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02/05/2017 Waves Waves revision Watch a “Mexican Wave” 02/05/2017 Some definitions… 1) Amplitude – this is “how high” the wave is: 2) Wavelength () – this is the distance between two corresponding points on the wave and is measured in metres: 3) Frequency – this is how many waves pass by every second and is measured in Hertz (Hz) 02/05/2017 02/05/2017 Transverse waves are when the displacement is at right angles to the direction of the wave… Displacement Transverse vs. longitudinal waves Displacement Direction Direction Longitudinal waves are when the displacement is parallel to the direction of the wave… Where are the compressions and rarefactions? Oscillating Systems 02/05/2017 Design an experiment that determines what the period of oscillation depends on for these two oscillating systems: T = 2π l g T = 2π m k Displacement-time graphs 02/05/2017 Consider a pendulum bob: Let’s draw a graph of displacement against time: Equilibrium position Displacement “Sinusoidal” Time Phase Difference 02/05/2017 There is a ‘phase difference’ between two waves when they have the same frequency but oscillate differently to each other. For example: These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase” These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians” Phase Difference What is the phase difference between each of these waves? 02/05/2017 The Wave Equation 02/05/2017 The wave equation relates the speed of the wave to its frequency and wavelength: Wave speed (v) = frequency (f) x wavelength () in ms-1 in Hz in m V f Some example wave equation questions 02/05/2017 1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving? 0.6ms-1 2) A water wave travels through a pond with a speed of 1ms-1 and a frequency of 5Hz. What is the wavelength of the waves? 0.2m 3) The speed of sound is 330ms-1 (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound? 0.5m 4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light? 3x108ms-1 Electromagnetic Waves 02/05/2017 Electromagnetic Radiation 02/05/2017 E-M radiation is basically a movement of energy in the form of a wave. Some examples: The Electromagnetic Spectrum 02/05/2017 Each type of radiation shown in the electromagnetic spectrum has a different wavelength and a different frequency: High frequency, _____ wavelength Gamma rays X-rays Low frequency, _____ (high) wavelength Ultra violet Visible light Infra red Microwaves Radio/TV γ Each of these types travels at the same speed through a _______ (300,000,000ms-1), and different wavelengths are absorbed by different surfaces (e.g. infra red is absorbed very well by ___________ surfaces). This absorption may heat the material up (like infra red and _______) or cause an alternating current (like in a __ _______). Words – black, microwaves, long, short, TV aerial, vacuum The Electromagnetic Spectrum 02/05/2017 Type of radiation Uses Dangers Gamma rays Treating cancer, sterilisation Cell mutation X rays Medical Cell mutation Ultra violet Sun beds Skin cancer Visible light Seeing things None (unless you look at the sun) Infra red Remote controls, heat transfer Sunburn Microwaves Satellites, phones Very few TV/radio Communications Very few Water Waves 02/05/2017 Q. Design an experiment that explores the relationship between the depth of water and the speed of a wave in that water. Reflection revision 02/05/2017 Reflection from a mirror: Normal Reflected ray Incident ray Angle of incidence Angle of reflection Mirror Refraction Revision 02/05/2017 Refraction through a glass block 02/05/2017 Light slows down and bends towards the normal due to entering a more dense medium Light slows down but is not bent, due to entering along the normal Light speeds up and bends away from the normal due to entering a less dense medium Refraction 02/05/2017 Refractive Index 02/05/2017 The Refractive Index of a material is a measure of the factor by which the material will slow down light: Speed in medium 1 Refractive index = Speed in medium 2 Using some interesting maths I turned this relationship into Snell’s Law: 1μ2 = sinθ1 sinθ2 = sin i sin r Willebrord Snellius, 1580-1626 1μ2 = v1 v2 02/05/2017 Questions on the Refractive Index The speed of light is 3x108ms-1 in air, 2.3x108ms-1 in water and 2x108ms-1 in glass. 