5.3 electricity - resistivity 2 - qs · 5/5/2019 · 5.3 electricity - resistivity 2 – questions...

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5.3 Electricity - Resistivity 2 – Questions

Q1. The change in resistance with temperature of a thermistor is used in thermostats to control the central heating in houses. Explain why the resistance of a negative temperature coefficient (ntc) thermistor decreases as the temperature rises.

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Q2. (a) Some materials exhibit the property of superconductivity under certain conditions.

• State what is meant by superconductivity.

• Explain the required conditions for the material to become superconducting.

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(b) The diagram below shows the cross–section of a cable consisting of parallel filaments that can be made superconducting, embedded in a cylinder of copper.

(i) The cross–sectional area of the copper in the cable is 2.28 × 10–7 m2. The resistance of the copper in a 1.0 m length of the cable is 0.075 Ω. Calculate the resistivity of the copper, stating an appropriate unit.

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answer = ____________________ (3)

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

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(Total 9 marks)

Q3. When transmitting electricity, energy is lost owing to the resistance of the cables.

Calculate the resistance of 200 km of copper cable with cross-sectional area 1.5 × 10−5 m2.

resistivity of copper = 1.7 × 10−8 Ω m

resistance ____________________ (Total 3 marks)

Q4. A manufacturer asks you to design the heating element in a car rear-window de-mister. The design brief calls for an output of 48 W at a potential difference of 12 V. The diagram below shows where the eight elements will be on the car window before electrical connections are made to them.

(a) Calculate the current supplied by the power supply.

Current = ____________________ (1)

(b) One design possibility is for the eight elements to be connected in parallel.

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(i) Calculate the current in each element in this parallel arrangement.

Current = ____________________ (1)

(ii) Calculate the resistance required for each element.

Resistance = ____________________ (2)

(c) Another design possibility is to have the eight elements connected in series.

(i) Calculate the current in each element in this series arrangement.

Current = ____________________ (1)

(ii) Calculate the resistance required for each element.

Resistance = ____________________ (2)

(d) State one disadvantage of the series design compared to the parallel arrangement.

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(e) The series design is adopted. Each element is to have a rectangular cross-section of 0.12 mm by 3.0 mm. The length of each element is to be 0.75 m.

(i) State the units of resistivity.

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(ii) Calculate the resistivity of the material from which the element must be made.

Resistivity = ____________________ (2)

(Total 11 marks)

Q5. The diagram below shows a graph of potential difference against current for a thermistor.

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(a) Sketch an experimental arrangement that you could use to collect the data for this graph.

(3)

(b) The thermistor is connected in parallel with a 2.0 kΩ resistor. The current in the resistor is 6.0 mA.

(i) Calculate the potential difference across the thermistor.

Potential difference = ____________________ (2)

(ii) Use the graph to calculate the power dissipated in the thermistor.

Power dissipated in thermistor = ____________________ (3)

(c) Describe and explain what happens to the resistance of the thermistor as its temperature increases.

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(Total 10 marks)

Q6. Sketch on the axes below the variation of resistance with temperature for a metal that becomes superconducting at –120 °C.

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(Total 2 marks)

Q7. The diagram below 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 1.3 × 105 Ω m and both resistors have dimensions of 12 mm by 2.5 mm by 1.5mm.

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(a) (i) Show that the resistance of one of these resistors is about 400 MΩ.

(3)

(ii) The potential difference across the resistors is 5.0 V.

Calculate the power dissipated in one resistor.

(2)

(iii) The heat energy from the resistors is lost through a base of size 7.5 mm by 12 mm.

Calculate the total heat energy lost through this base every second.

Total heat energy lost per second ____________________ (1)

(iv) Calculate the total rate at which heat energy is dissipated per unit area of the base.

Total heat energy lost per unit area every second ____________________ (2)

(b) The designer reduces the size of the circuit including the base by making every dimension smaller by a factor of 10. The potential difference across the resistors is unchanged.

(i) Show that this reduction in dimensions results in the resistance of each resistor increasing by a factor of 10.

(2)

(ii) Explain why this change results in an increase in the temperature of the

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components in the circuit.

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(Total 12 marks)

Q8. The heating circuit of a hairdryer is shown in the diagram below. It consists of two heating elements, R1 and R2, connected in parallel. Each element is controlled by its own switch.

The elements are made from the same resistance wire. This wire has a resistivity of 1.1 × 10–6 Ω m at its working temperature. The cross-sectional area of the wire is 1.7 × 10–8 m2 and the length of the wire used to make R1 is 3.0 m.

(a) Show that the resistance of R1 is about 190 Ω. (3)

(b) Calculate the power output from the heating circuit with only R1 switched on when it is connected to a 240 V supply.

