Physics Higher Unit 2. Note: The Radiation and Matter component of Higher Physics will appear on the following Science CD-ROM.

Transcription

1 Physics Higher Unit Note: The Radiation and Matter component of Higher Physics will appear on the following Science CD-ROM.

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3 Spring 1999 HIGHER STILL Physics Higher Support Materials

4 This publication may be reproduced in whole or in part for educational purposes provided that no profit is derived from the reproduction and that, if reproduced in part, the source is acknowledged. First published 1999 Higher Still Development Unit PO Box Ladywell House Ladywell Road Edinburgh EH12 7YH

5 HIGHER PHYSICS - STAFF NOTES Higher Physics course and units The Higher Physics course is divided into the following three units. Mechanics and Properties of Matter (40 hours) Electricity and Electronics (40 hours) Radiation and Matter (40 hours) The support materials For each of the three units the student material contains the following sections. Checklist Summary Notes Activities Problems (with numerical answers) In addition there is a separate section dealing with uncertainties, units and prefixes. It should be noted that the Content Statements associated with uncertainties are part of each of the three units, see the Arrangements for Physics. Although the Higher Physics units could be taught in any order, current practice indicates that the Mechanics and Properties of Matter is usually taught first. Hence the section dealing with uncertainties is placed at the start of this unit. The examples in the section on uncertainties are taken from topics in this unit. The problem sections of the other two units contain a few additional questions on uncertainties. The student materials are to provide assistance to the teacher or lecturer delivering a unit or the course. They are not a self standing open learning package. They require to be supplemented by learning and teaching strategies. This is to ensure that all the unit or course content is covered and that the students are given the support they need to acquire the necessary knowledge, understanding and skills demanded by the unit or the course. Checklists These are lists of the content statements taken directly from the Arrangements for Physics documentation. Summary Notes These notes are a brief summary of all the essential content and include a few basic worked examples. They are intended to aid students in their revision for unit and course assessment. Explanation of the concepts and discussion of applications are for the teacher or lecturer to include as appropriate. Physics: Mechanics and Properties of Matter (H) 1

6 Activities The activity pages provide suggestions for experimental work. A variety of practical activities have been included for each unit. The instruction sheet can be adapted to suit the equipment available in the centre. Some activities are more suitable for teacher demonstration and these have been included for use where appropriate. For each unit there is a range of activities. Although it is desirable that students are able to undertake practical investigations, it must be mentioned that this does not imply that all activities must be undertaken. The teacher or lecturer should decide what to select depending on the needs of their students and the learning and teaching approaches adopted. For Outcome 3 of each unit one report of a practical activity is required. Some activities suitable for the achievement of Outcome 3 have been highlighted and should be seen as an opportunity to develop good practice. Problems A variety of problems have been collated to give the student opportunity for practice and to aid the understanding of the unit or course content. Use of the materials The checklists may be issued at the end or at the beginning of a unit depending on the teacher s discretion. Hence for each unit the checklists are given with separate page numbers. The rest of the material for each unit is numbered consecutively through the summary notes, activities and problems. The uncertainties section is numbered separately. Some staff may wish to cover this material at the start of the course, others may prefer to introduce the concepts more gradually during early experimental work. (For unit assessment, uncertainties are covered in Outcome 3. The course assessment will contain questions which will sample uncertainties within the context of any of the units.) When photocopying a colour code for each section could be an advantage. For some units it could be preferable to split the unit into subsections. For example, the Mechanics and Properties of Matter unit might have a first subsection booklet for kinematics which would entail selecting appropriate summary notes, activities, problems and numerical answers. Learning and Teaching A variety of teaching methods can be used. Direct teaching whether it be to a whole class or small groups is an essential part of the learning process. A good introduction to a topic; for example, a demonstration, activity or video, is always of benefit to capture the minds of the students and generate interest in the topic. Applications should be mentioned and included wherever possible. Physics: Mechanics and Properties of Matter (H) 2

7 Further materials A course booklet will be issued which will contain additional problems including: examination type questions of a standard suitable for estimates of course performance and evidence for appeals revision home exercises for ongoing monitoring of progress. Outcome 3 The Handbook: Assessing Outcome 3 Higher Physics contains specific advice for this outcome together with exemplar instruction sheets and sample student reports. Specimen Course Assessment A specimen course question paper together with marking scheme has been issued by SQA. This pack also contains the updated Details of the instrument for external assessment from the Arrangements for Physics. Physics: Mechanics and Properties of Matter (H) 3

8 Checklist ELECTRICITY AND ELECTRONICS The knowledge and understanding for this unit is given below. Electric fields and resistors in circuits 1. State that, in an electric field, an electric charge experiences a force. 2. State that an electric field applied to a conductor causes the free electric charges in it to move. 3. State that work W is done when a charge Q is moved in an electric field. 4. State that the potential difference (V) between two points is a measure of the work done in moving one coulomb of charge between the two points. 5. State that if one joule of work is done moving one coulomb of charge between two points, the potential difference between the points is one volt. 6. State the relationship V = W/Q. 7. Carry out calculations involving the above relationship. 8. State that the e.m.f. of a source is the electrical potential energy supplied to each coulomb of charge which passes through the source. 9. State that an electrical source is equivalent to a source of e.m.f. with a resistor in series, the internal resistance. 10. Describe the principles of a method for measuring the e.m.f. and internal resistance of a source 11. Explain why the e.m.f. of a source is equal to the open circuit p.d. across the terminals of a source 12. Explain how the conservation of energy leads to the sum of the e.m.f. s round a closed circuit being equal to the sum of the p.d. s round the circuit. 13. Derive the expression for the total resistance of any number of resistors in series, by consideration of the conservation of energy. 14. Derive the expression for the total resistance of any number of resistors in parallel, by consideration of the conservation of charge. 15. State the relationship among the resistors in a balanced Wheatstone bridge. 16. Carry out calculations involving the resistance in a balanced Wheatstone bridge. 17. State that for an initially balanced Wheatstone bridge, as the value of one resistor is changed by a small amount, the out of balance p.d. is proportional to the change in resistance. 18. Use the following terms correctly in context: terminal p.d., load resistor, bridge circuit, lost volts, short circuit current. Alternating Current and Voltage 1. Describe how to measure frequency using an oscilloscope. 2. State the relationship between peak and r.m.s. values for a sinusoidally varying voltage and current. 3. Carry out calculations involving peak and r.m.s. values of voltage and current. 4. State the relationship between current and frequency in a resistive circuit. Physics: Electricity and Electronics (H) 4

9 Checklist Capacitance 1. State that the charge Q on two parallel conducting plates is directly proportional to the p.d. V between the plates. 2. Describe the principles of a method to show that the p.d. across a capacitor is directly proportional to the charge on the plates. 3. State that capacitance is the ratio of charge to p.d. 4. State that the unit of capacitance is the farad and that one farad is one coulomb per volt. 5. Carry out calculations using C = Q/V 6. Explain why work must be done to charge a capacitor. 7. State that the work done to charge a capacitor is given by the area under the graph of charge against p.d State that the energy stored in a capacitor is given by 2 (charge p.d.) and equivalent expressions Carry out calculations using 2 QV or equivalent expressions. 10. Draw qualitative graphs of current against time and of voltage against time for the charge and discharge of a capacitor in a d.c. circuit containing a resistor and capacitor in series. 11. Carry out calculations involving voltage and current in CR circuits (calculus methods are not required). 12. State the relationship between current and frequency in a capacitive circuit. 13. Describe the principles of a method to show how the current varies with frequency in a capacitive circuit. 14. Describe and explain the possible functions of a capacitor: storing energy, blocking d.c. while passing a.c. Analogue Electronics 1. State that an op-amp can be used to increase the voltage of a signal. 2. State that for the ideal op-amp: a) input current is zero; i.e. it has infinite input resistance b) here is no potential difference between the inverting and non-inverting inputs; i.e. both input pins are at the same potential. 3. Identify circuits where the op-amp is being used in the inverting mode. 4. State that an op-amp connected in the inverting mode will invert the input signal. 5. State the inverting mode gain expression: V 0 / V 1 = -R f / R i. 6. Carry out calculations using the above gain expression. 7. State that an op-amp cannot produce an output voltage greater that the positive supply voltage or less that the negative supply voltage. 8. Identify circuits where the op-amp is being used in the differential mode. 9. State that a differential amplifier amplifies the potential difference between its two inputs. 10. State the differential mode gain expression - V o = (V 2 - V 1 ) R f / R i. 11. Carry out calculations using the above gain expression. 12. Describe how to use the differential amplifier with resistive sensors connected in a Wheatstone bridge arrangement. 13. Describe how an op-amp can be used to control external devices via a transistor. Physics: Electricity and Electronics (H) 5

10 Checklist Uncertainties 1. State that measurement of any physical quantity is liable to uncertainty. 2. Distinguish between random uncertainties and recognised systematic effects. 3. State that the scale-reading uncertainty is a measure of how well an instrument scale can be read. 4. Explain why repeated measurements of a physical quantity are desirable. 5. Calculate the mean value of a number of measurements of the same physical quantity. 6. State that this mean is the best estimate of a true value of the quantity being measured. 7. State that where a systematic effect is present the mean value of the measurements will be offset from a true value of the physical quantity being measured. 8. Calculate the approximate random uncertainty in the mean value of a set of measurements using the relationship: maximum value - minimum value approximate uncertainty in the mean = number of measurements taken 9. Estimate the scale reading incurred when using an analogue display and a digital display. 10. Express uncertainties in absolute or percentage form. 11. Identify, in an experiment where more than one physical quantity has been measured, the quantity with the largest percentage uncertainty. 12. State that this percentage uncertainty is often a good estimate of the percentage in the final numerical result of the experiment. 13. Express the numerical result of an experiment in the form: final value uncertainty Units, prefixes and scientific notation 1. Use SI units of all physical quantities in the above checklist. 2. Give answers to calculations to an appropriate number of significant figures. 3. Check answers to calculations. 4. Use prefixes (p, n, µ, m, k, M, G) 5. Use scientific notation. Physics: Electricity and Electronics (H) 6