1) Calculate the refractive index for light passing from air into water, from air into glass and from water into glass. Air 2) Calculate the angles θW and θG for light incident at 40O to the air-water boundary: Water Glass More Questions… 02/05/2017 My law can often be stated as this: μ1 sin θ1 = μ2 sin θ2 1) Light passes from water (refractive index of 1.3) into crystal with a refractive index of 1.5. Calculate the angles of refraction for light incident at 20O, 30O, 40O and 50O. 2) A ray of light travels through a vacuum and is incident upon a glass block (of refractive index 1.5) at an angle of 30O. The ray then passes into water. Draw an accurate diagram to show the path of this light as it travels from the vacuum through the glass and into the water. Measuring the Refractive Index 02/05/2017 Using Snell’s Law we can measure the refractive index of a material: 1μ2 = sinθ1 sinθ2 = sin i sin r From this equation a graph of sin i against sin r will have a gradient of the refractive index: Sin i Sin r Finding the Critical Angle… 02/05/2017 1) Ray gets refracted 3) Ray still gets refracted (just!) THE CRITICAL ANGLE 2) Ray still gets refracted 4) Ray gets internally reflected 02/05/2017 Uses of Total Internal Reflection Optical fibres: An optical fibre is a long, thin, _______ rod made of glass or plastic. Light is _______ reflected from one end to the other, making it possible to send ____ chunks of information Optical fibres can be used for _________ by sending electrical signals through the cable. The main advantage of this is a reduced ______ loss. Words – communications, internally, large, transparent, signal Polarisation Consider a single wave of light: If you looked at it “end on” it might look like this: And lots of them might look like this: 02/05/2017 Polarisation 02/05/2017 Polarisation and Microwaves 02/05/2017 Describe an experiment that demonstrates that microwaves are polarised. 02/05/2017 Sugar Solution and Polarised Light Task: To investigate the amount of sugar dissolved in a solution using polarised light. Method: 1) Measure and dissolve 10g, 20g, 30g, 40g and 50g of sugar into 100ml of water 2) Investigate the angle of rotation needed to block out a light source using the solution and two polaroid filters 3) Draw a graph of angle against concentration 4) Use this graph to determine the amount of sugar in unknown solution x. 02/05/2017 Using polarized light to see stress Pulse-Echo techniques 02/05/2017 In pulse-echo techniques sound is reflected from an object to measure the distance to that object: Pulse-Echo techniques - Ultrasound 02/05/2017 Ultrasound is the region of sound above 20,000Hz – it can’t be heard by humans. It can be used in pre-natal scanning: How does it work? Ultrasonic waves are partly _________ at the boundary as they pass from one _______ to another. The time taken for these reflections can be used to measure the _______ of the reflecting surface and this information is used to build up a __________ of the object. Words – depth, reflected, picture, medium The Maths of Pulse-Echo 02/05/2017 Consider shouting at a wall: x The speed of sound is given by: v = 2x/t Therefore x = vt/2 The Maths of Pulse-Echo 02/05/2017 The echo takes 0.8 seconds to return and the speed of sound in water is 1500ms-1. How deep is the water? 25 50 75 100 125 150 175 200 t/μs Use the ultrasound scan to determine the width of the amniotic sac and the width of the baby’s body. The speed of sound in the fluid is 1500ms-1 and in soft tissue the speed is 1560ms-1. Ultrasound vs X Rays 1) Why are X Rays better than ultrasound? 