1. In the circuit shown, the battery has negligible internal resistance.

Transcription

1 1. In the circuit shown, the battery has negligible internal resistance. A 2. (a) Using the axes below, sketch the characteristic of a silicon semiconductor diode for forward bias and reverse bias. 30 Ω Indicate approximate values on the voltage axis. 6.0 V X I 60 Ω Y Calculate the current in the ammeter when 0 V (a) the terminals X and Y are short-circuited i.e. connected together, Describe, with reference to the characteristic you have drawn, how the resistance of the diode changes with the voltage across the diode. the terminals X and Y are connected to a 30 Ω resistor (Total 6 marks) (Total 7 marks) 3. (a) A cell of emf and internal resistance r is connected in series to a resistor of resistance R as shown. A current I flows in the circuit. r I R V R St Ivo School 1 St Ivo School 2

2 State an expression which gives in terms of I, r and R. Hence show how V R, the potential difference across the resistor, is related to, I and r. 4. 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 V 0 V copper A lamp, rated at 30 W, is connected to a 120 V supply. resistive material Calculate the current in the lamp. (a) Calculate the total resistance of the element. If the resistor in part (a) is replaced by the lamp described in part, determine how many cells, each of emf 1.5 V and internal resistance 1.2 Ω, would have to be connected in series so that the lamp would operate at its proper power. Hence show that the resistance of a single strip is about 11 Ω. (5) (5) (Total 7 marks) If each strip is 2.6 mm wide and 1.1 mm thick, determine the length of each strip. resistivity of the resistive material = Ω m (Total 8 marks) St Ivo School 3 St Ivo School 4

3 5. A sinusoidal alternating current (ac) source of frequency 50 Hz, is connected to a resistor of resistance 2.0 kω and an oscilloscope, as shown. The rms current through the resistor is 5.0 ma. Draw, on the grid, the signal you would expect to see on the oscilloscope. (Total 6 marks) 6. In the circuit shown, the battery has negligible internal resistance. 50Hz R 2.0 kω oscilloscope I R V (a) Calculate the peak value of the voltage across R.... R 2 V... (a) If the emf of the battery = 9.0 V, R l = 120 Ω and R 2 = 60 Ω, calculate the current I flowing in the circuit. The grid represents the screen of the oscilloscope, each square being 1 cm 1 cm. The time base of the oscilloscope is set at 5 ms cm 1 and the voltage sensitivity is 4.0 V cm 1. Calculate the voltage reading on the voltmeter. Calculate the period of the ac signal. St Ivo School 5 St Ivo School 6

4 The circuit shown in the diagram acts as a potential divider. The circuit is now modified by replacing R 1 with a temperature sensor, whose resistance decreases as the temperature increases. Explain whether the reading on the voltmeter increases or decreases as the temperature increases from a low value (Total 7 marks) 7. (a) The characteristic shown below is that of a filament lamp. I 0 V Explain why, as the voltage is increased either positively or negatively from zero, the characteristic has the form shown in the figure (5) At a certain point on the characteristic, the power developed in the lamp is 20 W and the current is 90 ma. Calculate the resistance of the filament at this point on the characteristic (Total 7 marks) St Ivo School 7 St Ivo School 8

5 8. (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. Draw a circuit diagram using some or all of this apparatus, which would enable you to determine the resistivity of the material. (iii) Show how a value of the resistivity is determined from your measurements. Describe how you would make the necessary measurements, ensuring that you have a range of values. (9) 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 240V is applied between the metal films, there is a current of 2.0 ma in the plastic. Calculate the resistivity of the plastic St Ivo School 9 St Ivo School 10

6 (c) If four of the units described in part are connected as shown in the diagram, calculate the total resistance of the combination. The signal displayed on the oscilloscope screen is shown below. initial pulse reflected pulse (Total 14 marks) If the time base of the oscilloscope is set to 2.0 ms per division, estimate the speed of sound in air (a) The diagram shows the apparatus required for a simple experiment to measure the speed of sound. glass tube M 1.5 m A pulse of sound is sent down a hollow glass tube and is reflected at the sealed end of the tube. A microphone, M, placed at the open end detects the initial pulse and, at a later time, the reflected pulse. The microphone is connected to an oscilloscope which gives a signal when the microphone detects a pulse of sound. St Ivo School 11 St Ivo School 12