11 Summary Notes ELECTRIC FIELDS AND RESISTORS IN CIRCUITS Force Fields In Physics, a field means a region where an object experiences a force without being touched. For example, there is a gravitational field around the Earth. This attracts masses towards the earth s centre. Magnets cause magnetic fields and electric charges have electric fields around them. Electric Fields In an electric field, a charged particle will experience a force. We use lines of force to show the strength and direction of the force. The closer the field lines the stronger the force. Field lines are continuous - they start on positive and finish on negative charge. The direction is taken as the same as the force on a positive test charge placed in the field. Electric Field Patterns Positive point charge + test charge has a force outwards Negative point charge + test charge has a force inwards These are called radial fields. The lines are like the radii of a circle. The strength of the field decreases as we move away from the charge. Electric Field Patterns Positive and negative point charges Parallel charged plates The field lines are equally spaced between the parallel plates. This means the field strength is constant. This is called a uniform field. Electric fields have certain similarities with gravitational fields. Physics: Electricity and Electronics (H) Student Material 1

12 Gravitational Fields Summary Notes h If a mass is lifted or dropped through a height then work is done i.e. energy is changed. If the mass is dropped then the energy will change to kinetic energy. If the mass is lifted then the energy will change to gravitational potential energy. Electric Fields Change in gravitational potential energy = work done. Consider a negative charge moved through a distance in an electric field. If the charge moves in the direction of the electric force, the energy will appear as kinetic energy. If a positive charge is moved against the direction of the force as shown in the diagram, the energy will be stored as electric potential energy. If the charge moved is one coulomb, then the work done is the potential difference or voltage. If one joule of work is done in moving one coulomb of charge between two points in an electric field, the potential difference, (p.d.) between the two points is one volt. 1 volt = 1 joule per coulomb Change in electric potential energy = work done W = QV In this section W will be used for the work done i.e. energy transferred. Example: A positive charge of 3 µc is moved, from A to B, between a potential difference of 10 V. (a) Calculate the electric potential energy gained. (b) If the charge is now released, state the energy change. (c) How much kinetic energy will be gained on reaching B the negative plate? + (a) W + + Q = QV= = J + (b) Electric potential energy to kinetic energy (c) By conservation of energy the energy will be the same, i.e J. A Physics: Electricity and Electronics (H) Student Material 2

13 Summary Notes Moving Charges in Electric Fields From the previous example, when the positive charge is released at plate B then the electical potential energy is converted to kinetic energy. Example QV = 1 2 mv2 An electron is accelerated (from rest) through a potential difference of 200 V. Calculate (a) the kinetic energy, E k gained. (b) the final speed of the electron. (Mass of an electron = kg, charge on an electron = -1.6x10-19 C) (a) E k = 1 2 mv2 = QV = 1.6x = J (b) 1 2 mv2 = v 2 31 m v = m s -1 Applications of electric fields (for background interest) A television involves the use of electron guns. The electrons gain kinetic energy by accelerating through an electric field. Deflection of the electrons is usually done by electromagnetic coils, although flat screen tubes are now dependent on electrostatic deflection. An oscilloscope also depends on electric fields acting on electrons. Electrostatic Spraying makes use of electric fields. Paint or powder particles are blown from a nozzle, where they acquire a charge. The object to be coated is earthed. The charged paint or powder particles follow the field lines and so reach the object, some reaching the back of the object as well as the front. Other applications include photocopiers, ink jet and laser printers. Physics: Electricity and Electronics (H) Student Material 3

14 Summary Notes Electric Current When S is closed, the free electrons in the conductor experience an electric field which cause them to move in one direction. Note: The electron current will flow from the negative terminal to the positive terminal of the battery. The energy required to drive the electron current around the circuit is provided by a chemical reaction in the battery or by the mains power supply. The electrical energy which is supplied by the source is converted to other forms of energy in the components which make up the circuit. The lamp has resistance R. In any circuit providing the resistance of a component remains constant, if the potential difference V across the component increases the current I through the component will increase in direct proportion. This is Ohm s Law which is summarised by the equation below. V = IR A component which has a constant resistance when the current through it is increased is said to be ohmic. Some components do not have a constant resistance, their resistance changes as the p.d. across the component is altered, for example the transistor. Electric Power For a given component the power P = I V where I is the current through that component and V is the potential difference across the component. Resistive Heating The expression I2 R gives the energy transferred in one second due to resistive heating. Apart from obvious uses in electric fires, cookers, toasters, etc. consideration has to given to heating effects in resistors, transistors and integrated circuits and care taken not to exceed the maximum ratings for such components. P = I R = V 2 2 R Electromotive Force (e.m.f) The energy given to a coulomb of charge by a source of electrical energy is called the e.m.f. of the source. This is measured in J C -1 or volts. Note: the potential difference between two points in the external circuit is also measured in volts, but this is concerned with electrical energy being transformed outside the source. Physics: Electricity and Electronics (H) Student Material 4

15 Sources of e.m.f. Summary Notes E.M.F s can be generated in a great variety of ways e.g: chemical cells, thermocouple, piezo - electric generator, solar cell, electromagnetic generator. Resistors in Series - Conservation of Energy Applying the conservation of energy to resistors in series for one coulomb of charge. Energy supplied by source = energy converted by circuit components e.m.f. = IR 1 + IR 2 + IR 3 IR S = IR 1 + IR 2 + IR 3 R s = equivalent series resistance R S = R 1 + R 2 + R 3 Resistors in Parallel - Conservation of Charge The total charge per second (current) passing through R 1, R 2 and R 3 must equal the charge per second (current) supplied from the cell i.e. passing through R P. Conservation of charge gives: I = I 1 + I 2 + I 3 (Since I = Q for each resistor) t E R = E R + E R + E R 4 R p = equivalent parallel resistance Physics: Electricity and Electronics (H) Student Material 5

16 Internal Resistance Summary Notes In choosing a suitable power supply for a circuit, you would have to ensure that it : gives the correct e.m.f is able to supply the required maximum current When a power supply is part of a closed circuit, it must itself be a conductor. All conductors have some resistance. A power supply has internal resistance, r. Energy will be wasted in getting the charges through the supply (the heat from the supply will be noticeable) and so the energy available at the output (the terminal potential difference) will fall. There will be lost volts. The lost volts = I r The greater the current, the more energy will be dissipated in the power supply until eventually all the available energy (the e.m.f.) is wasted and none is available outside the power supply. This maximum current is the short circuit current. This is the current which will flow when the terminals of the supply are joined with a short piece of thick wire. Open Circuit When no current is taken from the power supply, no energy is wasted. The terminal potential difference is therefore the maximum available and equals the e.m.f. General Circuit r Any power supply can be thought of as a source of constant e.m.f. E, in series with a small resistance, the internal resistance. E R S V With S open, the voltmeter reading gives the e.m.f. (an open circuit). With S closed, the voltmeter reading will fall (lost volts). The voltmeter now gives the output voltage, the terminal potential difference, t.p.d. With S closed and using the conservation of energy e.m.f. = lost volts + t.p.d. e.m.f. = lost volts + output voltage E = Ir + V which is: E = Ir + IR Notice that the total resistance of the circuit is R + r, giving the equation: E = I ( R + r) The short circuit current is the maximum which can be supplied by a source. This occurs when there is no external component and R = 0. Physics: Electricity and Electronics (H) Student Material 6

17 Example E r Summary Notes V R = 28 A cell of e.m.f. 1.5 V is connected in series with a 28 resistor. A voltmeter measures the voltage across the cell as 1.4 V. Calculate: (a) the internal resistance of the cell (b) the current if the cell terminals are short circuited (c) the lost volts if the external resistance R is increased to 58 Ω. (a) E = Ir + IR = Ir + V Lost volts = Ir = E - V = = 0.1 V r = lost volts I = I = V R = = 0.05 A r = = 2 (b) A short circuit occurs when R = 0 (no external resistance) I R + r = E r = = 0.75 A (c) Lost volts = Ir I R + r = = 0.05 A E = 1.5 Lost volts = = 0.1 V Physics: Electricity and Electronics (H) Student Material 7

18 Summary Notes Wheatstone Bridge Circuit Any method of measuring resistance using an ammeter or voltmeter necessarily involves some error unless the resistances of the meters themselves are taken into account. The use of digital voltmeters largely overcomes this as they tend to have very high resistances. Further error may be introduced if the meter is not correctly calibrated. The only situation where neither of these errors matter is if the meter reading is zero. The Wheatstone bridge circuit is one such example of using a meter as a null deflection indicator. Bridge Circuit If V OA = V OB there is no p.d. between A and B hence no current flows. The potentials at A and at B depend on the ratio of the resistors that make up each of the two voltage dividers. The voltmeter forms a bridge between the two voltage dividers to make up a bridge circuit. 5 V R1 A V R3 B Balanced Bridge No potential difference will exist across AB when 0 V R2 O R4 R R 1 2 R R 3 4 The bridge is balanced when the voltmeter or galvanometer (milliammeter) reads zero. Alternative diamond Representation with galvanometer Unbalanced Bridge If the bridge is initially balanced, and the resistor is altered by a small amount then the out of balance p.d. (reading on G) is directly proportional to the change in resistance, provided the change is small. Hence for small, Reading on G +1.5 V reading on G R1 R2 X/ G X+ X R4 Physics: Electricity and Electronics (H) Student Material 8