2) Why is ultrasound better than X Rays? 02/05/2017 The Doppler Effect 02/05/2017 Phase Difference Revision 02/05/2017 Phase difference means when waves have the same frequency but oscillate differently to each other. For example: These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase” These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians” Coherence 02/05/2017 Two waves are said to be “coherent” if they have the same frequency and the same constant phase difference. For example: These waves have a different frequency, so phase is irrelevant. Coherence 02/05/2017 These waves have the same frequency and the same constant phase difference, so they are “coherent” Superposition 02/05/2017 Superposition is seen when two waves of the same type cross. It is defined as “the vector sum of the two displacements of each wave”: Superposition patterns 02/05/2017 Consider two point sources (e.g. two dippers or a barrier with two holes): Stable interference patterns happen when these waves are the same type, coherent AND have similar amplitudes at the point of supperposition. Superposition of Sound Waves 02/05/2017 Path Difference Constructive interference Destructive interference 02/05/2017 1st Max Min Max Min 1st Max 2nd Max Young’s Double Slit Experiment 02/05/2017 D λ s O x λ s = x D λ = xs D A Screen 02/05/2017 Interference Patterns from 2 slits Intensity Distance Interferometers 02/05/2017 Task: Find out what an interferometer is. Include the following: 1) Where they are used 2) A diagram of how they are used 3) Some pictures 4) The physics principle behind how they work (i.e. the use of a path difference) How CD Players work 02/05/2017 CDs are made of millions of small bumps etched onto a silvery surface using a laser. Here’s how they work: Path difference between these two waves = 0, therefore constructive interference Path difference between these two waves = λ/2, therefore destructive interference λ/4 Silvery surface Stationary (Standing) Waves 02/05/2017 Usually waves are described as “travelling” or “progressive” waves, i.e. there is a net movement of energy. However, it is possible to set up a standing wave using two progressive waves of equal frequency and wavelength: This is hard to imagine, but if you put these two waves together you’d get this: Stationary (Standing) Waves 02/05/2017 3 nodes 2 antinodes 5 nodes 4 antinodes Harmonics 02/05/2017 l Fundamental frequency f0, λ=2l First overtone, second harmonic, f=2f0, λ=l Third overtone, fourth harmonic, f=4f0, λ=l/2 Wind Instruments 02/05/2017 Wind instruments are basically instruments that form standing waves using air. L Consider waves in an open pipe. They will always form an antinode at an open end: L=λ/2, f=f0 L=λ, f=2f0 L=3λ/2, f=3f0 Wind Instruments 02/05/2017 L Now consider a closed pipe, which will form a node at the closed end: L=λ/4, f=f0 L=3λ/4, f=3f0 L=5λ/4, f=5f0 Example Questions 02/05/2017 A tuning fork emits a frequency of 512Hz. It is held above a glass tube filled to the top with water. The water is allowed to drain out of the tube. When 17cm of water has drained out a standing wave is formed and resonance occurs. Calculate: 1) The wavelength of the sound From the previous slide 17cm=λ/4, therefore λ=68cm 2) The speed of sound in air v=fλ, therefore v=512x0.68 = 348ms-1 3) How far the water must run to form the next resonance Next standing wave and resonance occurs at 3λ/4 = 51cm Diffraction 02/05/2017 More diffraction if the size of the gap is similar to the wavelength More diffraction if wavelength is increased (or frequency decreased) 02/05/2017 Interference Patterns from 2 slits Intensity Distance 02/05/2017 Interference Patterns from 1 slit Intensity Distance Sound can also be diffracted… 02/05/2017 The explosion can’t be seen over the hill, but it can be heard. We know sound travels as waves because sound can be refracted, reflected (echo) and diffracted. Diffraction depends on frequency… 02/05/2017 A high frequency (short wavelength) wave doesn’t get diffracted much – the house won’t be able to receive it… Diffraction depends on frequency… 02/05/2017 A low frequency (long wavelength) wave will get diffracted more, so the house can receive it… Image Resolution 02/05/2017 Consider the rays of light from two distant objects going into the eye: When the rays pass through the pupil they are diffracted and they will form the normal one-slit diffraction pattern on the retina: Intensity Q. What will happen if the objects move closer together? Distance Electron Diffraction 02/05/2017 Electron diffraction patterns are seen when electrons are passed through graphite crystal. Diffraction is seen because the distance between the atoms is of the same order as the de Broglie wavelength of the electrons. de Broglie wavelength λ = h mv 1) What is the de Broglie wavelength of electrons travelling at around 2x107ms-1 (electron mass = 9.1x10-31kg)? 