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GCE JUN 2007 : A2 2 Electromagnetism and Nuclear Physics

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Centre Number 71 Candidate Number ADVANCED General Certificate of Education 2007 Physics assessing Module 5: Electromagnetism and Nuclear Physics A2Y21 Assessment Unit A2 2 [A2Y21] FRIDAY 8 JUNE, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Answer all six questions. Write your answers in the spaces provided in this question paper. INFORMATION FOR CANDIDATES The total mark for this paper is 90. Quality of written communication will be assessed in question 2(b). Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question. Your attention is drawn to the Data and Formulae Sheet which is inside this question paper. You may use an electronic calculator. Question 6 contributes to the synoptic assessment requirement of the Specification. You are advised to spend about 45 minutes in answering questions 1 5, and about 45 minutes in answering question 6. A2Y2S7 3195 For Examiner s use only Question Number 1 2 3 4 5 6 Total Marks Marks If you need the values of physical constants to answer any questions in this paper, they may be found on the Data and Formulae Sheet. Examiner Only Marks Remark Answer all six questions 1 (a) Fig. 1.1 shows a circuit to enable the capacitance of a capacitor to be determined by measuring the time constant . S1 C V R Fig. 1.1 The resistance of the resistor R is 47 k . With the switch S1 closed the voltmeter reads 18.2 V. S1 is opened and after 45 s the reading on the voltmeter drops to 6.7 V. (i) Show that the time constant of the circuit is 45 s. [1] (ii) Calculate the capacitance of the capacitor. Capacitance = _________ F A2Y2S7 3195 [2] 2 [Turn over (b) The 470 F capacitor in Fig. 1.2 is first charged by closing the switch S1 which connects it to a 12.0 V supply. The switch S2 is open. S1 Examiner Only Marks Remark S2 220 F 470 F Fig. 1.2 (i) Calculate the charge stored in the 470 F capacitor. Charge = __________________ C [1] (ii) Calculate the energy stored in the 470 F capacitor. Energy = _________ mJ A2Y2S7 3195 [2] 3 [Turn over (iii) S1 is now opened, disconnecting the 470 F capacitor from the supply. S2 is then closed connecting the charged 470 F capacitor to an uncharged 220 F capacitor. Examiner Only Marks Remark Calculate the resultant potential difference across the 220 F capacitor. Potential difference = _________ V [3] (iv) Calculate the total energy stored in the two capacitors. Total energy = _________ mJ A2Y2S7 3195 [1] 4 [Turn over 2 In part (b) of this question you should answer in continuous prose, where appropriate. You will be assessed on the quality of your written communication. Examiner Only Marks Remark (a) State Faraday s law of electromagnetic induction. _________________________________________________________ _________________________________________________________ ______________________________________________________ [1] (b) Lenz s law is sometimes thought of as being simply a statement of the law of conservation of energy. Consider the introduction of a magnet into a coil which has been connected to a resistor, as shown in Fig. 2.1. Explain how Lenz s law and the conservation law are related in this example. Make reference to Faraday s law, Lenz s law, the work done in pushing the magnet towards the coil, and the thermal energy generated in the resistor. S N Resistor Fig. 2.1 _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [4] Quality of written communication A2Y2S7 3195 [2] 5 [Turn over 3 (a) What is meant by the quantisation of charge? Examiner Only Marks Remark _________________________________________________________ _________________________________________________________ ______________________________________________________ [2] (b) Fig. 3.1 shows a charged particle held stationary between two parallel plates by an electric field of strength 23.0 kV m 1. + Fig. 3.1 (i) The plates are 20 mm apart. Calculate the potential difference between them. Potential difference = _________ V [1] (ii) The upper plate is negatively charged and the lower plate is positively charged. On Fig. 3.2 sketch electric field lines between the plates, indicating the direction of the field. [2] + Fig. 3.2 A2Y2S7 3195 6 [Turn over (iii) The mass of the particle is 1.31 10 14 kg. Examiner Only Marks Remark (1) Calculate the magnitude of the charge on the particle. Charge = _____________ C [3] (2) Estimate the number of unbalanced electrons the particle carries, stating whether it is a surplus or deficit. Number = _________ The particle carries a surplus of electrons c The particle has a