19 Summary Notes ALTERNATING CURRENT AND VOLTAGE Peak and r.m.s. values The graph of a typical alternating voltage is shown below. The maximum voltage is called the peak value. From the graph it is obvious that the peak value would not be a very accurate measure of the voltage available from an alternating supply. In practice the value quoted is the root mean square (r.m.s.) voltage. The r.m.s. value of an alternating voltage or current is defined as being equal to the value of the direct voltage or current which gives rise to the same heating effect (same power output). Consider the following two circuits which contain identical lamps. The variable resistors are altered until the lamps are of equal brightness. As a result the direct current has the same value as the effective alternating current (i.e. the lamps have the same power output). Both voltages are measured using an oscilloscope giving the voltage equation below. Also, since V=IR applies to the r.m.s. valves and to the peak values a similar equation for currents can be deduced. V r.m.s. = 1 2 Vpeak and I r.m.s. = 1 2 Ipeak Note: a moving coil a.c. meter is calibrated to give r.m.s. values. Physics: Electricity and Electronics (H) Student Material 9

20 Summary Notes Graphical method to derive relationship between peak and r.m.s. values of alternating current The power produced by a current I in a resistor R is given by I 2 R. A graph of I 2 against t for an alternating current is shown below. A similar method can be used for voltage. The average value of I 2 is I 2 Peak 2 An identical heating effect (power output) for a d.c. supply = I 2 r.m.s R [since I (d.c.) = I r.m.s.] Average power output for a.c. = I 2 Peak I 2 Peak 2 R I 2 r.m.s R = R hence I 2 r.m.s. = giving I r.m.s. = I I2 Peak Peak 2 2 Frequency of a.c. 2 To describe the domestic supply voltage fully, we would have to include the frequency i.e. 230 V 50 Hz. An oscilloscope can be used to find the frequency of an a.c. supply as shown below. Time base = s cm -1 Wavelength = 4 cm Time to produce one wave = = 0.02 s Frequency = 1 time to produce one wave = = 50 Hz Physics: Electricity and Electronics (H) Student Material 10

21 Summary Notes Mains supply The mains supply is usually quoted as 230 V a.c. This is of course 230 V r.m.s. The peak voltage rises to approximately 325 V. Insulation must be provided to withstand this peak voltage. Example A transformer is labelled with a primary of 230 V r.m.s. and secondary of 12 V r.m.s. What is the peak voltage which would occur in the secondary? V peak = 2 V r.m.s. V peak = V peak = 17.0 V Physics: Electricity and Electronics (H) Student Material 11

22 Summary Notes CAPACITANCE The ability of a component to store charge is known as capacitance. A device designed to store charge is called a capacitor. A typical capacitor consists of two conducting layers separated by an insulator. Circuit symbol Relationship between charge and p.d. The capacitor is charged to a chosen voltage by setting the switch to A. The charge stored can be measured directly by discharging through the coulomb meter with the switch set to B. In this way pairs of readings of voltage and charge are obtained. Q Charge is directly proportional to voltage. 0 V Q V = constant For any capacitor the ratio Q/V is a constant and is called the capacitance. farad (F) capacitance = charge voltage coulombs (C) volts (V) The farad is too large a unit for practical purposes. In practice the micro farad (µf) = F and the nano farad (nf) = F are used. Example A capacitor stores C of charge when the potential difference across it is 100 V. What is the capacitance? C = Q V = 4 µf Physics: Electricity and Electronics (H) Student Material 12

23 Summary Notes Energy Stored in a Capacitor A charged capacitor can be used to light a bulb for a short time, therefore the capacitor must contain a store of energy. The charging of a parallel plate capacitor is considered below. There is an initial surge of electrons from the negative terminal of the cell onto one of the plates (and electrons out of the other plate towards the +ve terminal of the cell). Once some charge is on the plate it will repel more charge and so the current decreases. In order to further charge the capacitor the electrons must be supplied with enough energy to overcome the potential difference across the plates i.e. work is done in charging the capacitor. Eventually the current ceases to flow. This is when the p.d. across the plates of the capacitor is equal to the supply voltage. For a given capacitor the p.d. across the plates is directly proportional to the charge stored Consider a capacitor being charged to a p.d. of V and holding a charge Q. Charge Q V p.d. The energy stored in the capacitor is given by the area under graph Area under graph= 1 Q x V 2 Energy stored = 1 Q x V 2 If the voltage across the capacitor was constant work done = Q x V, but since V is varying, the work done = area under graph. Q = C V and substituting for Q and V in our equation for energy gives: Energy stored in a capacitor = 1 2 QV = 1 2 CV = Q C Example A 40 F capacitor is fully charged using a 50 V supply. How much energy is stored? Energy = 1 2 CV = = J Physics: Electricity and Electronics (H) Student Material 13

24 Summary Notes Capacitance in a d.c. Circuit Charging Consider the following circuit:- When the switch is closed the current flowing in the circuit and the voltage across the capacitor behave as shown in the graphs below. current p.d. across capacitor Supply voltage 0 time 0 time Consider the circuit at three different times A A A As soon as the switch is closed there is no charge on the capacitor the current is limited only by the resistance in the circuit and can be found using Ohm s law. As the capacitor charges a p.d. develops across the plates which opposes the p.d. of the cell as a result the supply current decreases. The capacitor becomes fully charged and the p.d. across the plates is equal and opposite to that across the cell and the charging current becomes zero. Physics: Electricity and Electronics (H) Student Material 14

25 Summary Notes Discharging Consider this circuit when the capacitor is fully charged, switch to position B A If the cell is taken out of the circuit and the switch is set to A, the capacitor will discharge A A B A B While the capacitor is discharging the current flowing in the circuit and the voltage across the capacitor behaves as shown in the graphs below. Current p.d. across capacitor Supply voltage 0 0 time time Although the current/time graph has the same shape as that during charging the currents in each case are flowing in opposite directions. The discharging current decreases because the p.d. across the plates decreases as charge leaves them. Factors affecting the rate of charge/discharge of a capacitor When a capacitor is charged to a given voltage the time taken depends on the value of the capacitor. The larger the capacitor the longer the charging time, since a larger capacitor requires more charge to raise it to the same p.d. as a smaller capacitor as V= Q C When a capacitor is charged to a given voltage the time taken depends on the value of the resistance in the circuit. The larger the resistance the smaller the initial charging current, hence the longer it takes to charge the capacitor as Q = It (The area under this I/t graph = charge. Both curves will have the same area since Q is the same for both.) Current Current large capacitor small capacitor Time small resistor large resistor Time Physics: Electricity and Electronics (H) Student Material 15

26 Summary Notes Example The switch in the following circuit is closed at time t = 0 10 V 1 M Vs 1 µf Immediately after closing the switch what is: (a) the charge on C (b) the p.d. across C (c) the p.d. across R (d) the current through R. When the capacitor is fully charged what is: (e) the p.d. across the capacitor (f) the charge stored. (a) Initial charge on capacitor is zero. (b) Initial p.d. is zero since charge is zero. (c) p.d. is 10 V = V s - V c = 10-0 = 10 V (d) I R = V = = 10 A (e) Final p.d. across the capacitor equals the supply voltage = 10 V. (f) Q = CV = = C. Physics: Electricity and Electronics (H) Student Material 16

27 Summary Notes Resistors and Capacitors in a.c. Circuits Frequency response of resistor The following circuit is used to investigate the relationship between current and frequency in a resistive circuit. The results show that the current flowing through a resistor is independent of the frequency of the supply. Frequency response of capacitor The following circuit is used to investigate the relationship between current and frequency in a capacitive circuit. The results show that the current is directly proportional to the frequency of the supply. To understand the relationship between the current and frequency consider the two halves of the a.c. cycle. The electrons move back and forth around the circuit passing through the lamp and charging the capacitor one way and then the other (the electrons do not pass through the capacitor). The higher the frequency the less time there is for charge to build up on the plates of the capacitor and oppose further charges from flowing in the circuit More charge is transferred in one second so the current is larger. Physics: Electricity and Electronics (H) Student Material 17

28 Summary Notes Applications of Capacitors (for background interest) Blocking capacitor A capacitor will stop the flow of a steady d.c. current. This is made use of in the a.c./d.c. switch in an oscilloscope. In the a.c. position a series capacitor is switched in allowing passage of a.c. components of the signal, but blocking any steady d.c. signals. Flashing indicators A low value capacitor is charged through a resistor until it acquires sufficient voltage to fire a neon lamp. The neon lamp lights when the p.d. reaches 100 V. The capacitor is quickly discharged and the lamp goes out when the p.d. falls below 80V. 120 V 1-2 M Crossover networks in loudspeakers In a typical crossover network in low cost loudspeaker systems, the high frequencies are routed to LS-2 by the capacitor. LS 1 LS 2 Smoothing The capacitor in this simple rectifier circuit is storing charge during the half cycle that the diode conducts. This charge is given up during the half cycle that the diode does not conduct. This helps to smooth out the waveform. Capacitor as a transducer A parallel plate capacitor can be used to convert mechanical movements or vibration of one of its plates into changes in voltage. This idea forms the basis of many measuring systems, e.g. by allowing a force to compress the plates we have a pressure transducer. Physics: Electricity and Electronics (H) Student Material 18

29 ANALOGUE ELECTRONICS Summary Notes Analogue and Digital Signals An analogue system transmits information in the form of a continuously varying signal. A digital system has the information broken up into a series of discrete values or steps. A simple example showing these definitions would be analogue and digital watches. an analogue watch has a set of numbers in a circle and hands that point to them. The hands sweep round the face in a continuous way. a digital watch has a series of numbers that are displayed, the numbers changing at the end of each second, minute or hour. The Op-Amp (Operational Amplifier) As with any amplifier, the operational amplifier (op-amp) will change the size of an input electrical signal. A diagram of the basic set-up of an op-amp is shown below. The op-amp has two separate inputs - an inverting input ( - terminal) and a non-inverting input ( + terminal). The amplifier must have an energy supply and this is provided by the supply voltages +Vs and -Vs across the amplifier. Often the power supply voltages are not shown on circuit diagrams of op-amps. Physics: Electricity and Electronics (H) Student Material 19

