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GRADE 12A: Physics 5 UNIT 12AP.5 13 hours Electrostatic charge and force About this unit Previous learning Resources This unit is the fifth of seven units on physics for Grade 12 advanced. To meet the expectations of this unit, students should already know that opposite charges attract but like charges repel each other. They should know that electric current is the rate of flow of charged particles, define charge and the coulomb, and solve problems using the relationship Q = It. They should understand the construction of capacitors and their use in electrical circuits. They should be able to describe an electric field as an example of a field of force, know that electric field strength can be defined as force per unit positive charge, and define potential difference and the volt. They should understand and be able to use the concept of a gravitational field as an example of a force field and define gravitational field strength as force per unit mass, and should recall and be able to use Newton’s law of universal gravitation in the form F = G(m1m2) ⁄ r2. The main resources needed for this unit are: You can also supplement the activities with appropriate tasks and exercises from your school’s textbooks and other resources. Expectations Students should understand, use and spell correctly: Introduce the unit to students by summarising what they will learn and how this builds on earlier work. Review the unit at the end, drawing out the main learning points, links to other work and real world applications. By the end of the unit, students apply Coulomb’s law to charged particles in air, solve problems related to potential difference and potential energy and recognise the similarities between electric and gravitational fields. They understand capacitors and solve problems relating capacitance to voltage and current. • electrical potential, potential gradient, potential difference, electron-volt The unit is designed to guide your planning and teaching of physics lessons. It provides a link between the standards for science and your lesson plans. The teaching and learning activities should help you to plan the content and pace of lessons. Adapt the ideas to meet your students’ needs. For consolidation activities, look at the scheme of work for Grades 10A and 11A. • overhead projector (OHP) • double flame probe • ball, 10–20 cm diameter, coated with conductive paint • conductive paper (sometimes known as resistive paper) • electrolytic capacitor cut open to reveal its construction • gas discharge tube connected to vacuum pump • Van der Graaff generator, signal generator, cathode-ray oscilloscope • selection of circuit components and power supplies Key vocabulary and technical terms • electric field, Coulomb’s law • equipotential line, equipotential surface • capacitor, capacitance Students who progress further understand and use the concept of electric field. They can define electrical potential, relate field strength to potential gradient and solve problems involving potential energy and potential difference. They derive and use formulae for capacitors in series and in parallel, and relationships involving energy stored in a capacitor. 543 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Standards for the unit 13 hours 3 hours Uniform electric field 3 hours Field and potential 3 hours Coulomb’s law and non-uniform fields 4 hours Capacitors SUPPORTING STANDARDS 10A.30.3 Describe an electric field as an example of a field of force and know that electric field strength can be defined as force per unit positive charge and that an electric field can be represented by means of field lines. 10A.30.2 Know that … opposite charges Unit 12AP.5 CORE STANDARDS Grade 12 standards 12A.29.1 Recall and use E = V ⁄ d to calculate the field strength of a uniform field between charged parallel plates, calculate the forces on charges in uniform electric fields and describe the effect of a uniform electric field on the motion of charged particles. 12A.29.2 State and apply Coulomb’s law relating to the force between two or more attract but like charges repel each other. charged particles in air and on the field strength due to a charged particle. 10A.31.2 Define potential difference and the 12A.29.3 Define electrical potential at a point in an electric field, relate field strength volt ... 12A.25.3 Understand and use the concept of a EXTENSION STANDARDS to potential gradient, solve problems involving potential energy and potential difference and know and use the term electron-volt. 12A.29.4 Recognise the similarities between electrical and gravitational fields. gravitational field as an example of a force field and define gravitational field strength as force per unit mass. 12A.25.4 Recall and use Newton’s law of universal gravitation in the form F = G(m1m2) ⁄ r2 and relationships derived from it. 11A.30.1 Demonstrate an understanding of the construction of capacitors and their use in electrical circuits. 12A.29.5 Demonstrate an understanding of the construction and use of capacitors in electrical circuits, and of how the charge is stored. 12A.29.6 Define capacitance and solve problems using C = Q ⁄ V; derive and use formulae for capacitors in series and in parallel. 10A.31.1 Know that electric current is the rate of flow of charged particles, define charge and the coulomb, and solve problems using the relationship Q = It. 12A.29.7 Define and use the relationship between the energy stored in a capacitor, its charge and the potential difference between its plates. 