deficit of electrons c [2] (3) The particle then gains some electrons. In which direction does it start to move? ______________________ A2Y2S7 3195 [1] 7 [Turn over 4 A cathode ray oscilloscope (c.r.o.) can be used to measure the voltage and period of a wave form. Examiner Only Marks Remark (a) The amplifier connected to the y-plates of a particular c.r.o. has a sensitivity of 200 mV cm 1. Fig. 4.1 shows the position of the spot ( ) when a d.c. potential of +0.4 V is applied to the y-amplifier. Each square on the graticule is 1 cm. (i) On Fig. 4.1 mark the new position of the spot when the d.c. potential is 0.0 V. Label this position A. [1] (ii) On Fig. 4.1 mark the position of the spot when the d.c. potential is 0.8 V. Label this position B. [1] Fig. 4.1 (b) The linear timebase on a c.r.o. is used to show the variation of the input signal with time. Explain how this is achieved. _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [2] A2Y2S7 3195 8 [Turn over (c) Fig. 4.2 shows the trace produced by an a.c. signal applied to the y-amplifier. The y-sensitivity is set at 5 mV cm 1 and the timebase is set at 50 s cm 1. Each square is 1 cm. Examiner Only Marks Remark Fig. 4.2 (i) By taking measurements from the trace, calculate (1) the maximum (peak) voltage generated, Voltage = _________ mV [1] (2) the frequency of the signal. Frequency = _________ Hz A2Y2S7 3195 [3] 9 [Turn over (ii) Calculate the timebase setting needed to show only one complete wave over the complete screen. Setting = ________ s cm 1 A2Y2S7 3195 Examiner Only Marks Remark [1] 10 [Turn over 5 Radon-222 is an alpha emitter with a decay constant 2.1 10 6 s 1. It decays to polonium (Po). Examiner Only Marks Remark (a) Write a balanced equation for this decay process. The proton number (atomic number) of radon (Rn) is 86. 222 86 Rn [2] (b) A sample of radon-222 has mass 8.38 10 10 kg. One mole of radon-222 has mass 0.222 kg. (i) Show that the number of radon atoms in the sample is 2.27 1015. [2] (ii) Calculate the initial activity of the sample of radon. Activity = _____________ Bq [1] (iii) Calculate the activity of the sample after 12 days. Activity = _____________ Bq A2Y2S7 3195 [3] 11 [Turn over 6 Comprehension question Examiner Only Marks Remark This question contributes to the synoptic assessment requirements of the Specification. In your answer, you will be expected to bring together and apply principles and contexts from different areas of physics, and use the skills of physics, in the particular situation described. You are advised to spend about 45 minutes in answering this question. Read the passage carefully and answer the questions which follow. High voltage electricity Line 1 In the generation of electricity the most important criterion is to ensure the reliability of the supply to consumers. To help achieve this, the three power stations in Northern Ireland (NI) are connected by a grid system and also by interconnectors to Scotland and the Republic of Ireland (ROI). 5 The interconnection between Northern Ireland Electricity and Scottish Power is carried out using direct current (d.c.). There are two connecting links; these are submarine cables each approximately 55.1 km in length, as shown in Fig. 6.1. 55.1 km Cable 1 NI Converter a.c. to d.c. 250 kV d.c. Converter d.c. to a.c. Cable 2 Scotland Fig. 6.1 A2Y2S7 3195 12 [Turn over Each cable has two conductors and each conductor is made from strands of copper wire. There are 35 strands in each conductor, as illustrated in Fig. 6.2. 10 Examiner Only Marks Remark Strand conductor 35 strands in each conductor submarine cable conductor Fig. 6.2 The cables operate at 250 kV d.c. as two high voltage direct current transmission systems rated at 250 MW, thus providing 500 MW transfer capability. The convertor stations are located on Islandmagee in 15 Northern Ireland and at Auchencrosh in Scotland. Power can flow in either direction. Direct current is used in the interconnector links to reduce power loss. The convertor stations are the first in the world designed to use lighttriggered electronic switches. With this technology the switches are not 20 triggered by an electrical signal but by a pulse of light fed through optical fibres. The connection between NI and ROI consists of overhead transmission lines carrying a.c. This link is from Tandragee in NI to Co. Louth in the ROI and is capable of carrying 600 MW in either direction. Because 25 this is an a.c. link the phase of the generators in NI and the ROI must always be synchronous and their frequencies equal, unlike the undersea link to Scotland which uses d.c. Because the grid in the ROI operates at 220 kV and that in NI operates at 275 kV, a transformer is needed. This is 98% efficient. 