2) What would happen to the diffraction pattern if the voltage to the electrons (and therefore their speed) was increased? 02/05/2017 Electricity Electric Current Electric current is a flow of negatively charged particles (i.e. electrons). We call them “charge carriers” + e- - e- 02/05/2017 Note that electrons go from negative to positive Conventional Current 02/05/2017 As we said, technically electrons go from negative to positive. However, we usually talk about “conventional current” and we say that current moves from positive to negative: + - Basic ideas… 02/05/2017 Electric current is when electrons start to flow around a circuit. We use an _________ to measure it and it is measured in ____. Potential difference (also called _______) is how big the push on the electrons is. We use a ________ to measure it and it is measured in ______, a unit named after Volta. Resistance is anything that resists an electric current. It is measured in _____. Words: volts, amps, ohms, voltage, ammeter, voltmeter More basic ideas… 02/05/2017 If a battery is added the current will ________ because there is a greater _____ on the electrons so they move ______ If a bulb is added the current will _______ because there is greater ________ in the circuit, so the electrons move _____ Words – faster, decrease, slower, increase, push, resistance DC and AC 02/05/2017 V DC stands for “Direct Current” – the current only flows in one direction: Time 1/50th s AC stands for “Alternating Current” – the electrons change direction 50 times every second (frequency = 50Hz) 240V T V Charge and Current 02/05/2017 Recall the structure of an atom: PROTON – positively charged ELECTRON – negatively charged Notice: 1) Atoms have the same number of protons and electrons – they are NEUTRAL overall 2) Because electrons are on the outside of the atoms they can move around (this is what causes electrical effects) Static Electricity 02/05/2017 Static electricity is when charge “builds up” on an object and then stays “static”. How the charge builds up depends on what materials are used: - + - + - + + - - + - + - + - + + - - + Static Electricity + + - - + - - - - - 02/05/2017 - - Measuring Charge 02/05/2017 The charge on an electron is very small, so we measure charge using units called “coulombs” (C). One electron has a charge of 1.6 x 10-19 C. Charge can be measured using a coulombmeter, and they usually measure in nanocoloumbs (1nC = 10-9 C). For example, a charged polythene rod may carry a charge of a few hundred nanocoulombs Calculating Charge (Q) 02/05/2017 By definition, current is the rate of flow of charge. In other words, its how much charge flows per second. One amp (1 A) is equal to one coulomb per second (1 Cs-1). Charge and current are related by the equation: Current = rate of flow of charge I = ΔQ ΔT 1. A battery supplies 10 C over a period of 50 seconds. What is the current? 2. Another battery is connected for 2 minutes and provided a current of 0.4 A. How much charge flowed? 3. A car battery has a capacity of 24 Ah (amp hours). If it provides a current of 48A how long can it be used for? How much charge (in coulombs) does it contain? Current in a series circuit 02/05/2017 If the current here is 2 amps… The current here will be… The current here will be… And the current here will be… In other words, the current in a series circuit is THE SAME at any point. Current in a parallel circuit 02/05/2017 A PARALLEL circuit is one where the current has a “choice of routes” Here comes the current… Half of the current will go down here (assuming the bulbs are the same)… And the rest will go down here… Current in a parallel circuit 02/05/2017 If the current here is 6 amps And the current here will be… The current here will be… The current here will be… The current here will be… Some example questions… 02/05/2017 3A 6A Kirchoff’s First Law 02/05/2017 “The sum of the currents leaving a point is the same as the sum of the currents entering that point.” Gustav Kirchoff (1824-1887) For example: 6A If the current through here is 4A... …and the current through here is 2A… … then the current here will be 6A Voltage 02/05/2017 Earlier on we said that current