30 Activities The Inverting Amplifier If an amplifier is set up in the configuration shown below, it is said to be in the inverting mode. R f R 1 - V 1 V V The input potential, V 1, is applied to the inverting input (-ve input). The non-inverting input (+ve input) is connected straight to ground, 0 V. There is also a resistor, R f, (feedback resistor) connected between the output and the inverting input. This feedback resistor reduces the overall gain of the amplifier and allows the gain to be stabilised controlled. When the input voltage signal to the op-amp, d.c or a.c, is compared to the output voltage signal it is found that the sense or sign of the output is opposite to that of the input - the voltage has been inverted, hence the reason why this circuit is called the inverting mode. Some examples of this are given below: Physics Support Materials: Higher Resource Guide 20

31 Inverting Mode Gain Equation The ideal op-amp fulfils two conditions: Activities no current flows into the op-amp. Its input resistance is infinite. there is no potential difference between the inverting and non-inverting inputs. The following inverting mode gain equation can be verified by experiment. Saturation From the inverting mode gain equation, it would seem that by inserting any pair of resistors R 1 and R f in the inverting amplifier circuit it is possible to provide any gain required. It could therefore be possible to produce either very low or very high output voltages from any input voltage. This is not possible. The output of an op-amp circuit is limited by the size of the power supply used (conservation of energy). In theory, the maximum output voltage possible would be equal to the supply voltage. (However, in reality it is limited to approximately 85% of the supply voltage.) When the maximum output voltage has been reached, the amplifier is said to be saturated V In theory : -15V V V + -15V V 0 [In practice : -13V V V (13V 85% of 15 V)] Physics Support Materials: Higher Resource Guide 21

32 Example An inverting mode operational amplifier is set up as shown below. Summary Notes (a) If V 1 is set at +0.8 V, calculate the output voltage V 0. (b) If an a.c signal of peak voltage 1.5 V is applied to V 1, sketch the input voltage, V 1, and the output voltage, V 0. Physics Support Material: Electricity and Electronics (H) Student Material 22

33 Activities The Differential Amplifier If the amplifier is set up in the configuration shown below, it is said to be in the differential mode. There are two input potentials,v 1 and V 2, one applied to each of the input terminals of the opamp. There is a feedback resistor, R f, connected between the output and the inverting input. This allows control over the gain of the amplifier as it did for the inverting mode. When the op-amp is used in this mode, it amplifies the difference between the inputs V 1 and V 2, with a gain set by the ratio Physics: Electricity and Electronics (H) Student Material 23

34 Example A differential amplifier is set up as shown below. Summary Notes For the following values shown, calculate the output voltage, V 0. (a) (b) V 1 = +5.0 V, V 2 = +4.8 V V 1 = -2.0 V, V 2 = +4.5 V (a) V 1 = +5.0 V, V 2 = +4.8 V, R 1 =R 2 = 10 kω, R f = R 3 = 100 kω, V 0 =? R V 0 = f 100 (V 2 - V 1 ) V R 0 = ( ) 1 10 V 0 = V (b) V 1 = -2.0 V, V 2 = +4.5 V, R 1 =R 2 = 10 kω, R f = R 3 = 100 kω, V 0 =? R f 100 V 0 = (V 2 - V 1 ) V R 0 = (4.5 - (-2.0)) 1 10 V 0 = + 65 V in theory. But supply voltage = + 15 V hence output voltage, V 0, will saturate at + 15 V Physics Support Material: Electricity and Electronics (H) Student Material 24

35 The differential amplifier as part of a monitoring system Summary Notes +Vs 10 k V k R1 10 k R2 10 k - + Rf 100 k V0 0 V t 10 k Wheatstone Bridge input V2 R3 100 k Differential Amplifier 0 V The setting of the variable resistor can be adjusted so as to achieve an output voltage of zero for a particular temperature setting. The bridge circuit would then be balanced, that is the potential difference V 2 - V 1 = 0 V. The potential, V 2, will remain constant as long as the resistance of the variable resistor is not changed. Any change in temperature will change the potential, V 1, and will therefore produce a potential difference between V 2 and V 1. The amplifier will then amplify the difference between V 2 and V 1, giving an output potential, V 0. The output voltage will increase as the change in thermistor resistance, R t, increases. The amplifier is, effectively, amplifying the out-of-balance potential difference from the Wheatstone Bridge. Practical Application The output voltage could be calibrated by placing the thermistor in melting ice (0 o C), then in boiling water (100 o C), noting the output potential, V 0, for each case. The range could then be divided into 100 equal divisions to give an electronic thermometer over the range o C. Physics Support Material: Electricity and Electronics (H) Student Material 25

36 Summary Notes Control Circuits A transistor, such as those shown below, can act as an electrical switch. If the input voltage to these transistors, V i, is positive, then it switches on allowing a current to flow between the collector and emitter or source and drain, otherwise it is off. There are two types of transistor switches: bipolar n-p-n transistor n-channel enhancement MOSFET +V S -V S V i base collector emitter V i gate drain source 0V 0V (i) A positive (+ve) potential (>+0.7 V) is needed for the input, V i, to switch transistor on. (ii) The collector arm is connected to a positive (+ve) supply rail. (iii) If the input potential is negative (<0.7 V), the transistor is off. (i) A positive (+ve) potential >1.8 V is needed for the input, V i, to switch transistor on. (ii) The drain is connected to a positive (+ve) supply rail. (iii) if the input potential is negative or <1.8 V the transistor is off. These transistors can be used with a Wheatstone Bridge/differential amplifier circuit to switch a device on or off. Low light-level indicator Physics Support Material: Electricity and Electronics (H) Student Material 26

37 10K 10K 100K Activities The variable resistor in the Wheatstone Bridge is adjusted so that, at a particular light level, the output of the op-amp is zero or less so that the transistor is off. In practice, the variable resistor would be adjusted until the warning lamp is just off. In this situation, V 1 V 2. If the light level falls, the resistance of the LDR will increase causing the voltage V 1 to fall. If V 1 falls, then V 1 < V 2, therefore (V 2 - V 1 ) will be positive (+ve). This will cause the output voltage, V 0, to be positive also, switching on the transistor and the Warning Lamp lights. If the light level to the LDR increases, then the opposite will be true. The resistance of the LDR will decrease causing the voltage V 1 to increase. If V 1 increases, then V 1 >V 2, (V 2 - V 1 ) will be negative causing the output to be negative and the transistor will not switch on. The gain of the circuit (about 1000) is deliberately chosen to be large so that a small variation from the balance point of the Wheatstone Bridge produces a large enough output voltage to switch the transistor on. Modifications This circuit does have its limitations however. If the output device to be used has a high power rating requiring a current larger than the transistor can safely supply, then a relay switch must be used with the transistor to switch on an external circuit. An example of this type of switch is shown below. In this case, a relay can be energised by the current through the transistor (the collector current) and its contacts can then be used to switch on a high-power device such as a heater. 230 V +V s mains +Vs Rf t V1 0-10K R1 1K R2 1K K relay 0V V2 R3 V0 Vi heater Wheatstone Bridge input Differential Amplifier Transistor Switch and Output Notice that as the temperature falls the resistance of the thermistor increases, causing V 1 to fall. this means V 1 < V 2 giving a positive output voltage V 0. The transistor will be switched on, which will energise the relay switch. The heater will be turned on. Physics: Electricity and Electronics (H) Student Material 27

38 10K 10K Activities Control Circuit Diagrams The Wheatstone Bridge arrangement can be shown as two straight potential dividers or as a diamond arrangement. They are the same circuit, just drawn a different way. Straight potential dividers +Vs t V1 to differential amplifier V2 0V Diamond arrangement bridge circuit V2 +Vs t V1 +Vs 10 k to op-amp V2 to op-amp 10 k 10 k 0V t 10 k V1 0V All the above circuits are identical examples of the sensor bridge circuit that can be used with a differential amplifier. It is important to recognise each circuit for what it is and how it behaves. Physics: Electricity and Electronics (H) Student Material 28

39 ACTIVITY 1 Activities Title: Electric Field Patterns Apparatus: Van de Graaff generator, petri dish with oil and seeds, set of shaped electrodes overhead projector, some sawdust Instructions 2-D Patterns Connect up the apparatus as shown and use the Van de Graaff generator to produce a high voltage between two point electrodes in the oil. Draw the electric field pattern present between the two point electrodes as shown by the seeds. Repeat the above but using two plane electrodes, producing a uniform electric field between them. 3-D Patterns While the Van de Graaff is switched on and charging, throw a small amount of sawdust at the dome. Sketch the path taken by the pieces of sawdust after they came into contact with the dome. The sawdust is affected by the radial field around the dome. Explain the behaviour of the pieces of sawdust after they came into contact with the charging dome. Physics Support Material: Electricity and Electronics (H) Student Material 29

40 ACTIVITY 2 Activities Title: The Cathode Ray Tube Apparatus: Cathode Ray Deflection Tube and stand, EHT supply (for electron gun and heater), HT supply (for deflection plates) Instructions Work Done by Electric Field Note the value of the EHT voltage used in the electron gun. Calculate the work done on each electron by the electric field in the electron gun. Hence calculate the speed of the electrons as they leave the electron gun and enter the evacuated tube. Deflection Plates Sketch the path followed by the electron beam as it passes between the deflection plates when: (a) bottom plate is positive, top plate is negative (b) top plate is positive, bottom plate is negative. Explain the effect the following changes have on the path followed by the electron beam: (a) decrease EHT voltage on electron gun (b) decrease HT voltage on deflection plates Sketch the paths followed by the electron beam after the above changes. Physics: Electricity and Electronics (H) Student Material 30