7 Describe how the frequency of a sinusoidal alternating (ac) voltage source is measured using an oscilloscope. 10. A battery of emf 24 V and negligible intemal resistance is connected to a resistor network as shown in the circuit diagram in the diagram below. Your answer should include a sketch of the trace seen on the oscilloscope screen and explain how the frequency is obtained from this trace. A 30 Ω 40 Ω B 60 Ω 120 Ω R 1 24 V (a) Show that the resistance of the single equivalent resistor that could replace the four resistors between the points A and B is 50 Ω (5) (Total 8 marks) If R 1 is 50 Ω, calculate the current in R 1, St Ivo School 13 St Ivo School 14

8 the current in the 60 Ω resistor. (Total 8 marks) (iii) What property of the voltmeter allows us to assume that no current flows through it? What is the reading on the voltmeter? 11. (a) In the circuit shown in Figure 1, the battery has an emf of 12 V and negligible internal resistance. PQ is a potential divider, S being the position of the sliding contact. In the position shown, the resistance between P and S is 180 Ω and the resistance between S and Q is 60 Ω. I P The circuit in Figure 1 is modified as shown in Figure 2, by exchanging the voltmeter for a load R, whose resistance is about the same as the resistance of section SQ of the potential divider. I P 12 V S 12 V S Q V Q R Figure 1 Figure 2 Calculate the current, I, in the circuit, assuming that there is no current through the voltmeter V. St Ivo School 15 St Ivo School 16

9 Explain, without calculation, why the current through the battery increases in value from that in part (a). You may be awarded marks for the quality of written communication in your answer The time base of the oscilloscope is switched off throughout the experiment. Initially the switches S 1 and S 2 are both open. Under these conditions the spot on the oscilloscope screen is at A. Switch S 1 is now closed, with S 2 remaining open. The spot moves to B. State what the deflection AB represents (Total 6 marks) 12. (a) The circuit shown in Figure 1 may be used to determine the internal resistance of a battery. An oscilloscope is connected across the battery as shown. Figure 2 represents the screen of the oscilloscope. (iii) Switch S 1 is kept closed and S 2 is also closed. The spot moves to C. State what the deflection AC represents. The vertical sensitivity of the oscilloscope is 0.50 V div 1. Calculate the current through the 14 Ω resistor with both switches closed. oscilloscope B C (iv) Hence, calculate the internal resistance of the battery. S 1 A S 2 battery (6) 14 Ω The oscilloscope is now connected to an alternating voltage source of rms value 3.5 V. Figure 1 Figure 2 Calculate the peak value of the alternating voltage. St Ivo School 17 St Ivo School 18

10 Draw on Figure 3 what you would expect to see on the oscilloscope screen, if the time base is still switched off and the voltage sensitivity is altered to 2.0 V div 1. 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 (Total 4 marks) Figure 3 (Total 9 marks) 14. (a) On the axes in Figure 1 draw I V characteristics for two components, A and B, both of which obey Ohm s law. Component B has a lower resistance than component A. Label your characteristics clearly as A and B. I 13. (a) A metal wire of length 1.4 m has a uniform cross-sectional area = m 2. Calculate the resistance, R, of the wire. resistivity of the metal = Ωm V... Figure 1 St Ivo School 19 St Ivo School 20

11 On the axes in Figure 2 draw the I V characteristic for a silicon semiconductor diode, giving any relevant voltage values. (c) Figure 3 shows the I V characteristic of a filament lamp. Explain the shape of this characteristic. I I 0 V 0 V Figure 2 Figure (Total 9 marks) St Ivo School 21 St Ivo School 22

12 15. Columns A and B show some of the results from an experiment in which the current I through a component X was measured for various values of the potential difference V applied across it. column A column B column C column D potential difference V / V current I/ ma (V 0.55) / V In (I / ma) (c) By considering one other value of potential difference, explain whether or not X is an ohmic conductor. It is suggested that for potential differences greater than 0.55 V, the current voltage relationship for X is of the form. I = A e k(v 0.55) (a) Draw a diagram of a circuit which could have been used to obtain these results. where A and k are constants. Complete column C and column D in the abive Plot a graph of 1n (I /ma ) on the y-axis against (V 0.55) on the x-axis. (Allow one sheet of graph paper) (iii) Use your graph to determine the constants k and A. Calculate the resistance of X when the potential difference is 0.70 V. St Ivo School 23 St Ivo School 24