Power output ____________________ (2)

(c) With both elements switched on, the total power output is three times that of R1 on its own.

(i) Calculate the length of wire used to make the coil R2.

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Length ____________________ (3)

(ii) Calculate the total current with both elements switched on.

Total current ____________________ (2)

(Total 10 marks)

Q9. (a) Define the term electromotive force (emf).

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(b) Figure 1 shows very high resistance voltmeter placed across an 8.00 Ω resistor connected to a cell of emf 1.56 V.

Figure 1

The very high resistance voltmeter registers 1.40 V. Show that the internal resistance of the cell must be about 0.9 Ω.

(3)

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(c) A voltmeter, having resistance 24.0 Ω, replaces the very high resistance voltmeter.

(i) Calculate the combined resistance of this voltmeter and the 8.00 Ω resistor connected in parallel.

Combined resistance = ____________________ Ω (2)

(ii) Calculate the reading on this voltmeter.

Reading on voltmeter = ____________________ V (3)

(iii) Explain why the reading on this voltmeter is different from the reading on the very high resistance voltmeter in part (b).

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______________________________________________________________ (1)

(d) Each lead connecting the resistor to the cell is made from a single strand of copper wire. Each lead is 0.30 m long and has a diameter of 2.0 mm. Show that the total potential difference across the two leads is negligible when the cell delivers a current of 0.20 A. resistivity of copper, ρ = 1.7 × 10–8 Ω m.

(4)

(Total 15 marks)

Q10. (a) Calculate the length of copper wire that has a diameter of 1.6 × 10–3 m and a

resistance of 25 Ω.

resistivity of copper = 1.7 × 10–8 Ω m

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Length of wire ____________________ (3)

(b) The resistance of copper wire is not zero. Explain why this fact leads to the use of alternating current rather than direct current when transmitting electrical energy.

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(Total 6 marks)

Q11. In a test to find a suitable metal wire to use for a fuse, the following graph of current, I, against time, t, was obtained. The circuit, which was connected to a constant source of emf, was switched on at t = 0 s.

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(a) Calculate the total charge that flowed during this test.

Total charge ____________________ (2)

(b) Explain why the current decreased during the test before the fuse melted.

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(Total 4 marks)

Q12. Scientists have suggested that carbon dioxide emissions produced by power stations in the European Union could be reduced considerably if high temperature superconductors were used instead of ordinary conductors to improve the efficiency of power plants.

(a) Explain what is meant by a superconductor.

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(b) Explain why the use of superconductors would improve the efficiency of power stations and hence reduce carbon dioxide emissions.

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(Total 4 marks)

Q13. A resistance wire has a diameter 2.0 ×10–4 m and a resistivity of 4.5 × 10–7 Ω m.

(a) Calculate the length of this wire that has a resistance of 25 Ω.

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length of wire ____________________ (3)

(b) The resistivity of the wire increases as the current increases. Sketch, on the axes below, the variation of current, I, with potential difference, V, across the wire for both positive and negative potential differences.

(2)

(Total 5 marks)

Q14. A strain gauge is made from a constantan wire of original length 25 mm. If the wire stretches its resistance changes. The gauge is attached to an object that is then placed under tension, which causes the length of the constantan wire to increase. The resistance, R, was measured for various lengths, l, and the following results were obtained:

R / Ω 99.96 100.64 101.76 102.80 103.85 104.71

l / 10–2 m 2.500 2.508 2.523 2.536 2.548 2.557

When the wire is stretched, it may be assumed that for small extensions:

R ∝ l2

(a) Complete the table showing the value of l2 for each value of R. (2)

(b) Plot a graph of R on the y-axis against l2 on the x-axis. (4)

(c) Use your graph and the value for the resistivity of constantan given below to find the diameter of the wire when its resistance is 103.40 Ω.

resistivity of constantan = 4.7 × 10–7 Ωm

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(d) Define tensile strain. Use your graph to determine the strain when the resistance of the wire is 103.40 Ω.

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(Total 13 marks)

Q15. (a) (i) What is a superconductor?

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

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(b) Explain why superconductors are very useful for applications which require very large electric currents and name two such applications.

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(Total 6 marks)

Q16. A particular heating element consists of a 3.0 m length of a metal alloy wire of diameter 1.2 mm and resistivity 9.3 × 10–6 Ωm at the element’s operating temperature. The element is designed for use with a 230 V supply. Calculate the rating, in W, of the heating element when in use.

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Q17. (a) For a conductor in the form of a wire of uniform cross-sectional area, give an

equation which relates its resistance to the resistivity of the material of the conductor. Define the symbols used in the equation.