41 ACTIVITY 3 Activities Title: E.m.f. and Internal Resistance with parallel circuits Apparatus: 6 V battery, parallel circuit board, ammeter, voltmeter to measure the terminal potential difference (t.p.d.). A V L 1 Instruction Connect up the circuit above, with all lamps unscrewed L 3 so that they are off. Copy the table below. Note down the current (I) and corresponding t.p.d. (V) values when no lamps are screwed in, and enter them into the table. Repeat the above for each case as one, then two, then three lamps are screwed in and light up. Using Ohm s Law, complete the final column of the table by calculating the value of the internal resistance of the battery. L 2 No. of bulbs lit Current I (A) t.p.d. V (V) lost volts (V) Internal resistance ( ) Physics: Electricity and Electronics (H) Student Material 31

42 ACTIVITY 4 Activities Title: Internal resistance of a cell (Outcome 3) Apparatus: 1.5 V cell, variable resistor (1-10 ), voltmeter and ammeter Instructions Use the voltmeter to measure the e.m.f. of the cell. Connect the apparatus as shown in the circuit diagram. Set the variable resistor to its maximum setting. Record the readings on the ammeter and voltmeter. Adjust the variable resistor and take a range of readings. For each pair of readings determine the lost volts. Use an appropriate format to determine the internal resistance of the cell. Physics: Electricity and Electronics (H) Student Material 32

43 ACTIVITY 5 Activities Title: The Balanced Wheatstone Bridge Apparatus: Wheatstone Bridge board, 1.5 V cell, µa ammeter, 1 k /10 k resistance boxes, set of unknown resistances A, B and C, decade resistance board. Schematic diagram showing position of resistances Circuit diagram Instructions Part A Connect the 1 k resistances, decade resistance board and unknown resistance A as shown in the diagram above. By finding the value of resistance of the decade resistance board which exactly balances the Wheatstone Bridge, find the value of resistance A. Repeat to find the value of resistances B and C. Part B Replace R 2 with a 10 k resistor. Predict the value of the decade resistance board that will balance the Wheatstone Bridge for each of the resistors A, B and C with this value of R 2. Confirm your predictions by experiment. Physics: Electricity and Electronics (H) Student Material 33

44 ACTIVITY 6 Activities Title: The Out-of-Balance Wheatstone Bridge Apparatus: Wheatstone Bridge board, 1.5 V cell, µa ammeter, 1 k /10 k resistance boxes, set of resistances A, B and C, decade resistance board. R1 R2 1 k 1 k µa Resistance Board Resistor B Instructions Connect the circuit as shown in the diagram. Adjust the resistance of the decade resistance board so that the Wheatstone Bridge is balanced. Increase the resistance of the decade resistance board in 10 steps, noting the value of the out-of- balance current each time. Record your results and complete the table. Plot a graph of change in resistance, R ( ), on the -axis and out-of-balance current, I, (µa) on the y-axis. Physics: Electricity and Electronics (H) Student Material 34

45 ACTIVITY 7 Activities Title: The Out-of-Balance Wheatstone Bridge - Applications Apparatus: Wheatstone Bridge board, 6 V battery, µa ammeter, 1 k /10 k resistance boxes, decade resistance board, LDR, thermistor probe, strain gauge (already set up). Instructions Part A - Light Meter Connect the circuit up as shown. Balance the Wheatstone Bridge circuit with the LDR on your bench. There is no need to remove the protective resistor as the circuit is quite sensitive. Take care not to cast shadows over the LDR when finding balance. Find the out-of-balance current when the LDR is in a light place then in a dark place. Explain why the measured current is greater than zero for one condition and less than zero for the other. Part B -Thermometer Place the probe in an ice/water mixture in a beaker. (0 C) Balance the Wheatstone Bridge with the probe in the ice/water mixture. Place the probe in a beaker of boiling water. (100 C) Measure and record the out-of-balance current obtained with the probe in the boiling water. Predict the current obtained when the probe is removed and is measuring room temperature. Calculate the value of room temperature from your results. What assumptions are you making about the temperature of the probe, its resistance, and the out-of-balance current? Continued... Physics: Electricity and Electronics (H) Student Material 35

46 ACTIVITY 7 (continued) Activities Instructions (continued) Part C - Strain Gauge The hacksaw blade has been fitted with two strain gauges, one on each side of the blade. The resistance of a strain gauge changes when its shape is deformed - either stretched or compressed. When the hacksaw blade is bent, one of the strain gauges will stretch while the other one will compress. The two strain gauges are connected to one arm of a Wheatstone Bridge circuit. The strain gauge circuit should already be set up for you. Balance the Wheatstone Bridge circuit when the hacksaw blade is straight. Bend the hacksaw blade in one direction. Note the out-of-balance current. Strain gauge (back) µa Strain gauge (front) Bend the hacksaw blade in the other direction. Note the out-of-balance current. Explain how the out-of-balance current is used to show - (a) the amount of bending/strain put on the hacksaw blade (b) the direction of the bending/strain put on the hacksaw blade. 680 Resistance Board 4.5 V Physics: Electricity and Electronics (H) Student Material 36

47 ACTIVITY 8 Activities Title: Alternating Current Peak and r.m.s. values Aim: To establish a relationship between peak and equivalent direct (r.m.s.) values of voltage. Apparatus: Lab pack, 6 V battery, oscilloscope, variable resistor (0-22 Ω), V lamps, connecting leads. Circuit 1 Circuit 2 variable a.c. supply to oscilloscope to oscilloscope Instructions Set up Circuit 1. Switch the time-base on the oscilloscope OFF. Adjust the supply and the oscilloscope to give a measured peak alternating voltage of 1 V on the oscilloscope Leave Circuit 1 switched on. Set up Circuit 2. Adjust the variable resistor until the lamp is the same brightness as the lamp in Circuit 1. Use the oscilloscope to measure the direct voltage across this lamp. Repeat the measurements for peak voltages of 2 V, 3 V, 4 V and 5 V. Plot a graph of direct voltage against peak voltage. Determine the gradient of the graph. State the relationship between V d.c. and V peak using the value obtained from the gradient of the graph. Physics: Electricity and Electronics (H) Student Material 37

48 ACTIVITY 9 Activities Title: Calibration of Signal Generator Aim: To calibrate the frequency scale on a signal generator. Apparatus: Oscilloscope, signal generator, connecting leads Instructions Connect the output of the signal generator to the Y-inputs of the oscilloscope as shown. Switch the time-base ON. Set the signal generator to 10 Hz and switch on. Adjust the oscilloscope controls to obtain a recognisable waveform. Calculate the frequency from the trace on the screen. It is useful to record : the timebase setting, divisions for one cycle, and time for one cycle with the frequency in your table of readings. Repeat for other frequency values of 100 Hz, Hz and 10,000 Hz. Compare the measured and stated values of frequency. Include a column for percentage uncertainty in your table and complete this column assuming the oscilloscope is 100% accurate. State which scale on the signal generator is most prone to uncertainty. Physics: Electricity and Electronics (H) Student Material 38

49 ACTIVITY 10 Activities Title: Charge and potential difference for a capacitor (Outcome 3) Apparatus: Electrolytic capacitor (about 5000 µf), coulomb meter, voltmeter, V battery, changeover switch A B V Coulomb meter Instructions Discharge the capacitor by shorting with connecting lead. Connect the circuit and set the switch to charge the capacitor as shown in the diagram. Allow enough time for the capacitor to charge fully. Set the switch to B to fully discharge the capacitor through the coulomb meter. Repeat for other charging voltages. Use an appropriate format to show the relationship between charge and voltage. Physics: Electricity and Electronics (H) Student Material 39

50 ACTIVITY 11 Activities Title: Charging and Discharging Characteristics for a Capacitor Aim: To observe the variation of the current through, and the p.d. across, a capacitor during the charge and discharge cycles. Apparatus 2200 µf capacitor, 10 kω resistor, ammeter and voltmeter, 6 V battery stopclock Instructions Part 1 Charging Set up the circuit as shown with the switch open. Close the switch and start the stopclock. Record values of current I and p.d. V every 10 seconds until the measured p.d. becomes constant. Plot graphs of current I and p.d. V against time for the charging cycle. Describe the change in the current and p.d. during the charging cycle. Part 2: Discharging Fully charge the capacitor as in Part 1. Disconnect the leads from the battery and join them together, as shown above. Close the switch and note values for current I and p.d. V for the capacitor every 10 seconds from time t = 0. Plot graphs of current I and p.d. V against time for the discharge cycle. Explain the change in current and p.d. during the discharging cycle. Compare the direction of current during the charging and discharging cycles and explain any differences. Physics: Electricity and Electronics (H) Student Material 40

51 ACTIVITY 12 Activities Title: Response of resistance in a variable frequency a.c. circuit Aim: To establish a relationship between the current through a resistor and the frequency of the a.c. supply. Apparatus: resistor (20-50 ), signal generator, a.c. ammeter, a.c. voltmeter V A Instructions Set up the circuit as shown with the supply switched off. Set the frequency of the supply to 300 Hz. Switch on and note the ammeter reading. Repeat in steps of 50 Hz up to 800 Hz, ensuring the p.d. of the supply is kept constant. Comment on the current through the resistor as the frequency is increased State if the resistance of a resistor is affected by the frequency of the a.c. supply. State why the p.d. of the supply must remain constant. Physics: Electricity and Electronics (H) Student Material 41

52 ACTIVITY 13 Activities Title: Current and frequency in a capacitive circuit (Outcome 3) Apparatus: Signal generator, a.c. voltmeter or oscilloscope, a.c. ammeter, 4.7 µf capacitor. ~ Instructions Connect the circuit as shown in the circuit diagram. An oscilloscope may be used in place of the voltmeter. Set the output of the signal generator to about 3 V. Vary the source frequency and record readings of current and frequency using a range of 100 Hz to 1 khz. Ensure that the supply voltage remains constant. Use an appropriate format to show the relationship between current and frequency. Physics: Electricity and Electronics (H) Student Material 42