544 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Activities Unit 12AP.5 Objectives Possible teaching activities 3 hours Using electric fields Uniform electric field To set the scene for this unit and to help review work from earlier grades, divide students into small groups and set each the task of using the Internet and other resources to research one application of electric fields. Where possible, they should collect (for later discussion) data on the strengths of the fields used and the potential differences used to produce them. Suitable examples include: Recall and use E = V ⁄ d to calculate the field strength of a uniform field between charged parallel plates, calculate the forces on charges in uniform electric fields and describe the effect of a uniform electric field on the motion of charged particles. Notes ICT opportunity: Use of the Internet. Enquiry skills 12A.1.6, 12A.1.8 School resources Use this column to note your own school’s resources, e.g. textbooks, worksheets. • ink-jet printing; • LCD displays; • photocopying; • particle accelerators (e.g. LINACs and/or cyclotrons); • electrostatic dust precipitators; • electrostatic spraying (e.g. crop spraying, paint spraying). If necessary, remind students that an electric field is a region where a charged object experiences a force. Ask each group to prepare a poster summarising their findings, giving particular emphasis to the role played by electric fields and including an acknowledgment of the sources consulted. Display the posters and allow time for students to view and talk about them. Uniform electric field By means of some quick-fire questions, ascertain how much students recall from work on electric fields in earlier grades. By suitable questioning, remind them how electric field strength is defined, and how this can be expressed in SI units of N C–1. Demonstrate these two examples of a uniform electric field. • Support two metal plates vertically on insulating stands so that they are parallel and a few centimetres apart. Connect them to the terminals of an EHT supply and set the voltage to a few kilovolts. Fix a small piece of thin flexible metal foil to the end of an insulating rod. Charge the foil by touching it on one of the plates. Using the rod, move the foil around within the space between the plates; note the size and direction of its deflection. Safety: When using an EHT supply, ensure that the safety resistor is connected and that no one can come into electrical contact with the terminals. • Pour some glycerol into a transparent, flat-bottomed container, float grass seeds or rice grains on its surface and place it on an OHP. Using flexible leads, connect two metal strips to either side of the spark gap of a piezo-electric gas lighter. Place the strips in the glycerol so that they are parallel, and use the lighter to produce an electric field within the glycerol. Observe the electric field lines revealed by the grains. Use suitable questioning to remind students that the field direction is defined to be that of the force on a positive charge. Also remind them how a field can be represented by electric field lines, and how field strength is related to the spacing of the lines: the closer the lines, the stronger the field. Ask students to suggest how the strength of an electric field between two parallel metal plates might be controlled. Drawing on their own researches in the previous activity, and by discussing the two examples demonstrated, they will probably be able to suggest that increasing the voltage and/or moving the plates closer together would produce a stronger field. 545 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities On the board or OHP, show students how potential difference and distance are related to field strength in the case of a uniform field produced by connecting a potential difference V between two parallel plates separated by a distance d. Remind them of the term potential difference (encourage them to use it in place of the looser ‘voltage’) and of the relationship between change, pd and energy. Show that, if a charge q moves through a pd V, then the work done is W = qV. Then remind them that the work done by a force F moving something through a distance d is W = Fd and show that V ⁄ d = F ⁄ q = E. Notes School resources This discussion also relates to Standard 10A.25.1 Students should be able to show that 1 N C–1 = 1 V m–1, and hence that either unit can be used to express electric field strength. Provide numerical and algebraic examples that allow students to practise using relationships involving force, charge and electric field expressed in N C–1 and V m–1. Potential gradient Set up and demonstrate a double flame probe as shown in the diagram on the right. Explain the probe’s operation to students and establish the following points. • The small flames at the needle tips ionise the air, allowing charge to flow until there is no potential difference between the needle tips and their surroundings. • The deflection of the gold-leaf electroscope indicates the potential difference, V, between its plate and case. Connect the plate and case to an EHT supply and calibrate the electroscope by noting the deflection of the leaf for various pds. (Shine a lamp through the electroscope so that a shadow of the leaf is cast on the translucent casing. Use an erasable felt-tip pen to mark positions of the shadow.) • The probe allows the field strength to be calculated: E = V ⁄ d, where d is the separation of the needle-tips. • In a uniform field such as that between two parallel plates connected to a potential difference, the potential gradient V ⁄ d is the same everywhere in the field. • The probe also reveals the direction of the field: when the needle tips are aligned along a field line, the deflection of the gold leaf is maximum, and, if the probes are at right-angles to the field, the deflection is zero. Source: Salters Horners Advanced Physics A2 Teacher and Technician Resource Pack, Heinemann Educational. © 2001 University of York Science Education Group. Use two parallel plates and an EHT supply to produce a uniform field. Show that the field as indicated by the flame probe is indeed uniform and acts at right-angles to the plates. Ask students to produce a brief written account of this demonstration. 546 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities 3 hours Acceleration and ionisation Field and potential Carry out some demonstrations that show gas ‘discharge’ (i.e. ionisation by an electric field) and discuss them with the class. Establish the following points. Define electrical potential at a point in an electric field, relate field strength to potential gradient, solve problems involving potential energy and potential difference and know and use the term electronvolt. • Within any gas, there are always a few charged particles (i.e. electrons and positive ions). • In an electric field, the charged particles accelerate. • The accelerated particles collide with other particles in the gas. • If the collisions are sufficiently energetic, energy is transferred to electrons within atoms and molecules, which are then said to be excited. • If the collisions are still more energetic, electrons can be dislodged from neutral atoms and molecules, causing ionisation. • Excited electrons lose their excess energy by emitting visible light. • Electrons liberated during ionisation undergo acceleration in the electric field, giving rise to further excitation and ionisation (i.e. a discharge or spark is produced). Notes School resources Suitable demonstrations include the following. • An air-filled tube that can be connected to an EHT supply and a vacuum pump. Begin with the tube containing air at normal atmospheric pressure: the EHT fails to produce a discharge. With the EHT still connected, evacuate air from the tube until a discharge is produced (the gas will glow pink). • A Van der Graaff generator producing a spark between the main dome and a nearby small sphere. • A fluorescent lighting tube connected in a domestic light fitting. Discuss why a discharge or spark occurs more readily in low-pressure gas. Establish that reducing the pressure reduces the gas density, and hence increases the average distance between particles. In a high-pressure gas, accelerated particles can only move a short distance before being involved in a collision and transferring some of their energy. If the pressure is reduced, the accelerated particles can move further and hence acquire more energy between collisions. On the board or OHP, remind students how the energy acquired by a charged particle accelerating in an electric field can be related to the field strength E and to the distance travelled d. Establish that when a particle of charge q moves through a distance d along the direction of the field, it moves through a potential difference V = Ed so that it acquires kinetic energy Ek = qV = qEd. Explain that, when dealing with the acceleration of individual ions and electrons, it is convenient to express charge in units of the electron charge, e, and energy in electron-volts (eV). Students should be able to show that 1 eV = 1.60 × 10–19 J. Explain that the eV is a non-SI unit of energy, but that it is very widely used to express small energies and is not restricted to energies of electrically accelerated charged particles. Provide students with plenty of examples that allow them to practise using the electron-volt as an energy unit. 547 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Potential at a point In a whole-class discussion and demonstration, introduce the concept of potential at a point, first within an electric circuit and then within an electric field. Connect a long potentiometer wire to a battery. Use a voltmeter to measure the pd between several pairs of points. Point out that the term potential difference implies a difference between two values of a quantity called potential. Explain that, in a DC electric circuit, it is conventional to define the zero of potential as being at the negative battery terminal, so that all other points in the circuit are at a positive potential. Go on to explain that this choice is arbitrary, and that any point in the circuit could in principle be defined as the zero without altering the potential differences measured anywhere in the circuit. Remind students of the relationship between pd and energy, and establish that a pd of 1 V corresponds to an energy difference of 1 J for 1 C (1 coulomb) of charge. Establish that electrical potential at a point is thus the potential energy of 1 C of charge at that point. Remind students that, like the zero level of electrical potential, the choice of zero level of gravitational potential energy is also arbitrary: in both cases, we only ever measure differences rather than absolute values. Provide plenty of examples that allow students to practise using the relationships between pd and energy and describing them using