30 A simple a.c. generator has a coil which rotates inside a fixed magnetic field. Large generators, such as those used in power stations, interchange the arrangement and have fixed coils placed around a rotating magnetic field. The magnetic field is generated by an electromagnet which is energised with d.c. using slip rings. Because the coils are stationary the 35 electrical connections to them are permanent and can carry currents of up to 4000 A at 25 kV. To extract this amount of power using slip rings and brushes would be impossible because of arcing and heating of the carbon brushes. By rotating the electromagnet (called a rotor) only A2Y2S7 3195 13 [Turn over the current needed to maintain its magnetism is fed through brushes. 40 For this d.c. is used and a typical rotor would consume 1 MW of power. Examiner Only Marks Remark The rotating magnetic field can be used to induce an emf in more than one coil. In practice three sets of coils at 120 to each other are used. This is called three-phase generation. Because the rotating field (driven by a steam turbine) is producing peak power six times on each 45 revolution, rather than twice as in a simple a.c. generator, the power from the turbine is much smoother and can be shown to be virtually constant. This reduces the vibration in the system considerably. A2Y2S7 3195 14 [Turn over Answer ALL the questions which follow Examiner Only Marks Remark (a) Write a few words, or a short sentence, to show the meaning of the following words or phrases as they are used in the passage. (i) direct current (line 7), _____________________________________________________ __________________________________________________ [1] (ii) triggered (line 21), _____________________________________________________ __________________________________________________ [1] (iii) optical fibres (line 22), _____________________________________________________ __________________________________________________ [1] (iv) frequency (line 27), _____________________________________________________ __________________________________________________ [1] (v) synchronous (line 27), _____________________________________________________ __________________________________________________ [1] (vi) transformer (line 29), _____________________________________________________ _____________________________________________________ __________________________________________________ [1] A2Y2S7 3195 15 [Turn over (vii) electromagnet (line 34), Examiner Only Marks Remark ____________________________________________________ ____________________________________________________ _________________________________________________ [1] (viii) slip rings (line 35), ____________________________________________________ _________________________________________________ [1] (ix) turbine (line 45), ____________________________________________________ _________________________________________________ [1] (x) peak (line 45). ____________________________________________________ _________________________________________________ [1] (b) (i) Each strand of copper wire in the conductor shown in Fig. 6.2 has diameter 8.31mm and length 55.1km. The resistivity of copper is 1.65 10 8 m. Calculate the resistance of one strand of wire in the conductor. Give your answer to three significant figures. Strand resistance = _________ A2Y2S7 3195 [4] 16 [Turn over (ii) Calculate the resistance of one conductor in the cable. Examiner Only Marks Conductor resistance = _________ Remark [2] (iii) Calculate the current carried by a conductor when the power transmitted is 250 MW. Current = _________ A [2] (iv) Estimate the power loss in a cable (remember there are two identical conductors in a cable, carrying current in opposite directions). Power loss = _________ kW A2Y2S7 3195 [2] 17 [Turn over (v) (1) Calculate the power loss per metre in the cable in (b)(iv). Examiner Only Marks Power loss per metre = _________ W m 1 Remark [1] (2) This loss appears as heat. Comment on the likely effect on an underwater cable. __________________________________________________ __________________________________________________ _______________________________________________ [2] (c) The switches (line 20) are controlled by a short pulse of light travelling along the axis of a straight optical fibre. The length of the optical path is 1.40 m. The refractive index of the fibre is 1.52. Calculate the time it takes a pulse of light to travel along the fibre. Time = _________ ns [3] (d) The transformer (line 29) is 98% efficient. (i) Calculate the power loss when transforming 180 MW from 275 