53 ACTIVITY 14 Activities Title: Uses of Capacitors - the photographic flash Aim: To show the principle behind the operation of a photographic flash. In photography, where light has to be supplied by the flash unit, the light has to be supplied in the short period of time that the shutter is open. In this time a large amount of light energy must be emitted. This is stored as electrical energy in a capacitor until it is needed. Apparatus: 1.5 µf capacitor, neon lamp, 100 k resistor, 120 d.c. supply, 1 SPST switch 1 push switch 120 V dc F 100 k S neon lamp Instructions Set up the circuit as shown. To switch on the flash unit, close switch F. To simulate the shutter opening for a very short time, close switch S and release quickly. Note what happens. Explain what happens to the p.d. across the capacitor when switch F is closed? If switch F remains closed state what will happen to the capacitor after switch S has been released and the lamp has flashed. The neon lamp requires a p.d. of 100 V across it to make it light. Explain why the lamp is able to light in this circuit. Physics: Electricity and Electronics (H) Student Material 43

54 ACTIVITY 15 Activities Title: Uses of Capacitors - d.c. power supply Aim: To show the effect of capacitors in the production of a smooth d.c. supply from an a.c. supply. In the following circuits, the 120 resistor represents the load resistor or device being driven by the supply e.g. a radio. The oscilloscope indicates the form of the output p.d. across the load resistor. Instructions diode 12 V a.c V a.c. 120 CIRCUIT 1 CIRCUIT 2 12 V a.c C V a.c µf CIRCUIT 3 C = (a) 5 µf (b) 10 µf (c) 20 µf CIRCUIT 4 Set up circuit 1 as shown. Draw the circuit and sketch the waveform displayed on the oscilloscope screen. Set up each of the other circuits, in turn. Draw the circuits and sketch the waveforms produced. Explain whether the waveform produced in circuit 2 is a.c. or d.c. Describe the effect of the capacitor on the waveforms produced in circuit 3. State what effect the size of the capacitance has on the smoothing of the supply. Physics: Electricity and Electronics (H) Student Material 44

55 INFORMATION SHEET FOR ACTIVITIES 16, 17, 18, 19, 20, 21 AND 22 Activities The Amplifier Circuit Board A diagram of the Nuffield Operational Amplifier circuit board is shown below. It is important to become familiar with the input potentiometers in order to work successfully with the op-amp circuit board. Physics: Electricity and Electronics (H) Student Material 45

56 ACTIVITY 16 Activities Title: Familiarisation - Using The Input Potentiometers Apparatus: Op-Amp Board, Dual Rail V Power Supply, Multimeter and leads. Instructions Part A: Positive (+ve) input potential. Connect up the top input potentiometer and voltmeter using the connections shown. Adjust the top input potentiometer to confirm that you can obtain a range of voltages on the voltmeter from 0 to +15 V. Repeat the above but this time connecting up the bottom input control to obtain a range of voltages from 0 to +15 V also. continued... Physics: Electricity and Electronics (H) Student Material 46

57 ACTIVITY 16 (continued) Activities Instructions (continued) Part B: Negative (-ve) input potential. Connect up the top input potentiometer and voltmeter using the connections shown below. Negative supply rail -V s V Zero volt rail 0V Adjust the top input potentiometer to confirm that you can obtain a range of voltages on the voltmeter from 0 to -15 V. Repeat the above but this time connecting up the bottom input control to obtain a range of voltages from 0 to -15 V also. Physics: Electricity and Electronics (H) Student Material 47

58 ACTIVITY 17 Activities Title: The Inverting Amplifier Apparatus: Op-Amp Board, Dual Rail V Power Supply, Multimeter and leads. The circuit diagram for the circuit and results table are shown below. R f ( ) 100K 100K 100K 100K R 1 ( ) Instructions 10K 10K -0.8 Connect up the top input potentiometer and two voltmeters using the connections shown. The circuit board connections shown above are for positive (+ve) input potentials and a gain of 10, since R 1 = 10 k and R f is set to 100 k. Connect R 1 at 10 k and R f at 100 k. Set V 1 to 1.2 V. Measure the output voltage and record in your own table. Repeat this measurement for the other values of V 1 and R f shown in the sample table Complete the last two columns of your table. Write a conclusion to your experiment including a comment on the polarity of V 0 compared to V 1. 10K 10K 10K 10K 10K 10K 10K 10K 10K 10K V 1 (V) V 0 (V) R f R 1 V 0 V 1 Physics: Electricity and Electronics (H) Student Material 48

59 ACTIVITY 18 Activities Title: Saturation Apparatus: Op-Amp Board, Dual Rail V Power Supply, Multimeter and leads. R f 100K R 1 V 1 10K - V 0 V + V Instructions Connect up the following circuit using the top input potentiometer and two voltmeters from the circuit diagram below. This circuit is identical to the circuit used in Activity 17. Set the value of the input voltage, V 1, to the values shown in the tables and record the corresponding value of the output voltage, V 0 in your own table. Graph the results of both tables from your experiment on axes similar to those below. 0V State the gain setting of the inverting amplifier used? Describe what happens to the value of the output voltage, V 0, as the input voltage, V 1, is increased. State the maximum output voltages available from the amplifier. Physics: Electricity and Electronics (H) Student Material 49

60 ACTIVITY 19 Activities Title: Square Wave Generator Apparatus: Op-Amp Board, Dual Rail V Power Supply, Multimeter and leads. Instructions Connect the op-amp board as an inverting amplifier, using the resistor values shown. Connect the signal generator to the input of the inverting amplifier. Connect the oscilloscope across the inputs of the op-amp, AB. Set the signal generator to approximately 3 V at a frequency of 200 Hz. Adjust the Y-gain and time-base controls of the oscilloscope until you obtain a steady wave pattern. Accurately sketch the wave pattern produced. Now connect the oscilloscope across the outputs of the op-amp, CD. Without adjusting any of the controls on the oscilloscope or signal generator, sketch the wave pattern produced at the output. Accurately sketch the wave pattern produced this time. State how the phase of the output potential, V 0, compares to that of the input potential, V 1. Compare the frequency of the output potential, V 0, to V 1. State the gain of the amplifier in this circuit. Hence state the minimum value of V 1 that will produce a saturated output potential, V 0. As the input potential from the signal generator, V 1, is increased, explain what happens to the output potential, V 0. Physics: Electricity and Electronics (H) Student Material 50

61 ACTIVITY 20 Activities Title: The Differential Amplifier Apparatus: Op-Amp Board, Dual Rail V Power Supply, Multimeter and leads., 100 kω and 10 kω resistor panels. The circuit diagram for the circuit is shown below and the results table is given on the following page. R 1 - V 1 R 2 V 0 V 2 R 3 + R f In this circuit, R f and R 3 will always be taken as 100 k due to the limitations of the board. Instructions Connect up the two input potentiometers using the connections shown. The circuit board is shown for positive (+ve) input potentials with a gain of 1, but negative (-ve) input potentials are also used as are different settings for the gain. V 0V (Continued...) Physics: Electricity and Electronics (H) Student Material 51

62 ACTIVITY 20 (Continued) Activities Rf & R3 R1 & R2 Rf R1 V2 V1 V2-V1 ( ) ( ) (V) (V) (V) (V) (V) V0 Rf R1 (V2-V1) 100K 100K K 100K K 100K K 100K K 10K K 10K K 10K K 10K Instructions (continued) Set R f and R 3 at 100 kω. For each of the values of R 1 and R 2, V 2 and V 1 given on the sample table record the output voltage V 0 in your own table. Complete the other columns in your table. Write a conclusion, including a comment on the polarity of V 0 compared to (V 2 -V 1 ). Comment on the maximum gain you could obtain if V 1 = 1 V and V 2 = 1.5 V. Physics: Electricity and Electronics (H) Student Material 52

63 ACTIVITY 21 Activities Title: The Inverting Amplifier used to Control Heavier Loads Aim: To investigate the use of a transistor and relay in a control circuit The circuit below uses a transistor, relay and op-amp to control high current devices. Some devices, such as motors or heaters, require a current which is too large for small transistors to supply. The transistor can, however, be used to energise the coil of a relay which can then switch on a separate supply to the high current device. Apparatus: op-amp board, 2 5 V d.c supplies, n-p-n transistor board, relay, 6 V motor, ammeter. +Vs 100 k Reed Relay +5 V M 5 V supply Rv 0-10k V1 1 M V 0V Instructions Connect up the circuit. Gradually increase the input voltage, V 1. At some point, the relay contacts should close and the motor will work. Redraw the circuit, marking in the positions of ammeters required to measure (a) the output current from the op-amp (b) the current in the relay coils (c) the current in the motor. Ensure your circuit diagram is correct, then connect up an ammeter in the correct positions and note the three current values above. State the value of the gain of this circuit. If the n-p-n transistor requires 0.7 V to switch on, state the value of V 1 required to operate the reed relay and also the motor. Explain the operation of this circuit. Physics: Electricity and Electronics (H) Student Material 53

64 ACTIVITY 22 Activities Title: The Differential Amplifier used to Monitor Light Level Aim: To investigate the use of a differential amplifier with a Wheatstone Bridge to monitor light level. The circuit below uses a LDR as a resistive sensor in a Wheatstone Bridge circuit. With the op-amp, it can be used to monitor light level changes. The two potential dividers, R 1, R 2 and R 3, R 4 are connected as a Wheatstone Bridge circuit. Any out of balance potential difference from the Wheatstone Bridge is applied across the inputs of the op-amp. The resistance of R 4 can be adjusted to balance the bridge at any desired light level. The output of the op-amp is therefore proportional to the change in resistance of the LDR caused by the change in light level. Apparatus: op-amp board, LDR panel, 2 10 kω resistor panels. +Vs R1 10 k R3 10 k 100 k 10 k 10 k - + R2 R k 100 k V 0 V 0 V Instructions Ideally, this experiment should be carried out in a darkened room. Connect up the circuit shown. Place a 60 W lamp facing the LDR at a distance of 50 cm, and adjust R 4 until the voltmeter reads zero. Move the lamp closer, 5 cm at a time, and record the output voltage readings. Plot a graph of output voltage against distance. Physics: Electricity and Electronics (H) Student Material 54