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(b) (i) An electrical heating element, made from uniform nichrome wire, is required to dissipate 500 W when connected to the 230 V mains supply. The cross-sectional area of the wire is 8.0 × 10–8 m2. Calculate the length of nichrome wire required.

resistivity of nichrome = 1.1 × 10–6 Ω m

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(ii) Two heating elements, each rated at 230 V, 500 W are connected to the 230 mains supply

(A) in series, (B) in parallel.

Explain why only one of the circuits will provide an output of 1 kW.

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(Total 8 marks)

Q18. (a) Show that the unit of resistivity is Ω m.

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(b) A cable consists of seven straight strands of copper wire each of diameter 1.35 mm as shown in the diagram.

Calculate

(i) the cross-sectional area of one strand of copper wire,

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(ii) the resistance of a 100 m length of the cable, given that the resistivity of copper is 1.6 × 10–8 Ωm.

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(c) (i) If the cable in part (b) carries a current of 20 A, what is the potential difference between the ends of the cable?

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(ii) If a single strand of the copper wire in part (b) carried a current of 20 A, what would be the potential difference between its ends?

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

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(Total 8 marks)

Q19. (a) The resistivity of a material in the form of a uniform resistance wire is to be

measured. The area of cross-section of the wire is known.

The apparatus available includes a battery, a switch, a variable resistor, an ammeter and a voltmeter.

(i) Draw a circuit diagram using some or all of this apparatus, which would enable you to determine the resistivity of the material.

(ii) Describe how you would make the necessary measurements, ensuring that you have a range of values.

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(iii) Show how a value of the resistivity is determined from your measurements.

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(b) A sheet of carbon-reinforced plastic measuring 80 mm × 80 mm × 1.5 mm has its two large surfaces coated with highly conducting metal film. When a potential difference of 240 V is applied between the metal films, there is a current of 2.0 mA in the plastic. Calculate the resistivity of the plastic.

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(c) If four of the units described in part (b) are connected as shown in the diagram, calculate the total resistance of the combination.

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(Total 14 marks)

Q20. (a) (i) Give the equation which relates the electrical resistivity of a conducting

material to its resistance. Define the symbols in the equation.

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(ii) A potential difference of 1.5 V exists across the ends of a copper wire of length 2.0 m and uniform radius 0.40 mm. Calculate the current in the wire.

resistivity of copper = 1.7 × 10–8 Ω m

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(b) In the circuit shown, each resistor has the same resistance. The battery has an e.m.f. of 12 V and negligible internal resistance.

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(i) Calculate the potential difference between A and B.

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(ii) Calculate the potential difference between B and C.

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(iii) A high resistance voltmeter is connected between A and C. What is the reading on the voltmeter?

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(Total 10 marks)

Q21. A heating element, as used on the rear window of a car, consists of three strips of a resistive material, joined, as shown in the diagram, by strips of copper of negligible resistance. The voltage applied to the unit is 12 V and heat is generated at a rate of 40 W.

(a) (i) Calculate the total resistance of the element.

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(ii) Hence show that the resistance of a single strip is about 11 Ω.

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(b) If each strip is 2.6 mm wide and 1.1 mm thick, determine the length of each strip.

resistivity of the resistive material = 4.0 × 10–5 Ω m

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(Total 8 marks)

Q22. The wire in an electric heater has a resistance of 75 Ω. It is 9.5 m long and has a cross-sectional area of 1.4 × 10–7 m2. Calculate the resistivity of the material from which the wire is made. Give an appropriate unit for your answer.

resistivity ____________________ (Total 3 marks)

Q23. (a) A metal wire of length 1.4 m has a uniform cross-sectional area = 7.8 × 10–7 m2.

Calculate the resistance, R, of the wire. resistivity of the metal = 1.7 × 10–8 Ωm

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(b) The wire is now stretched to twice its original length by a process that keeps its volume constant. If the resistivity of the metal of the wire remains constant, show that the resistance increases to 4R.

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(Total 4 marks)

Q24. In an experiment to determine the resistivity of a wire, a student made the following measurements:

potential difference across the wire

current in the wire diameter of the wire

length of the wire

= 2.5 V = 0.29 A = 2.4 × 10–4 m = 0.75 m

(a) Calculate the resistivity of the material from which the wire is made. (3)

(b) Calculate the power dissipated per metre of the wire. (2)

(Total 5 marks)

Q25. (a) An electric shower heats water from 15°C to 47°C when water flows through it at a

rate of 0.045 kg s–1.

(i) Calculate the energy supplied to the water each second by the heating element in the shower.

specific heat capacity of water = 4200 J kg–1 K–1

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(ii) Show that the power of the heating element is 6.0 kW. Assume there is no heat loss to the surroundings.

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(b) (i) The heating element in part (a) is connected to an alternating supply at 230 V rms. Calculate the rms current passing through the heating element in normal operation.