13 (iv) On the basis of your graph, discuss the validity of the above relationship. Between A and B, as in Figure 2. B (10) (Total 15 marks) A 50Ω 50Ω 50Ω 50Ω C D 16. Four resistors, each having resistance of 50 Ω, are connected to form a square. A resistance meter measured the resistance between different corners of the square. Determine the resistance the meter records when connected between the following corners. (a) Between A and C, as in Figure 1. Figure A 50Ω B 50Ω C (Total 5 marks) 50Ω 50Ω D Figure In the circuit shown, the battery has an emf of 12 V and an internal resistance of 2.0 Ω. The resistors A and B each have resistance of 30 Ω. P A B Q V 2.0Ω... Calculate the total current in the circuit, St Ivo School 25 St Ivo School 26

14 the voltage between the points P and Q, The two lamps are connected in the circuit shown. The battery has an emf of 27 V and negligible internal resistance. The resistors R 1 and R 2 are chosen so that the lamps are operating at their rated voltage. (iii) the power dissipated in resistor A, R V Y R 2 X V high resistance voltmeter (iv) the energy dissipated by resistor A in 20 s (Total 8 marks) What is the reading on the voltmeter? 18. (a) X and Y are two lamps. X is rated at 12 V, 24 W and Y at 6.0 V, 18 W. Calculate the current through each lamp when it operates at its rated voltage. X:... Y:... Calculate the resistance of R 2. (iii) Calculate the current through R 1. (iv) Calculate the voltage across R 1. St Ivo School 27 St Ivo School 28

15 (v) Calculate the resistance of R 1. (7) (Total 9 marks) (iii) Describe how the results would be used to determine an accurate value for the resistance of the wire. 19. (a) A student wishes to measure the resistance of a fixed length of uniform constantan wire. The apparatus available includes a battery, a switch, a milliammeter and a voltmeter. You may be awarded marks for the quality of written communication in your answer. (8) Draw a circuit diagram using the apparatus listed above. Include in your diagram an extra piece of apparatus which will enable a range of measurements to be made. A heating element for an electric fire consists of a single strand of nichrome wire wound around an insulator. The heater is required to produce 1.2 kw when connected to the 230 Vrms ac mains. Calculate the working resistance of the nichrome wire. Calculate the length of nichrome wire required to make the element. State how the student should make the necessary measurements, ensuring that a range of readings is recorded. cross-sectional area of the wire = m 2 resistivity of nichrome = Ω m (5) (Total 13 marks) St Ivo School 29 St Ivo School 30

16 20. (a) In the circuit in Figure 1, the battery, of emf 15 V and the negligible internal resistance, is connected in series with two lamps and a resistor. The three components each have a resistance of 12 Ω. 15 V 12 Ω Show that the current supplied by the battery is 0.83 A. 12 Ω 12 Ω Figure 1 Hence show that the current in each lamp is the same as the current in the lamps in the circuit in Figure 1. What is the voltage across each lamp? Calculate the current through the lamps. (c) How does the brightness of the lamps in the circuit in Figure 1 compare with the brightness of the lamps in the circuit in Figure 2? Explain your answer.... The two lamps are now disconnected and reconnected in parallel as shown in Figure V 12 Ω... (Total 8 marks) 12 Ω 12 Ω Figure 2 St Ivo School 31 St Ivo School 32

17 21. The graph shows the I - V characteristics for two conductors, the tungsten filament of a lamp and a length of constantan wire. I/A 3.0 Explain why the values of resistance, calculated in part, differ from each other. You may be awarded marks for the quality of written communication in your answer. 2.0 tungsten filament 1.0 constantan wire V/V (c) Use the graph to determine the resistivity of constantan, given that the wire is 0.80 m long with a uniform cross-sectional area of m (a) State, with a reason, which conductor obeys Ohm s law across the full voltage range. conductor:... reason: Calculate the resistance of the tungsten filament when V = 1 V and V = 10 V. V = 1 V:... V = 10 V: St Ivo School 33 St Ivo School 34