65 PROBLEMS Activities Revision of Circuits 1. If a current of 40 ma passes through a lamp for 16 s, how much charge has passed any point in the circuit? 2. A lightening flash lasted for 1 ms. If 5 C of charge was transferred during this time, what was the current? 3. The current in a circuit is A. How long does it take for 500 C of charge to pass any given point in the circuit? 4. What is the p.d. across a 2 k resistor if there is a current of 3 ma flowing through it? 5. Find the readings on the meters in the following circuits. (a) 10 V A (b) 12 V A (c) A 15 6 V V V 6. Find the unknown values of the following resistors. (a) (b) 40 V I = 2 A A 40 V A 5 R =? 4 R =? V Physics Support Material: Electricity and Electronics (H) Student Material 55

66 Answers 7. Find the total resistance of the following combinations. (a) (b) (c) (d) (e) (f) If the ammeter reads 2 ma, find the voltmeter reading. 3 k 5 k A V Physics: Electricity and Electronics (H) Student Material 56

67 Answers 9. Calculate the power in each of the following cases. (a) A 12 V accumulator delivering 5 A. (b) A 60 Ω heater with a 140 V supply. (c) A 5 A current in a 20 heater coil. 10. An electric kettle has a resistance of 30. (a) What current will flow when it is connected to a 230 V supply? (b) Find the power rating of the kettle. 11. A 15 V supply produces a current of 2 A for 6 minutes. How much energy is supplied in this time? 6 V 12. Find the readings on the A ammeters and the voltmeter. 6 V Assuming each of the four cells cell to be identical, find: (a) the reading on the ammeter (b) the current through the 20 resistor (c) the voltage across the 2 resistor. 2 6 V A A coil has a current of 50 ma flowing through it when the applied voltage is 12 V. Find the resistance of the coil. 15. Write down the rules which connect the (a) potential differences and (b) the currents in series and parallel circuits. 16. Draw the symbol for a fuse, diode, capacitor, variable resistor, battery and a d.c. power supply. 17. What is the name given to the circuit opposite. Write down the relationship between V 1, V 2, R 1 and R V R1 V1 R2 V2 18. Find the values of V 1 and V 2 of the circuit in question 17 if: (a) R 1 = 1 kω R 2 = 49 kω (b) R 1 = 5 kω R 2 = 15 kω. Physics: Electricity and Electronics (H) Student Material 57

68 Answers 19. Explain what would happen to the readings on V1 and V2 if light was shone onto the L.D.R. 10 V R1 V1 Suppose the L.D.R. was replaced with a thermistor which was then heated. Explain the effect on the readings. V2 20. (a) What would be the polarity of A and B when connected to a 5 V supply, so that the LED would light? A R (b) What is the purpose of R in the circuit shown above? (c) If the L.E.D. rating is 200 ma at 1.5 V, find the value of R. B Physics: Electricity and Electronics (H) Student Material 58

69 Answers ELECTRICY AND ELECTRONICS PROBLEMS Electric fields and resistors in circuits 1. Draw the electric field pattern for the following charges: (a) (b) (c) 2. Describe the motion of the small test charges in each of the following fields. (a) + test charge (b) + test charge + - (c) Q (d) Q An electron volt is a unit of energy. It represents the change in potential energy of an electron which moves through a potential difference of 1 volt. If the charge on an electron is 1.6x10-19 C, what is the equivalent energy in joules? 4. Mass of an electron = kg Charge on an electron = C The electron shown opposite is accelerated across a p.d. of 500 V. (a) How much electrical work is done? (b) How much kinetic energy has it gained? (c) What is its final speed? e +500 V Electrons are fired from an electron gun at a screen. The p.d. across the gun is 2000 V. After leaving the positive plate the electrons travel at a constant speed to the screen. Assuming the apparatus is in a vacuum, at what speed will the electrons hit the screen? Physics: Electricity and Electronics (H) Student Material 59

70 Answers 6. What would be the increase in speed of an electron accelerated from rest by a p.d. of 400 V? 7. An -ray tube is operated at 25 kv and draws a current of 3 ma. (a) Calculate (i) the kinetic energy of each electron as it hits the target (ii) the velocity of impact of the electron as it hits the target (iii) the number of electrons hitting the target each second. (mass of electron = kg charge on electron = C) (b) What happens to the kinetic energy of the electrons? 8. Sketch the paths which (a) an a-particle, (b) a b-particle, and (c) a neutron, would follow if each particle entered the given electric fields with the same velocity. (Students only studying this unit should ask for information on these particles). 9. State what is meant by (a) the e.m.f. of a cell (b) the p.d. between 2 points in the circuit. 10. Prove the expressions for the total resistance of resistors in (a) a series and (b) a parallel circuit. 11. In the circuit below: (a) what is the total resistance of the circuit (b) what is the resistance between X and Y (c) find the readings on the ammeters (d) calculate the p.d. between X and Y (e) what power is supplied by the battery? 3 12 V X A 1 A Y 12. The circuit opposite uses the 230 V alternating mains supply. Find the current flowing in each resistor when: (a) switch S is open (b) switch S is closed. 230 V 12 8 S 24 Physics: Electricity and Electronics (H) Student Material 60

71 Answers 13. An electric cooker has two settings, high and low. It takes 1 A at the low setting and 3 A at the high setting. R1 230 V R2 (a) Find the resistance of R 1 and R 2. (b) What is the power consumption at each setting? 14. (a) Find the value of the series resistor which would allow the bulb to operate at its normal rating. (b) Calculate the power dissipated in the resistor. 15. In the circuit below, r represents the internal resistance of the cell and R represents the external resistance of the circuit. r When S is open, the voltmeter reads 2.0 V. When S is closed, it reads 1.6 V and the ammeter reads 0.8 A. V (a) What is the e.m.f. of the cell? (b) What is the terminal potential difference when S is closed? S (c) Calculate the values of r and R. (d) If R was halved in value, calculate the new readings on the ammeter and voltmeter. R A 16. The cell in the diagram has an e.m.f. of 5 V. The current through the lamp is 0.2 A and the voltmeter reads 3 V. Calculate the internal resistance of the cell. r V 17. A cell of e.m.f. 4 V is connected to a load resistor of 15 W. If 0.2 A flows round the circuit, what must be the internal resistance of the circuit? A Physics: Electricity and Electronics (H) Student Material 61

72 Answers 18. A signal generator has an e.m.f. of 8 V and internal resistance of 4. A load resistor is connected to its terminals and draws a current of 0.5 A. Calculate the load resistance. 19. (a) What will be the terminal p.d. across the cell in the circuit below. (b) (c) Will the current increase or decrease as R is increased? Will the terminal p.d. then increase or decrease? Explain your answer. 20. A cell with e.m.f. 1.5 V and internal resistance 2 is connected to a 3 Ω resistor. What is the current? 21. A pupil is given a voltmeter and a torch battery. When he connects the voltmeter across the terminals of the battery it registers 4.5 V, but when he connects the battery across a 6 resistor, the voltmeter reading decreases to 3.0 V. (a) (b) Calculate the internal resistance of the battery. What value of resistor would have to be connected across the battery to reduce the voltage reading to 2.5 V. 22. In the circuit shown, the cell has an e.m.f. of 6.0 V and internal resistance of 1. When the switch is closed, the reading on the ammeter is 2 A. What is the corresponding reading on the voltmeter? 23. In order to find the internal resistance of a cell, the following sets of results were taken. Voltage (V) Current (A) (a) (b) (c) (d) Draw the circuit diagram used. Plot a graph of these results and from it determine (i) the e.m.f. (ii) the internal resistance of the cell. Use the e.m.f. from part (b) to calculate the lost volts for each set of readings and hence calculate 6 values for the internal resistance. Calculate the mean value of internal resistance and the approximate random uncertainty. Physics: Electricity and Electronics (H) Student Material 62

73 Answers 24. The voltage across a cell is varied and the corresponding current noted. The results are shown in the table below. Voltage (V) Current (A) Plot a graph of V against I. (a) What is the open circuit p.d? (b) Calculate the internal resistance. (c) Calculate the short circuit current. (d) A lamp of resistance 1.5 is connected across the terminals of this supply. Calculate (i) the terminal p.d. and (ii) the power delivered to the lamp. 25. Calculate the p.d. across R 2 in each case. +5 V +5 V (a) (b) (c) +5 V 2 k R 1 4 k 500 t 8 k R 2 1 k R R 2 0 V 0 V 0 V 26. Calculate the p.d. across AB (voltmeter reading) in each case. (a) (b) (c) +12 V +5 V +10 V 3 k A V 9 k B 5 k A 10 k V B 3 k A V 6 k B 3 k 3 k 2 k 8 k 2 k 4 k 0V 0V 27. (a) Calculate the reading on the voltmeter. 0 V 0V +9 V (b) What alteration could be made to balance the bridge circuit? 6 k A 9 k V 3 k B 6 k Physics: Electricity and Electronics (H) Student Material 63