is when electrons move: + - e- “Voltage” is the force that- pushes the electrons. For e electrons to move there must be a “voltage difference”, sometimes called a “potential difference” (p.d.). A higher p.d. means a stronger push, which causes an increase in current. Voltage in a series circuit 02/05/2017 If the voltage across the battery is 6V… V …and these bulbs are all identical… …what will the voltage across each bulb be? V V 2V Voltage in a series circuit 02/05/2017 If the voltage across the battery is 6V… …what will the voltage across two bulbs be? V V 4V Voltage in a parallel circuit 02/05/2017 If the voltage across the batteries is 4V… What is the voltage here? 4V V And here? V 4V Summary 02/05/2017 In a SERIES circuit: Current is THE SAME at any point Voltage SPLITS UP over each component In a PARALLEL circuit: Current SPLITS UP down each “strand” Voltage is THE SAME across each”strand” An example question: 6V A3 3A A1 V1 A2 V2 V3 02/05/2017 Another example question: 02/05/2017 10V A3 3A A1 V1 A2 V2 V3 Electromotive force and p.d. 02/05/2017 Components like batteries and power supplies provide a force that pushes the current around a circuit: we call this the “electromotive force” (e.m.f). Other components like bulbs and motors have work done to them by the current – the voltage across them is called the “potential difference” (p.d.) The sum of these EMFs… Definition of EMF – “the total work done by a cell per coulomb of charge” Is equal to the sum of the p.d.s Kirchoff’s Second Law 02/05/2017 “Around any closed loop, the sum of the e.m.f.s is equal to the sum of the p.d.s.” Gustav Kirchoff (1824-1887) For example: The voltage across each bulb will be 1V If the e.m.f of the batteries is 3V Voltage at a point The voltage here is 6V The voltage here is 4.5V The voltage here is 3V The voltage here is 1.5V Take this point as being 0V 02/05/2017 Voltage-position graphs 6V 5.9V 4.5V 1.5V 0.1V 0V 02/05/2017 Work done 02/05/2017 Definition of a volt: The voltage between two points is the work done per coulomb travelling between the two points Voltage = work done charge We can see that 1V = 1JC-1 V=W Q Example Questions 02/05/2017 1) A battery does 9J of work. If it transfers 6C of charge what is the battery’s voltage? 2) A powerpack does 100J of work in transferring 20C of charge. What is the voltage? 3) A 9V battery transfers 20C of charge. How much work did it do? 4) If the current of the battery is 0.2A how long was it used for? 5) 240J of work is done to a 12V motor. How much charge flowed through it? 6) If this motor was used for 40 seconds how much current did it draw? Electrical Power Voltage = work done 1) Recall: charge 2) Also, recall that power = rate of doing work 3) Therefore 4) But I = Q so T 02/05/2017 W = QV Power = work done P=W time T Power = charge x voltage P = Q x V time Power = current x voltage P = IV or V2/R or I2R T Using voltmeters and ammeters 02/05/2017 A V The resistance of an ammeter is assumed to be very small – this ammeter will only have a very small voltage across it. The resistance of a voltmeter is assumed to be very large, so only a small current will go through it. Resistance 02/05/2017 Resistance is anything that will RESIST a current. It is measured in Ohms, a unit named after me. Georg Simon Ohm 1789-1854 The resistance of a component can be calculated using Ohm’s Law: Resistance (in ) = V Voltage (in V) Current (in A) I R An example question: 02/05/2017 Ammeter reads 2A A V Voltmeter reads 10V 1) What is the resistance across this bulb? 2) Assuming all the bulbs are the same what is the total resistance in this circuit? More examples… 02/05/2017 3A 6V 12V 3A 2A 4V 2V 1A What is the resistance of these bulbs? Resistance 02/05/2017 Resistance is anything that opposes an electric current. Resistance (Ohms, ) = Potential Difference (volts, V) Current (amps, A) What is the resistance of the following: 1) A bulb with a voltage of 3V and a current of 1A. 2) A resistor with a voltage of 12V and a current of 3A 3) A diode with a voltage of 240V and a current of 40A 4) A thermistor with a current of 0.5A and a voltage of 10V Resistors in Series I R1 02/05/2017 “In a series circuit current stays the same but voltage splits up” V1 VT = V1 + V2 VT = IRT VT R2 V2 But V1 = IR1 and V2 = IR2 IRT = IR1 + IR2 R T = R1 + R2 Resistors in Parallel IT I1 “In a parallel circuit voltage stays the same but current splits up” IT = I1 + I2 I2 IT = V R1 R2 RT V V = V + V RT IT 02/05/2017 R1 R2 1 = 1 + 1 RT R1 R2 Example questions 02/05/2017 Calculate the equivalent resistance: 1) 40Ω 10Ω 2) 20Ω 10Ω 3) 100Ω 100Ω 20Ω 20Ω 4) 100Ω 50Ω 50Ω Power through a resistor 02/05/2017 Recall: 1) P = IV Putting these two equations together gives us: 2) V = IR Power = I x IR = I2R or V2/R 1) A 10Ω resistor has 2A flowing through it. Calculate the power dissipated by the resistor. 