18 (d) A student is required to obtain the I V characteristic for a filament lamp using a datalogger, so that the data can be fed into a computer to give a visual display of the characteristic. Draw a labelled circuit diagram for such an experiment. (An account of the experiment is not required). 22. An oscilloscope is connected to a sinusoidal ac source as shown in Figure 1. The frequency and the voltage output of the ac source can be varied. ac source oscilloscope Figure 1 At a certain frequency the ac signal has an rms output of 7.1 V. Figure 2 shows the trace obtained on the screen of the oscilloscope when one horizontal division corresponded to a time of 5.0 ms. (Total 12 marks) 5.0 ms Figure 2 St Ivo School 35 St Ivo School 36

19 (a) Calculate, for the signal shown in Figure 2, 23. In the circuit shown the battery has emf and internal resistance r. the peak voltage, r the frequency. V S 2.4 Ω The voltage output and frequency of the signal are now changed so that the peak voltage is 80 V and the frequency is 200 Hz. State which two controls on the oscilloscope have to be altered so that four full cycles again appear on the screen but the peak to peak distance occupies the full screen. Determine the values at which these two controls have to be set. control 1:... value of the setting: control 2:... value of setting:... (a) State what is meant by the emf of a battery. When the switch S is open, the voltmeter, which has infinite resistance, reads 8.0 V. When the switch is closed, the voltmeter reads 6.0 V. Determine the current in the circuit when the switch is closed (5) (Total 8 marks) (iii) Show that r = 0.80 Ω. The switch S remains closed. Calculate the power dissipated in the 2.4 Ω resistor, St Ivo School 37 St Ivo School 38

20 the total power dissipated in the circuit, (iv) Calculate the resistance of the conductor... (iii) the energy wasted in the battery in 2 minutes. (Total 8 marks).. (Total 6 marks) 25. (a) Figure 1 shows two possible arrangements of connecting three resistors, each resistor having a resistance of 40 Ω. 24. A battery is connected across a uniform conductor. The current in the conductor is 40 ma. Calculate the total charge that flows past a point in the conductor in 3 minutes Figure 1 Calculate the equivalent resistance in each case. Using data from the Data Sheet calculate the number of electron charge carriers passing the same point in the conductor in this time..... (iii) If 8.6 J of energy are transferred to the conductor in this time, calculate the potential difference across the conductor St Ivo School 39 St Ivo School 40

21 The designer of a heating element for the rear window of a car decides to connect six separate heating elements together as shown in Figure 2. Each element has a resistance of 6.0 Ω and the unit is connected to a 12 V dc supply having zero internal resistance. 26. In the circuit shown, a battery of emf and internal resistance r is connected to a variable resistor R. The current I and the voltage V are read by the ammeter and voltmeter respectively. r 12 V R A V Figure 2 (a) The emf is related to V, I and r by the equation = V + Ir Calculate the current in each single element. Rearrange the equation to give V in terms of, I and r.... (1) In an experiment, the value of R is altered so that a series of values of V and the corresponding values of I are obtained. Using the axes, sketch the graph you would expect to obtain as R is changed. V With the aid of a similar calculation give a reason why the heater would not be as effective if all six were connected in series. (5) (Total 8 marks) I 3 St Ivo School 41 St Ivo School 42

22 (c) State how the values of and r may be obtained from the graph.... r... (Total 5 marks) Without recalculating the resistance of the carbon film, explain how you would expect the resistance to change if the current flowed as in Figure 2. You should consider the numerical ratio or factor by which each dimension affecting the resistance has changed. You may be awarded marks for the quality of written communication in your answer. I 27. (a) Give an expression for the resistivity of a material in the form of a uniform wire. Define all the symbols used I Figure 2 A thin film of carbon may be used in some electronic systems. Typical dimensions of such a film are shown in Figure 1. I m I (Total 6 marks) m m Figure 1 Calculate the resistance of the carbon film to a current I passing through it as shown in Figure 1. resistivity of carbon = Ω m St Ivo School 43 St Ivo School 44

23 28. A student carried out an experiment to investigate how the resistance of a coil made from iron wire varied as its temperature changed. In the experiment, a constant potential difference of 2.00 V was maintained across the coil as the student measured the current through it at various temperatures. Complete the table to show the value of the resistance, R, of the iron coil at each temperature. Use the data to plot a graph to confirm the equation. (a) Draw a circuit diagram to show how such measurements could be made using a 3.0 V battery and other necessary apparatus. (One sheet of graph paper should be provided.) (6) (c) Use your graph to determine the value of the resistance of the coil at 0 C (R 0 ). Use your graph to determine the value of the constant α and state its unit. The results are shown in the table. temperature θ/ C p.d. across the coil /V current /ma resistance R / Ω (5) The resistance, R, of a metal wire varies with temperature according to the equation R = R 0 (1 + αθ) where R 0 is the resistance of the wire at 0 C, θ is the temperature of the wire in C, and α is a constant which depends on the material from which the wire is made. St Ivo School 45 St Ivo School 46