appropriate terminology. Place a sheet of conductive paper on a pin-board. Attach a straight metal strip close to each end of the paper so that there is good electrical contact between paper and metal. Connect the metal strips to a low-voltage battery to produce an electric field within the paper. Connect one terminal of a voltmeter to the negative strip, and show students how to use a flying lead connected to the other terminal to identify points within the paper that are at a potential of, say, 1 V relative to the negative strip. Introduce the terms equipotential line and equipotential surface and establish that these must always be at right-angles to electric field lines. Suitable field configurations include the following: Ask students to work in pairs using conductive paper to explore the equipotential lines in various two-dimensional electric field configurations. Explain how to record the equipotentials by placing a sheet of carbon paper face down under the conductive paper and on top of a sheet of plain white paper, and pressing down onto the paper with the flying lead. Then tell them to remove the record of the equipotentials and draw in the field lines by inspection. • combinations of one metal strip and one point. • two non-parallel straight metal strips; • two ‘point charges’ (i.e. metal pins) inserted into the board; • combinations of straight and curved metal strips; Enquiry skills 12A.3.1, 12A.3.2, 12A.4.1 Display and discuss students’ records of field and equipotential lines and establish that field lines and equipotential each provide a graphic means of representing electric field strength. Establish that in a uniform field the equipotentials are equally spaced, whereas in a non-uniform field they are closest together in regions where the field is strongest. Point out that the field lines converge towards ‘point charges’ and that in such regions the equipotentials are close together. 548 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities 3 hours Field of a point charge Coulomb’s law and nonuniform fields Ask students each to make a rough sketch showing the electric field lines that they would expect to be associated with a point, or a uniform sphere, of charge. (If necessary, remind them that the field lines indicate the direction of the force acting on a positive charge placed in the field.) Discuss students’ ideas and establish that the field lines must radiate equally in all directions from the charge. State and apply Coulomb’s law relating to the force between two or more charged particles in air and on the field strength due to a charged particle. Recognise the similarities between electrical and gravitational fields. Notes School resources Display a clear diagram on the board or OHP showing some of the field lines from a point charge passing through a square window of side x placed a distance r from the centre of the charge (x should be smaller than r ). Add a second square, side 2x, at a distance 2r. Establish that the number of lines per unit area is an indicator of field strength. Ask students to predict the relative strength of the field at the two distances shown, then ask them to predict the strength at distance 3r. Establish that the field is predicted to vary inversely with the square of the distance. Remind students that they have met a very similar pattern when studying gravitational fields. Demonstrate the use of a double flame probe to explore the strength and direction of the field of a uniform sphere of charge. Coat a large ball (10–20 cm diameter) with conducting paint and hang it from an insulating suspension at least 1 m from the bench top and other surfaces. Connect the ball to the positive terminal of an EHT supply (use metal foil and a crocodile clip to ensure a good electrical contact). Use the flame probe to show that the field direction is radial and the field strength diminishes with distance. (Measurements of leaf deflection will probably not be precise enough to show conclusively that the field obeys an inverse-square law.) 549 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Coulomb’s law Establish by suitable questioning and discussion that, if the field from a point charge follows an inverse-square law, then so should the force between two charges. Tell students that this is indeed the case and introduce Coulomb’s law F = Q1Q2 ⁄ 40r 2. Show how Coulomb’s law leads to an expression for the strength of the electric field of a point charge. Tell students that the same expression also describes the field of a uniform spherical charge distribution, where r is the distance from its centre. Ask students to deduce the SI units of the constant 0 (the permittivity of free space). Point out that its value could, in principle, be determined by experiment. Ask students, in pairs or small groups, to use the apparatus shown on the right to explore Coulomb’s law and obtain an order-of-magnitude estimate of the value of 0. Tell them to try to obtain data relating force, charge and distance, and plot suitable graphs to see how closely their data follow an inverse-square law. Emphasise that they should pay particular attention to the accuracy and precision of their measurements and suggest ways in which the method could be improved. Provide plenty of algebraic and numerical examples for students to practise using Coulomb’s law and the related expression for electric field strength. Source: Salters Horners Advanced Physics A2 Teacher and Technician Resource Pack, Heinemann Educational, p.139. © 2001 University of York Science Education Group. Enquiry skills 12A.1.1–12A.1.3, 12A.1.5, 21A.3.1–12A.3.3 This activity also relates to Standard 10A.25.2. In practice, it is difficult to obtain reliable data from this experiment since charge leaks away rapidly. Humid conditions increase the difficulty. Use a hair-drier to keep the apparatus as dry as possible. 