2) A motor takes a current of 10A. If its resistance is 2.2MΩ calculate the power dissipated by the motor. 3) A 2KW heater has a resistance of 20 Ω. Calculate the current through it. Carrier Density Consider a copper atom: 02/05/2017 The diameter of a copper atom is about 0.25nm This means that there will be 1 / 0.25nm = 4 x 109 copper atoms in 1 metre. Consider a copper cube of sides 1m: Theoretically ,in this cube there must be (4 x 109)3 = 6.4 x 1028 copper atoms. Assuming each atom has one free electron there are 6.4 x 1028 free charges per cubic metre – this is called the “charge carrier density” (n) Some questions… 02/05/2017 1) If, for copper, n = 6.4 x 1028 and each electron has a charge of 1.6 x 10-19C how much free charge was in the cubic metre? 2) How much free charge would be in 1mm3 instead? 3) Calculate the carrier density for a cubic metre of another atom with diameter 0.3nm. Assume each atom has one free electron again. Drift Speed 02/05/2017 Definition: Drift speed is the speed with which electrons will move down a wire. How do we work it out? Consider a wire of cross sectional area A and charge carrier density n, where each carrier has the charge q and they are moving with a drift speed of v. 1) Every second the volume of charge carriers that pass a point will be Av 2) Therefore the number of charge carriers that pass by every second is given by nAv 3) Therefore the charge that passes by every second will be nAvq 4) But charge per second IS current, so… I = nAqv Example questions 02/05/2017 1) Calculate the current down a 1mm2 wire where the drift speed is 1mms-1 and the carrier density is 6.4 x 1028m-3 (remember that the charge on an electron is 1.6 x 10-19C) 2) Calculate the drift speed down a 2mm2 wire which has a current of 0.5A passing through it and a carrier density of 6.4 x 1028m-3. This seems slow… 02/05/2017 The drift speeds in the previous questions seemed very slow – why is it that when you turn on a light bulb it lights straight away then? Consider the electrons in the wire: Bulb Battery When an electron is pushed in it knocks on the others so that electrons “come out” at the other end. Simple really… Comparing Drift Speeds 02/05/2017 Consider two wires connected in series: 1 2 Q. The area of wire 2 is twice that of wire 1. Which wire do electrons travel fastest in? In wire 1 I1 = n1A1q1v1 In wire 2 I2 = n2A2q2v2 However, in series I1=I2 therefore n1A1q1v1 = n2A2q2v2 Also, q1 = q2 and n1 = n2… Therefore A1v1 = A2v2 Resistivity 02/05/2017 The resistance of a wire depends on 3 things: the length of the wire, the width of the wire and what the wire is made of: Resistance = resistivity x length area R = ρL A Calculate the following: 1) The resistance of a copper wire of length 2m, area 2mm2 and resistivity 1.7x10-8 Ωm 2) The resistance of an iron wire of length 100m, area 5mm2 and resistivity 1x10-7 Ωm 3) A copper wire has a resistance of 5Ω. If the wire is 20m long and the wire is cylindrical what is the radius of the wire? Electron Drift 02/05/2017 What happens inside a conducting material? The following model of a metal wire could help: Electrons Ions At normal temperatures, with no current flowing, electrons hurtle around continuously. They collide with ions but because their movement is random there is no net energy transfer. Electron Drift 02/05/2017 Now apply a voltage: Negative Electrons Ions Positive This time we can see that the electrons are accelerated from negative to positive. This movement is superimposed on top of the random velocities and is responsible for electrical effects. Understanding Resistance 02/05/2017 1) Increase