24 (d) Explain why the resistance of a metal wire changes when its temperature is increased. (a) Calculate the current through the ammeter when the switch S is You may be awarded marks for the quality of written communication in your answer open, closed (Total 16 marks).. The switch S is now replaced with a voltmeter of infinite resistance. Determine the reading on the voltmeter. 29. In the circuit shown in Figure 1, the battery, of emf 6.0V, has negligible internal resistance.... A V 20 Ω... (Total 5 marks) S 60 Ω Figure 1 St Ivo School 47 St Ivo School 48

25 30. (a) The graph in Figure 1 shows the I V characteristic for a semiconductor diode. Describe how the apparatus would be used. I A You may be awarded marks for the quality of written communication in your answer..... B O V Figure 1 In order to produce this characteristic in the laboratory, a student is given suitable apparatus, including a data logger. The output of the data logger is connected to a computer to give a visual display. (iii).... What change would have to be made to the circuit in order to obtain the characteristic from O to B in Figure 1? Draw a labelled circuit diagram of the apparatus that would be used to obtain the characteristic from O to A in Figure (6) On the axes in Figure 2 draw the characteristic for a filament lamp. I 0 V Figure 2 Explain why the I V characteristic has the shape you have drawn. St Ivo School 49 St Ivo School 50

26 You may be awarded marks for the quality of written communication in your answer. (a) Give the values of the resistance R R and R Th at a temperature of 200 C R R...R Th... (1) The resistor and thermistor are connected in series to a 12V battery of negligible internal resistance, as shown in Figure V A... (5) (Total 11 marks) Figure 1 B 31. The graph shows how the resistance, R R, of a metal resistor and the resistance, R Th, of a thermistor change with temperature. 200 resistance/ω Calculate the voltage across the terminals AB when both the resistor and thermistor are at 200 C resistor Assuming that the temperature of the resistor always equals the temperature of the thermistor, deduce the temperature when the voltage across the resistor equals the voltage across the thermistor thermistor temperature/ C St Ivo School 51 St Ivo School 52

27 (c) A lamp and a switch are now connected across the terminals AB, as shown in Figure 2. The temperature of the thermistor does not change from that obtained in part. 32. (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 V A S lamp B Figure 2 The lamp is rated at 2.0 W at a voltage of 6.0 V. Calculate the resistance of the lamp at this rating..... The switch S is now closed. Explain, without calculation, why the voltage across the thermistor will fall from the value in part (Total 9 marks) 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 m 2. Calculate the length of nichrome wire required. resistivity of nichrome = Ω m St Ivo School 53 St Ivo School 54

28 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. The settings on the oscilloscope are timebase: 250 µs per division, voltage sensitivity: 5.0 V per division. Draw on the grid, which represents the screen of the oscilloscope, the trace that would be seen (6) (Total 8 marks) 33. A sinusoidal alternating voltage source of frequency 500 Hz is connected to a resistor of resistance 2.0 kω and an oscilloscope, as shown in Figure Hz 2.0 kω oscilloscope (Total 6 marks) Figure 1 (a) The rms current through the resistor is 5.3 ma. Calculate the peak voltage across the resistor St Ivo School 55 St Ivo School 56

29 34. A student investigates the variation of electric potential with distance along a strip of conducting paper of length l and of uniform thickness. The strip tapers uniformly from a width 4w at the broad end to 2w at the narrow end, as shown in Figure 1. A constant pd is applied across the two ends of the strip, with the narrow end at positive potential, V l, and the broad end at zero potential. The student aims to produce a graph of pd against distance x, measured from the broad end of the strip. By reference to the physical principles involved, explain why the increase of V with x is greater than a linear increase w x 2w l Figure (a) Draw a labelled circuit diagram which would be suitable for the investigation. (c) The potential, V, at a distance x from the broad end is given by V = k 1.44V l ln (2l x), where V l is the potential at the narrow end, and k is a constant. The student s results are given below. Complete the table. l = m distance x/m potential V/V (2l x)/m 1n (2l x) The student obtained some preliminary measurements which are shown below. pd, V/V Distance, x/m St Ivo School 57 St Ivo School 58