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(ii) The live wire and the neutral wire in the connecting cable are insulated copper wires of diameter 2.4 mm. Calculate the resistance per metre length of copper wire of this diameter.

resistivity of copper = 1.7 × 10−8 Ωm

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(iii) Show that in normal operation, the potential drop per metre along the cable is 0.20 V m–1.

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(iv) Electrical safety regulations require the potential drop along the cable to be less than 6.0 V. Calculate the maximum safe distance along the cable from the distribution board to the heating element.

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(Total 12 marks)

Q26. (a) Figure 1 and Figure 2 show two circuits in which a supply of e.m.f. 6.0 V and

internal resistance 5.0 Ω is delivering power to a pair of resistors.

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Figure 1 Figure 2

When maximum power is dissipated in an external circuit, the resistance of the external circuit is equal to the internal resistance of the supply.

(i) For the circuit in Figure 1, determine the value of R which results in the maximum power being delivered to the external circuit.

(3)

(ii) Calculate the terminal potential difference when the supply is delivering maximum power to the circuit in Figure 1.

(1)

(iii) Calculate the power that will be dissipated by the 15 Ω resistor when the supply is delivering maximum power to the external circuit.

(2)

(iv) For the circuit in Figure 2, explain why the supply cannot deliver maximum power in this circuit for any value of the resistor R.

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(b) (i) The 15 Ω resistor is made from wire of length 2.3 m. The wire has a diameter of 3.0 × 10–4 m. Calculate the resistivity of the material from which the wire is made.

(3)

(ii) Sketch below a graph showing how the resistance of 2.3 m of wire made from this material varies with the diameter of the wire. The value for a wire of diameter 3.0 × 10–4 m has been plotted for you.

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(2)

(Total 13 marks)

Q27. (a) A 3.0 kW electric kettle heats 2.4 kg of water from 16°C to 100°C in 320 seconds.

(i) Calculate the electrical energy supplied to the kettle.

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(ii) Calculate the heat energy supplied to the water. specific heat capacity of water = 4200 J kg–1 K–1

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(iii) Give one reason why not all the electrical energy supplied to the kettle is transferred to the water.

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(b) The potential difference supplied to the kettle in part (a) is 230 V.

(i) Calculate the resistance of the heating element of the kettle.

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(ii) The heating element consists of an insulated conductor of length 0.25 m and diameter 0.65 mm. Calculate the resistivity of the conductor.

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(Total 9 marks)

Q28. (a) A student wishes to measure the resistivity of the material of a uniform resistance

wire. The available apparatus includes a battery, a switch, a variable resistor, an ammeter and a voltmeter.

(i) Draw a circuit diagram which incorporates some or all of this apparatus and which enables the student to determine the resistivity of the material.

(ii) State the measurements which must be made to ensure that a reliable value of the resistivity is obtained.

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(iii) Explain how a value of the resistivity would be obtained from the measurements.

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(b) A wire made from tin with cross-sectional area 7.8 × 10–9 m2, has a pd of 2.0 V across it. Calculate the minimum length of wire needed so that the current through it does not exceed 4.0 A.

resistivity of tin = 1.1 × 10–7 Ω m

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(Total 12 marks)

Q29. Two resistors R1 and R2 are made of wires of the same material. The wire used for R1 has half the diameter and is twice as long as the wire used for R2.

What is the value of the ratio ?

A 8

B 4

C 1

D 0.5 (Total 1 mark)

Q30. The diagram shows two wires, P and Q, of equal length, joined in series with a cell. A voltmeter is connected between the end of Q and a point X on the wires. The p.d. across the cell is V. Wire Q has twice the area of cross-section and twice the resistivity of wire P. The variation of the voltmeter reading as the point X is moved along the wires is best shown by

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(Total 1 mark)

Q31. A 1.5 m length of wire has a cross-sectional area 5.0 × 10–8 m 2. When the potential difference across its ends is 0.20 V, it carries a current of 0.40 A. The resistivity of the material from which the wire is made is

A 6.0 × 107 Ω m

B 1.7 × 10–8 Ω m

C 1.1 × 106 Ω m

D 9.4 × 10–7 Ω m

(Total 1 mark)

Q32. Copper metal is a good conductor of electricity because copper atoms in copper metal

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A have gained an extra or “free” electron

B are ionised so that both ions and “free” electrons can move

C have a negative charge because of the “free” electrons

D have lost an electron to form positive ions and “free” electrons

(Total 1 mark)

Q33. The resistance of a metallic conductor increases with temperature because, at higher temperatures,

A more electrons become available for conduction

B the conductor becomes a superconductor

C the amplitude of vibration of lattice ions increases

D the length and cross-sectional area of the conductor both increase

(Total 1 mark)s

5.3 electricity - resistivity 2 - qs · 5/5/2019 · 5.3 electricity - resistivity 2 – questions...

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