74 Answers 28. Three pupils are asked to construct balanced Wheatstone bridges. Their attempts are shown V +1.5 V +1.5 V 5 A 10 9 A 12 7 A 14 G G G 10 B 5 12 B B 20 Pupil A Pupil B Pupil C One of the circuits gives a balanced Wheatstone bridge, one gives an off - balance Wheatstone bridge and one is not a Wheatstone bridge. (a) Identify each circuit. (b) How would you test that balance has been obtained? (c) In the off balance Wheatstone bridge ; (i) calculate the potential difference across the galvanometer. (ii) in which direction will electron current flow through the galvanometer. 29. Calculate the value of the unknown resistor in each case. 2 V 2 V 120 x 4 k 15 k G G k x 30. The circuit shown opposite is balanced. 10 k 25 k G 3.6 k x +1.5 V 2 V (a) What is the value of resistance? (b) Will the bridge be unbalanced if (i) a 5 resistor is inserted next to the 10 resistor (ii) a 3 V supply is used. G R (c) What is the function of resistor R and what is the disadvantage of using it as shown? 5 X Physics: Electricity and Electronics (H) Student Material 64

75 31. The following Wheatstone bridge circuit is used to monitor the mechanical strain on a girder in an oil rig V Answers Strain gauges (a) (b) Explain how the circuit can be used to monitor the strain. Sketch the graph of current through the galvanometer against the strain. R3 G R4 32. An automotive electrician needed to accurately measure the resistance of a resistor. She set up a circuit using an analogue milliammeter and a digital voltmeter. The two meter readings were: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) What are the readings? What is the nominal resistance calculated from these readings? Which reading is likely to cause the greatest uncertainty? What is the smallest division on the milliammeter? What is the absolute uncertainty on the milliammeter? What is the absolute uncertainty on the voltmeter? What is the percentage uncertainty on the milliammeter? What is the percentage uncertainty on the voltmeter? Which is the greatest percentage uncertainty? What is the percentage uncertainty in the resistance? What is the absolute uncertainty in the resistance? Express the final result as (resistance ± uncertainty)ω Round both the result and the uncertainty to the relevant number of significant figures or decimal places. Physics: Electricity and Electronics (H) Student Material 65

76 Answers Alternating Current and Voltage 1. (a) What is the peak voltage of the 230 V mains supply? (b) The frequency of the mains supply is 50 Hz. How many times does the voltage fall to zero in one second. 2. The circuit below is used to compare the a.c. and d.c. supplies when the lamp is at the same brightness with each supply. The variable resistor is used to adjust the brightness of the lamp. A B (a) (b) (c) Explain how the brightness of the lamp is changed using the variable resistor. What additional apparatus would you use to ensure the brightness of the lamp was the same for each supply? In the oscilloscope traces shown below diagram 1 shows the voltage across the lamp when the switch is in position B and diagram 2 shows the voltage when the switch is in position A. Y Gain set to 1 V cm -1 From the oscilloscope traces, how is the root mean square voltage numerically related to the peak voltage. (d) Redraw diagrams 1 and 2 to show what would happen to the traces if the time base was switched on. 3. The root mean square voltage produced by a low voltage power supply is 10 V r.m.s. (a) Calculate the peak voltage of the supply. (b) If the supply was connected to an oscilloscope, Y-gain set to 5 V cm -1 with the time base switch off, describe what you would see on the screen. Physics: Electricity and Electronics (H) Student Material 66

77 Answers 4. (a) A transformer has a peak output voltage of 12 V. What is the r.m.s. output voltage? (b) A vertical line 6 cm long appears on an oscilloscope screen when the Y gain is set to 20 V cm -1. Calculate: (i) the peak voltage of the input (ii) the r.m.s. voltage of the input. 5. The following trace appears on an oscilloscope screen when the time base is set at 2.5 ms cm -1. (a) (b) What is the frequency of the input including the uncertainty to the nearest Hz? Sketch what you would see on the screen if the time base was changed to (i) 5 ms cm -1 (ii) 1.25 ms cm An a.c. input of frequency 20 Hz is connected to an oscilloscope with time base set at 0.01 s cm -1. What would be the wavelength of the waves appearing on the screen? Capacitance 7. A 50 µf capacitor is charged till the voltage across its plates reaches 100 V. (a) (b) How much charge has been transferred from one plate to the other? If it was discharged in 4 milliseconds, what would be the average current? 8. A capacitor holds a charge of C when it is charged to 600 V. What is the value of the capacitor? 9. A 30 µf capacitor holds a charge of C. (a) What is the voltage that it is charged to? (b) If the tolerance of the capacitor is ± 5 µf, express this uncertainty as a percentage. (c) What is the greatest voltage which could occur across the plates of the capacitor? 10. A 15 µf capacitor is charged from a 1.5 V battery. What charge will be stored on the plates? 11. (a) A capacitor has a voltage of 12 V across its plates and stores a charge of C. Calculate its capacitance. (b) A 0.1 µf capacitor is connected to a 8 volt direct supply. How much charge will it store? Physics: Electricity and Electronics (H) Student Material 67

78 12. Using the circuit below a capacitor is charged at a constant charging current of 2.0x10-5 A. Answers The time taken to charge the capacitor is 30 s and during this time the voltage across the capacitor rises from 0 V to 12 V. What is the capacitance of the capacitor? 13. A 100 µf capacitor is charged from a 20 V supply. (a) How much charge is stored? (b) How much energy is stored in the capacitor? 14. A 30 µf capacitor stores C of charge. How much energy is stored in the capacitor? 15. The circuit below is used to investigate the charging of a capacitor. A 12 V 10 k 2000 µf (a) (b) (c) (d) What is the response of the ammeter when switch S is closed? How can you tell when the capacitor is fully charged? What would be a suitable range for the ammeter? If the 10 k resistor is replaced by a larger resistor, what will be the effect on the maximum voltage across the capacitor? Physics: Electricity and Electronics (H) Student Material 68

79 Answers 16. In the circuit below the neon lamp flashes at regular intervals. The neon lamp requires a potential difference of 100 V across it before it will conduct and flash. It continues to glow until the potential difference across it drops to 80 V. While lit, its resistance is very small compared with R. R 120 V dc C (i) (ii) Explain why the neon bulb flashes. Suggest two methods of decreasing the flash rate. 17. In the circuit below the capacitor C is charged with a steady current of 1mA by carefully adjusting the variable resistor R. A 9 V dc C V The voltmeter reading is taken every 10 seconds. The results are shown in the table. Time p.d.(v) (a) Plot a graph of charge against voltage for the capacitor and hence find its capacitance (use graph paper). (b) Calculate the capacitance for each of the readings (ignoring readings for t = 0). (c) Calculate the mean capacitance and the approximate random uncertainty in the mean to two decimal places. Physics: Electricity and Electronics (H) Student Material 69

80 Answers 18. The circuit below is used to charge and discharge the capacitor (a) What position should the switch be set (i) to charge and (ii) to discharge the capacitor? (b) Draw graphs of V R against time for the capacitor charging and discharging, and of V C against time for the capacitor charging and discharging. (c) If the capacitor has capacitance of 4.0 µf and the resistor has resistance of 2.5 M calculate: (i) the maximum charging current in the circuit above (ii) the maximum charge stored by the capacitor when fully charged in the above circuit M 3 V 3 µf (a) (b) For the above circuit draw graphs of (i) V C against time during charging and (ii) V A against time during charging. Calculate the final voltage across the capacitor and the final charged stored by it. 20. For each of the circuits below state what happens to the current flowing when the frequency is (i) increased and (ii) decreased. Physics: Electricity and Electronics (H) Student Material 70

81 Answers 21. In the circuit below the signal generator is set at 6.0 Vr.m.s., 1000 Hz. The lamp operates normally. (a) (b) Explain why the lamp can operate normally when the plates of the capacitor are separated by an insulator. What happens to the brightness of the lamp when the frequency of the signal generator is increased. Why does this happen? 22. For each of the following circuits sketch a graph of current against frequency. A A Signal generator Diagram A Diagram B 23. A B Signal generator The supply frequency to the above circuit is increased from a very low frequency, while the supply voltage remains constant. What will happen to the brightness of lamp A and B? Physics: Electricity and Electronics (H) Student Material 71

82 Answers Analogue Electronics 1. Calculate the values of V 1 and V 2 in the circuit shown for the following situations. (a) V S = 12 V R 1 = 40 k R 2 = 20 k (b) V S = 6 V R 1 = 150 k R 2 = 30 k (c) V S = 10 V R 1 = 3 k R 2 = 5 k Vs R 2 V 2 2. Calculate the values of R 1 in the following circuits. R 1 V 1 (a) (b) (c) 5 k 1 k 1 k 4 V 2 V 12 V R 1 V 1 3 V R 1 V V R 1 V V 3. Calculate the values of V 1 and V 2 in the circuits shown. (a) (b) (c) +1.5 V +1.5 V +5 V 15 k V k V k V 2 3 k V k V k V 1 0 V 0 V 0 V 4. Explain what happens to the value of V 1 in each of the following situations - (a) brightness increasing (b) temperature increasing (c) brightness decreasing V +1.5 V +1.5 V 0 V V 1 0 V t V 1 0 V V 1 Physics: Electricity and Electronics (H) Student Material 72

83 Answers 5. The thermistor shown has a resistance of 31 k at 30 C and 35 k at 25 C. (a) (b) (c) (d) (e) If the variable resistor is set at 5 k, calculate the input voltage to the transistor in each case. Hence, explain how the circuit shown works. Explain the purpose of the variable resistor. Suggest a possible use for the circuit. Why is the relay switch necessary? 6. Draw a circuit diagram similar to the circuit of Question 5 that would switch on a mains voltage lamp when the ambient light level drops below a certain level. 7. The circuits shown in questions 5 & 6 could use a different type of transistor called an n-channel enhancement MOSFET. Draw the symbol for this transistor and label each terminal. 8. The following signals are fed into an inverting amplifier with a gain of 5. Draw the expected output trace. (a) (b) (c) (d) (e) (f) Physics: Electricity and Electronics (H) Student Material 73