kV to 220 kV. Power loss = _________ kW A2Y2S7 3195 [1] 18 [Turn over (ii) The primary of the transformer has 200 turns. Calculate the number of turns in the secondary. Number of turns in the secondary = _________ Examiner Only Marks Remark [2] (iii) Name three causes of power loss in a transformer. State the part of the transformer in which each arises: Cause of loss Part of transformer 1 2 3 [4] (iv) For one of the sources of power loss you named in (iii), give a method used to reduce this source of loss. ___________________________________________________ [1] A2Y2S7 3195 19 [Turn over (v) Transformers of this size use oil to keep them cool. The oil circulates between the windings and then rises by convection passing through cooling fins. A typical large transformer contains a volume of 7.50 m3 of oil of density 760 kg m 3. The oil used has specific heat capacity 1370 J kg 1 K 1. Examiner Only Marks Remark Using your answer to (d)(i), estimate the initial rate of rise of temperature of the oil. Assume that all the oil is heated at the same time. Rate of rise of temperature = _________ K s 1 [4] (e) Explain why a simple a.c. generator generates power which varies in magnitude reaching a peak value twice per revolution. _________________________________________________________ _________________________________________________________ ______________________________________________________ [2] A2Y2S7 3195 20 [Turn over (f) Fig. 6.3 shows how the output voltages V generated in a three-coil system vary with time t. output voltage/kV 400 coil 1 coil 2 coil 3 200 0 20 40 t/ms 200 400 Fig. 6.3 Examiner Only Marks These sine waves may be added using the principle of superposition. (i) State the principle of superposition of waves. _____________________________________________________ _____________________________________________________ __________________________________________________ [3] (ii) Take measurements from the graphs at time t = 30 ms for each of the three coils. Then apply the principle of superposition to find the resultant of the three outputs. Coil 1 = _________ kV Coil 2 = _________ kV Coil 3 = _________ kV Resultant = _________ kV [2] A2Y2S7 3195 21 Remark THIS IS THE END OF THE QUESTION PAPER A2Y2S7 3195 22 [Turn over S 1/07 7-154-1 [Turn over GCE Physics (Advanced Subsidiary and Advanced) Data and Formulae Sheet Values of constants speed of light in a vacuum c = 3.00 108 m s 1 permeability of a vacuum 0 = 4 10 7 H m 1 permittivity of a vacuum 0 = 8.85 10 12 F m 1 1 = 8.99 109 F 1 m 4 0 ( ) elementary charge e = 1.60 10 19 C the Planck constant h = 6.63 10 34 J s unified atomic mass unit 1 u = 1.66 10 27 kg mass of electron me = 9.11 10 31 kg mass of proton mp = 1.67 10 27 kg molar gas constant R = 8.31 J K 1 mol 1 the Avogadro constant NA = 6.02 1023 mol 1 the Boltzmann constant k = 1.38 10 23 J K 1 gravitational constant G = 6.67 10 11 N m2 kg 2 acceleration of free fall on the Earth s surface g = 9.81 m s 2 electron volt 1 eV = 1.60 10 19 J A2Y2INS A2Y2S7 3195.02 USEFUL FORMULAE The following equations may be useful in answering some of the questions in the examination: Thermal physics Mechanics Momentum-impulse relation mv mu = Ft for a constant force Average kinetic energy of a molecule 1 m<c2> 2 Power P = Fv Kinetic theory pV = 1 Nm <c2> 3 Conservation of energy 1 mv 2 2 1 mu 2 = Fs 2 for a constant force Simple harmonic motion Displacement x = x0 cos t or x = x0 sin t Velocity v = x 0 2 x 2 Simple pendulum T = 2 l / g Loaded helical spring T = 2 m / k Medical physics Sound intensity level/dB = 10 lg10(I/I0) Sound intensity difference/dB = 10 lg10(I2/I1) Resolving power sin = / D Waves Capacitors Capacitors in parallel 11 1 1 = + + C C1 C 2 C 3 C = C1 + C2 + C3 Time constant = RC Capacitors in series Electromagnetism Magnetic flux density due to current in (i)i long straight (i)i solenoid B= (ii) long straight (i)i conductor B= 0NI l 0I 2 a Alternating currents A.c. generator E = E0 sin t = BAN sin t Particles and photons Two-slit interference = ay/d Diffraction grating d sin = n Lens formula Stress and Strain Hooke s law F = kx Strain energy E = <F > x (= 1 Fx = 1 kx 2 2 2 if Hooke s law is obeyed) Electricity Potential divider 3195.02 Vout = R1Vin/(R1 + R2) A = N A = A0e t t1 = 0.693/ 2 Photoelectric effect 1 mv2 = max 2 de Broglie equation 1/u + 1/v = 1/ f Radioactive decay Half life Light A2Y2S7 = 3 kT 2 = h /p Particle Physics Nuclear radius 1 r = r0 A3 hf hf0

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Additional Info : Gce Physics June 2007 Assessment Unit A2 2, Module 5: Electromagnetism and Nuclear Physics
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