30 (iii) the resistance of each lamp, Plot a graph of V against ln (2l x) and explain whether or not it confirms the equation (iv) the total electrical energy transferred by the set of lights in 2 hours..... (5) When assembled at the factory, one set of lights inadvertently contains 10 lamps too many. All are connected in series. Assume that the resistance of each lamp is the same as that calculated in part (a) (iii). Calculate the current in this set of lights when connected to a 230 V supply. (iii) Use the graph to calculate V l..... (10) (Total 16 marks) 35. (a) A set of decorative lights consists of a string of lamps. Each lamp is rated at 5.0 V, 0.40 W and is connected in series to a 230 V supply. Calculate How would the brightness of each lamp in this set compare with the brightness of each lamp in the correct set? (Total 8 marks) the number of lamps in the set, so that each lamp operates at the correct rating, the current in the circuit, St Ivo School 59 St Ivo School 60

31 36. (a) A student is given three resistors of resistance 3.0 Ω, 4.0 Ω and 6.0 Ω respectively. Draw the arrangement, using all three resistors, which will give the largest resistance. The three resistors are now connected to a battery of emf 12 V and negligible internal resistance, as shown in Figure Ω 4.0 Ω 6.0 Ω 12 V Figure 1 Calculate the resistance of the arrangement you have drawn. Calculate the total resistance in the circuit. (iii) Draw the arrangement, using all three resistors, which will give the smallest resistance. Calculate the voltage across the 6.0 Ω resistor. (Total 9 marks) (iv) Calculate the resistance of the arrangement you have drawn. (5) St Ivo School 61 St Ivo School 62

32 37. (a) In the circuit shown in Figure 1, the battery has an emf of 6.0 V. With the switch closed and the lamp lit, the reading on the voltmeter is 5.4 V. Calculate the internal resistance of each cell. = 6.0 V lamp V (5) Figure 1 Explain without calculation, why the voltmeter reading is less than the emf of the battery. You may be awarded marks for the quality of written communication in your answer.... (c) In the circuit in Figure 2 the cell has emf and internal resistance r. The voltage V across the cell is read on the voltmeter which has infinite resistance, and the current I through the variable resistor R is read on the ammeter. A cell r V R... A torch is powered by two identical cells each having an emf of 1.5 V and an internal resistance r. The cells are connected in series. The torch bulb is rated at 1.6 W and the voltage across it is 2.5 V. Figure 2 Draw the circuit described. St Ivo School 63 St Ivo School 64

33 By altering the value of the variable resistor R, a set of values of V and I is obtained. These values, when plotted, give the graph shown in Figure 3. V 38. The graph shows how the current through a thermistor varies with the potential difference across it. 0.6 current/ma I 0.2 Figure 3 Show how the values of and r may be obtained from this graph. Explain your method potential difference/v (Total 11 marks) (a) Draw the circuit of an experimental arrangement which could be used to collect the data necessary to produce this graph. On your circuit diagram label clearly a component which would enable the current to be changed continuously across the range. Using information obtained from the graph, calculate the resistances of the thermistor when the current is 0.10 ma and also when the current is 0.60 ma. St Ivo School 65 St Ivo School 66

34 Using the results of part deduce how the resistance of the thermistor changes as its temperature increases. You may be awarded marks for the quality of written communication in your answer. The torch bulb is now connected to a battery of negligible internal resistance. The battery supplies a steady current of 0.25 A for 20 hours. In this time the energy transferred in the bulb is J. Calculate the potential difference across the bulb, (5) (Total 9 marks) the power of the bulb.. (Total 5 marks) 39. (a) A steady current of 0.25 A passes through a torch bulb for 6 minutes. Calculate the charge which flows through the bulb in this time In the circuit shown in the figure below, the battery, of negligible internal resistance, is connected to two resistors which form a potential divider. A 160 Ω V X 110 Ω Y St Ivo School 67 St Ivo School 68