550 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Electric and gravitational fields Draw students’ attention to the fact that both electrical and gravitational fields and forces due to point charges or masses are described by inverse-square laws. Divide students into small groups and ask them to brainstorm for a few minutes and list all the similarities and differences that they can think of between the two types of field and force. Discuss students’ suggestions with the whole class and summarise them on the board or OHP. If necessary, prompt students by suitable questioning if there are important comparisons that they have not thought of, including the following: • for point objects, both obey an inverse-square law; • both can be represented by field lines; • gravitational force is always attractive whereas electrostatic forces can be attractive or repulsive; • the forces due to several objects combine vectorially ...; • ... so electrostatic forces can cancel one another. Tell students to make a chart or table comparing the two types of field. Understanding electricity Ask students to describe any models (mental pictures) that they have used to aid their understanding of electricity, such as the carrier and driver models (outlined in Unit 10AP.7). Tell them that such models have played – and continue to play – an important role in our understanding of electricity. Ask students to work in pairs to use books and the Internet to trace the historical development of ideas about electricity. Assign each pair to a different topic, or scientist, and ask them to produce a short summary (1–2 pages) of their findings, preferably in word-processed electronic form. Suitable topics include the following: ICT opportunities: Use of the Internet; use of word processing. Enquiry skills 12A.1.6, 12A.1.8, 12A.2.1 • early two-fluid models (Du Fay); • single-fluid model (Franklin); • the modern atomic model of matter; • the development of ideas about field to describe ‘action at a distance’; • particle exchange models to describe ‘action at a distance’. Collect all the students’ contributions together and copy and distribute them to the whole class. 551 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities 4 hours Capacitors in circuits Capacitors Remind students of their work in earlier grades by setting up several circuits demonstrating the behaviour of capacitors. Either arrange these in a circus so that pairs of students visit each in turn, or perform a sequence of demonstrations to the whole class. Students should make brief notes on each. Suitable examples include the following. Demonstrate an understanding of the construction and use of capacitors in electrical circuits, and of how the charge is stored. Define capacitance and solve problems using C = Q ⁄ V; derive and use formulae for capacitors in series and in parallel. Define and use the relationship between the energy stored in a capacitor, its charge and the potential difference between its plates. Notes School resources Safety: When using an EHT supply, ensure that the safety resistor is connected and that no one can come into electrical contact with the terminals. • Charge a large capacitor by connecting it to a battery, then discharge it through a lamp. Repeat, replacing the lamp by (in turn) a small motor, an LED and a microammeter. • Connect a capacitor in series with a resistor and a signal generator set to give a square-wave input. Either connect a cathode-ray oscilloscope (CRO) in parallel first with the capacitor then with the resistor or use a dual-beam CRO to show both outputs simultaneously. Select the resistance R and capacitance C capacitor so that RC is about 0.1 s. Start with the signal frequency set to about 50 Hz then observe the effect of gradually increasing and reducing the frequency: at low frequencies there is time for complete charge and discharge, while at high frequencies the pd across the resistor is indistinguishable from the square-wave input. • Connect a single diode in series with a resistor and a low-voltage AC power supply. Connect a CRO across the diode to show half-wave rectification. Show the smoothing effect of connecting a capacitor into the circuit. Repeat, replacing the single diode with a full-wave rectifier made from four diodes. • Set up a delayed-action switching circuit. Show how changing the resistance and/or the capacitance affects the time delay. • Establish that a capacitor stores electric charge and, when connected into a circuit, can act as a short-lived battery whose terminal pd falls to zero during discharge. • Set up two metal plates (e.g. 20 cm × 20 cm) so that their planes are vertical and parallel to each other a few centimetres apart. Connect the plates to the terminals of an EHT supply. Previously, students have focused on the electric field between the plates, but now they should describe what they think is happening within the wires and plates when the EHT is switched on and the plates become charged. Explain that the pair of plates is acting as a capacitor: charge can flow to and from the plates but cannot cross the gap. Show students the construction of an electrolytic capacitor and establish that the foils are behaving like the metal plates: there is no conducting path between them. Charging and discharging Provide each pair of students with a large capacitor and resistor, two analogue ammeters and a battery that can be tapped to provide 1.5, 3, 4.5 and 6 V. Provide a briefing sheet that guides students through the following sequence of experiments illustrating capacitor charge and discharge. Enquiry skills 12A.4.1, 12A.4.2 1 Connect one meter to each side of the capacitor in series with the resistor and to a pd of 1.5 V. Observe the meter readings as the capacitor is charged. 