the length and cross-sectional area of the wire.

cie-ial-images535png

When the length of the wire is stretched by 5%, what is the percentage change in the resistance of the wire? Assume that the volume of a wire remains constant when it is stretched.

  • + 5%

  • – 5%

  • + 10%

  • – 10%

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101 mark

Aluminum and copper rods are designed to have the same length and the same resistance.

 The resistivity of copper is half that of aluminum, but its density is three times that of aluminum.

 Determine the ratio of the mass of the aluminum rod to the mass of the copper rod.

  • 1 over 6

  • 2 over 3

  • 3 over 2

  • 6 over 1

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11 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.

cie-ial-images509png

What is the ratio  fraction numerator c u r r e n t space i n space P over denominator c u r r e n t space i n space Q end fraction ?

  • 2 over 3

  • 2 over 9

  • 1 over 6

  • 1 over 18

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21 mark

In the circuit below, the reading VT on the voltmeter changes from high to low as the temperature of the thermistor changes. The reading VL on the voltmeter changes from high to low as the level of light on the light-dependent resistor (LDR) changes.

cie-ial-images510png

The readings VT and VL are both high.

 What are the conditions of temperature and light level ?

 

Temperature

Light level

A

B

C

D

low

low

high

high

low

high

low

high

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31 mark

In a fire alarm system, a thermistor T has a resistance of 2000 Ω at room temperature. Its resistance decreases as the temperature increases. The alarm is triggered when the potential difference between X and Y reaches 4.5 V.

cie-ial-images511png

What is the resistance of the thermistor when the alarm is triggered ?

  • 90 Ω

  • 150 Ω

  • 250 Ω

  • 1300 Ω

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41 mark

Two electrically-conducting cylinders X and Y are made from the same material.

Their dimensions are as shown.

cie-ial-images512png

The resistance between the ends of each cylinder is measured.

 What is the ratio fraction numerator r e s i s tan c e space o f space X over denominator r e s i s tan c e space o f space Y end fraction ?

  • 2 over 1

  • 1 over 1

  • 1 half

  • 1 fourth

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51 mark

The graph shows the variation with length l of resistance R for two wires X and Y made from the same material.

cie-ial-images513png

What does the graph show?

  • cross-sectional area of X = 2 × cross - sectional area of Y

  • resistivity of X = 2 × resistivity of Y

  • when equal lengths of X and Y are connected in series to a battery, power in X = 2 × power in Y

  • when equal lengths of X and Y are connected in parallel to a battery, current in X = 2 × current in Y

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61 mark

A light-dependent resistor R has a resistance of about 1 MΩ in the dark and about 1 kΩ when illuminated. It is connected in series with a 5 kΩ resistor to a 1.5 V cell of negligible internal resistance.

cie-ial-images514png

The light-dependent resistor is illuminated (in an otherwise dark room) by a flashing light.

 Which graph best shows the variation with time t of potential difference V across R ?

cie-ial-physics-images-9-3-m-q6

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71 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.

cie-ial-images519png

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 increases and the cross-sectional area decreases

  • 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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81 mark

The resistance of a thermistor depends on its temperature, and the resistance of a light-dependent resistor (LDR) depends on the illumination.

 Under which conditions will the resistance of both a thermistor and an LDR be highest ?

 

Thermistor

LDR

A

B

C

D

highest temperature

highest temperature

lowest temperature

lowest temperature

highest illumination

lowest illumination

highest illumination

lowest illumination

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91 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.

cie-ial-images520png

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.

cie-ial-images521png

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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101 mark

Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10–8 Ωm, and wire Y is made of a metal of resistivity 5.6 × 10–8 Ωm.

 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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