35 (a) Calculate the current through the ammeter. 41. (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. Draw a circuit diagram which incorporates some or all of this apparatus and which enables the student to determine the resistivity of the material. A 20 Ω resistor is now connected between X and Y. State and explain, without further calculation, whether the current through the ammeter will increase or decrease. You may be awarded marks for the quality of written communication in your answer. State the measurements which must be made to ensure that a reliable value of the resistivity is obtained. The 20 Ω resistor is now removed and replaced with a voltmeter. Stating the assumption made, show that the reading on the voltmeter is 4.9 V (iii) Explain how a value of the resistivity would be obtained from the measurements. (c) The voltmeter is now removed and the terminals X and Y joined together with a wire. Calculate the reading on the ammeter (Total 8 marks) (10) St Ivo School 69 St Ivo School 70

36 A wire made from tin with cross-sectional area m 2, 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 = Ω m A student wishes to measure and r. Using the circuit shown in the figure above the value of R is decreased in steps and at each step the readings V and I on the voltmeter and ammeter respectively are recorded. These are shown in the table. reading on voltmeter/v reading on ammeter/a (Total 12 marks) Give an expression relating V, I, and r. 42. A battery of emf and internal resistance r is connected in series to a variable resistor R and an ammeter of negligible resistance. A voltmeter is connected across R, as shown in the figure below. Draw a graph of V (on the y-axis) against I (on the x-axis) on graph paper. (Allow one sheet of graph paper) r (iii) Determine the values of and r from the graph, explaining your method. :... R V A r:. (8) (Total 10 marks) (a) State what is meant by the emf of the battery. The reading on the voltmeter is less than the emf. Explain why this is so. St Ivo School 71 St Ivo School 72

37 43. (a) On the axes below draw the I V characteristic for a silicon semiconductor diode in both forward bias and reverse bias. Indicate any relevant voltage values on the axis. I You may be awarded additional marks to those shown in brackets for the quality of written communication in your answer V The figure below shows the I V characteristic for a filament lamp. Explain the shape of the characteristic. I (Total 8 marks) 44. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and its resistance is 12 Ω. V 10 Ω A 18 Ω 15 Ω 12 Ω B 30 V (a) Show that the total resistance of the circuit is 20 Ω St Ivo School 73 St Ivo School 74

38 Calculate the current supplied by the battery, 45. The battery of an electric car consists of 30 cells, connected in series, to supply current to the motor, as shown in the figure below. the pd between the points A and B, M (iii) the current in the lamp. (a) Assume that the internal resistance of each cell is negligible and that the pd across each cell is 6.0 V. (c) What is the power of the lamp, in W? State the pd across the motor. What percentage of the power supplied by the battery is dissipated in the lamp? (Total 10 marks) The battery provides 7.2 kw to the motor when the car is running. Calculate the current in the circuit. (iii) The battery can deliver this current for two hours. Calculate how much charge the battery delivers in this time. St Ivo School 75 St Ivo School 76

39 (iv) Calculate the energy delivered to the motor in the two hour period. 46. The circuit in Figure 1 shows a sinusoidal ac source connected to two resistors, R 1 and R 2, which form a potential divider. Oscilloscope 1 is connected across the source and oscilloscope 2 is connected across R 2. Figure 1 (7) R 1 In practice, each cell has a small but finite internal resistance. Explain, without calculation, the effect of this resistance on oscilloscope 1 R 2 oscilloscope 2 the current in the circuit, and the time for which the battery can deliver the current in part (a). You may assume that the motor behaves as a constant resistance. You may be awarded additional marks to those shown in brackets for the quality of written communication in your answer (Total 10 marks) (a) Figure 2 shows the trace obtained on the screen of oscilloscope 1. The time base of the oscilloscope is set at 10 m s per division and the voltage sensitivity at 15 V per division. For the ac source, calculate Figure 2 the frequency, St Ivo School 77 St Ivo School 78

40 the rms voltage. The resistors have the following values: R 1 = 450 Ω and R 2 = 90 Ω. Calculate the rms current in the circuit, the rms voltage across R 2... (c) Oscilloscope 2 is used to check the calculated value of the voltage across R 2. The screen of oscilloscope 2 is identical to that of oscilloscope 1 and both are set to the same time base. Oscilloscope 2 has the following range for voltage sensitivity: 1 V per div., 5 V per div., 10 V per div. and 15 V per div. State which voltage sensitivity would give the most suitable trace. Explain the reasons for your choice (Total 9 marks) St Ivo School 79