2 Replace the battery by a conducting wire to discharge the capacitor. 3 Repeat, using 3 V instead of 1.5 V. 4 Charge the capacitor first by connecting to 1.5 V, then, without discharging, to 3 V, then 4.5 V, then 6 V. 552 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources As an extension, ask students to explore the effect of using different capacitors and resistors. Discuss students’ observations and establish the following points. • During charge and discharge, charge flows throughout the circuit. There is no net transfer of charge from battery to capacitor: rather, charge is redistributed so that one terminal of the capacitor becomes negative (gains electrons) and the other becomes positive (loses electrons). • The amount of charge flowing can be estimated by observing the ammeter readings. Increasing the battery pd in equal steps gives rise to the same amount of charge flowing each time. • When a capacitor is charged from zero, the total amount of charge flowing is directly proportional to the battery pd. Introduce and define capacitance, C, as the proportionality constant relating charge Q to pd V: Q = CV. Introduce the SI unit of capacitance, the farad, F: 1 F = 1 C V–1. Explain that most practical capacitors have capacitances much less than 1 F, so values are usually expressed in F or pF. On the board or OHP, explain to students how the current, pd and charge vary while a capacitor is discharging though a resistor. Use graphs to show how each of these quantities varies with time. Start with a graph of pd against time: students will have already seen this displayed as a trace on a CRO. Establish that, as the stored charge, Q, is proportional to V, a graph of Q against t will have the same shape as the V–t graph. Ask students to sketch their suggested shape for a graph of discharge current, I, against time. Then establish that, as I = V ⁄ R, where R is the resistance in the circuit, this graph, too, will have the same shape. Extend this discussion to include the shapes of graphs associated with a charging capacitor. Ask students to suggest how changing the capacitance and/or the resistance would affect the discharge graphs. Establish that increasing either or both will increase the time taken for the pd and other quantities to fall by a given fraction, and that a suitable choice of R and C underlies the successful design of capacitor timing circuits, Provide plenty of algebraic and numerical examples that allow students to practise using the relationship between charge, pd, current and capacitance. Measuring capacitance Show students how to use a vibrating reed switch, driven by a signal generator, to produce repeated charging and discharging of a capacitor made from two large metal plates. Discuss how the discharge current I is related to the charge Q stored and discharged during each cycle, and the switch frequency f: I = Qf = CVf. Discuss how measurements of this current can be used in conjunction with a knowledge of the supply pd, V, to determine the value of C. Enquiry skills 12A.1.1–12A.1.3, 12A.1.5, 12A.3.1–12A.3.3, 12A.4.1, 12A.4.2 Ask students to consider the strengths and weaknesses of this method. A strength is that current can be measured at several different frequencies and C determined from the gradient of a graph of I against f, thus averaging over several sets of measurements. A weakness is that, at high frequencies, there might not be time for the capacitor to discharge fully. If resources permit, let students work in small groups to carry out this experiment themselves. 553 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Combining capacitors If there is enough apparatus, ask students to work in pairs or small groups to study the charging and discharging of various combinations of capacitors using a CRO and a signal generator. Alternatively demonstrate this to the whole class. Connect a single capacitor in series with a resistor and a signal generator giving a square-wave output, and connect a CRO across the capacitor. Choose values of R and C and/or adjust the signal frequency so that there is almost complete discharge during each cycle. Without making any further alterations to the resistance or the frequency or the CRO settings, connect a second and then a third identical capacitor in parallel with the first: the discharge takes longer, indicating that the capacitance has increased. Return to the single capacitor, then connect a second and then a third identical capacitor in series with it: now the capacitance has decreased so the discharge takes a shorter time. On the board or OHP, show students how to derive expressions for combining capacitors in series and in parallel. Explain that when they are joined in parallel the capacitors all have the same pd across them, and the charge stored by the combination is equal to the sum of the individual charges: Q = Q1 + Q2 + Q3 + ..., hence C = Q ⁄ V = C1 + C2 + C3 + ... Then explain that, when capacitors are joined in series, charge must be distributed in such a way that each stores the same charge Q, which is the same as the charge stored by the combination. Therefore Q ⁄ C = V = V + V + V = Q ⁄ C1 + Q ⁄ C2 + Q ⁄ C3 + ..., and hence 1 ⁄ C = 1 ⁄ C1 + 1 ⁄ C2 + 1 ⁄ C3 + ... Point out that, while these expressions resemble those for combining resistors, here the simple additive relationship applies to capacitors in parallel, whereas a similar relationship applies to resistors in series. Provide plenty of algebraic and numerical examples that allow students to practise using the relationships for capacitors in series and parallel. Energy in capacitors Perform some short demonstrations to show that capacitors store energy. Suitable examples include: Mathematics: A knowledge of integral calculus is helpful but not required. Enquiry skills 12A.1.2, 12A.4.1, 12A.4.2 • a camera flash-gun; • discharge a large capacitor through a motor set to lift a small weight; • discharge a large capacitor through a coil of wire wrapped around a temperature sensor. On the board or OHP, show students how to derive an expression for the energy stored in a charged capacitor. Depending on the mathematical fluency of the students, use a graphical method and/or integral calculus to show that energy = ½ QV. Ask students to deduce expressions for stored energy in terms of (a) C and V, and (b) C and Q. Point out the analogy between charging a capacitor and stretching a spring. 554 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Objectives Possible teaching activities Notes School resources Ask students to work in pairs to explore the energy stored in a capacitor. Provide each pair with apparatus and a briefing sheet to guide them though the following sequence of experiments. 1 Charge a large capacitor by connecting it to a 1.5 V cell, then discharge it through a single torch bulb. Repeat a few times and note the visual appearance of the bulb during discharge. 2 Charge the same capacitor using a 3 V battery. Discharge it through two bulbs connected in series (so as to ensure the same initial pd across each). Note the brightness of the flash (it is brighter than in step 1). 3 Connect a second pair of bulbs in parallel with the first and repeat step 2. Note the brightness of the flash from each bulb (the flash from each bulb is now similar to that produced in step 1). 4 Predict the effect of charging the same capacitor with a 6 V battery. Decide how many bulbs, and in what arrangement, would allow each one to give the same flash as the single bulb in step 1. (Nine bulbs are required, connected in a 3 × 3 array.) Discuss the outcome of this activity and establish that the results are as expected (i.e. energy is directly proportional to V 2). Provide plenty of algebraic and numerical examples that allow students to practise using relationships involving energy storage in a capacitor. 555 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005 Assessment Examples of assessment tasks and questions Assessment Set up activities that allow students to demonstrate what they have learned in this unit. The activities can be provided informally or formally during and at the end of the unit, or for homework. They can be selected from the teaching activities or can be new experiences. Choose tasks and questions from the examples to incorporate in the activities. Unit 12AP.5 Notes School resources A potential difference of 2.5 kV is applied to a pair of parallel metal plates separated by 8 cm. What is the force experienced by a charge of 6.0 mC within the space between the plates? Use Coulomb’s law to derive an expression for the magnitude of the electric field strength E at a distance r from a point charge Q. In a hydrogen atom, the average distance between the proton and the electron is about 0.037 nm. Calculate the magnitude of the force between them. (Electron charge e = 1.60 x10–19 C.) List at least two ways in which electrical and gravitational fields are similar, and at least two ways in which they differ. At particle physics laboratories such as CERN, the kinetic energies of accelerated particles are often expressed in MeV. a. What is 1 MeV expressed in joules? b. If a proton has kinetic energy 1.5 MeV, what is its speed? (Electron charge e = 1.60 x 10–19 C. Proton mass mp = 1.67 x 10–27 kg.) Draw a diagram showing the electric field lines and the lines of equipotential around two positive point charges placed a few centimetres apart. Draw a labelled set of sketch graphs to show how the pd across a capacitor, the charge stored and the current in the circuit change with time as the capacitor discharges through a resistor. On the same axes, draw another set of graphs showing how the pd, charge and current would change with time if the original resistor were replaced by one with greater resistance. A 100 F capacitor is connected to a 3 V battery then discharged through a 500 resistor. Calculate: a. the initial charge stored; b. the initial discharge current; c. the discharge current when the capacitor has lost half its initial charge. Three capacitors, of capacitance 1, 2 and 4 pF, are connected (a) in series, (b) in parallel. Calculate the resulting capacitance in each case. A 10 000 F capacitor is connected to a 12 V battery then discharged through a lamp. How much energy is emitted? 556 | Qatar science scheme of work | Grade 12 advanced | Unit 12AP.5 | Physics 5 © Education Institute 2005