length 2) Increase area 3) Decrease resistivity Therefore Resistance = resistivity x length area R = ρL A Understanding Current Recall the equation: 02/05/2017 Increasing the temperature of a metal will increase the ___________ of the ions. This will increase the ________ of the metal and decrease the current because it lowers the ____ _____. I = nAqv In semiconductors the carrier density is small but _________ with temperature, so the resistivity of a semiconductor decreases with temperature (e.g. a ________). These devices have a “negative temperature coefficient”. In insulators n is very low. Words – thermistor, resistivity, vibrations, drift speed, increases Potential Dividers 02/05/2017 VIN R1 VOUT R2 0V 0V The Potential Divider equation: VOUT VIN x (R2) (R1 + R2) Some example questions 12V 50V 100 100 0V 10 VOUT 0V 3V 75 0V VOUT 0V 1.5V 75 25 0V 02/05/2017 50 VOUT 0V 45 0V VOUT 0V Practical applications Here’s a potential divider that is used to control light-activated switches… 02/05/2017 Vin VOUT 0V When the light intensity on the LDR decreases its resistance will ________. This causes VOUT to _______ so the processor and output will probably turn _____. The variable resistor can be adjusted to change the ________ of the whole device. Words – decrease, sensitivity, increase, off An example Calculate the missing values (from June 2006) 6V A ? 4Ω ? ? R A ? V 15Ω 0.24A A 02/05/2017 More examples 02/05/2017 ? 18V ? ? ? 0.5A 10Ω 20Ω A 10Ω ? 40Ω 10Ω 18V ? ? ? Current-Voltage Graphs Voltage on powerpack/V 12 10 … 0 … -10 -12 Current/A 02/05/2017 Voltage/V Two simple components: 1) Light dependant resistor – resistance DECREASES when light intensity INCREASES Resistance 02/05/2017 2) Thermistor – resistance DECREASES when temperature INCREASES (“negative temperature coefficient”) Resistance Amount of light Temperature Current-voltage graphs 02/05/2017 Consider a resistor: I R V Current increases in proportion to voltage V Resistance stays constant Current-voltage graphs 02/05/2017 Now consider a bulb: I R V As voltage increases the bulb gets hotter and resistance increases – “non-Ohmic behaviour” V Resistance increases as the bulb gets hotter Current-voltage graphs Now consider a diode: I 02/05/2017 Now consider a thermistor: I V A diode only lets current go in the “forward” direction V Resistance decreases as the (“negative-temperaturecoefficient”) thermistor gets hotter Internal Resistance + 02/05/2017 - V The voltage across the terminals of a battery is called the “terminal p.d.” Internal Resistance + 02/05/2017 - V This voltage DECREASES when more components are added… Internal Resistance 02/05/2017 All sources of EMF behave as though they have a “built-in” resistor. This is called the “internal resistance” and can be thought of as the resistance to the flow of current inside the power supply itself. V It’s useful to think of the internal resistance as part of the external circuit. Measuring Internal Resistance 02/05/2017 From Kirchoff’s 2nd law: EMF = lost volts + p.d Lost volts E = Ir + V V = E - Ir EMF V = (-r)I + E Terminal p.d. V I Short Circuit Current 02/05/2017 In this “short circuit” the only significant resistance is the internal resistance, so… Current = EMF Internal resistance Usually power supplies should have low internal resistances. However, high voltage supplies can have large resistances to avoid supplying too much current. Numerical quiz 02/05/2017 1) What is the resistance of a bulb with a voltage of 12V and a current of 2A through it? 2) This bulb transfers 100C of electrical energy. How long was it used for? 3) A power supply does 4,800J of work. If it transfers 20C of charge what is the EMF of the supply? 4) What is the resistance of a thermistor when the p.d. across it is 20V and the current through it is 2A? 5) Work out the total resistance of the following: 10Ω each 20Ω each Numerical quiz 02/05/2017 6) A thermistor has a resistance of 200 when 20V is applied across it. What is the current through the thermistor? 7) The same thermistor is put in a warm water bath. The resistance drops to 120. What is the current through it now? 8) A resistor takes a current of 2A. If the resistor has a resistance of 10Ω calculate the power dissipated in the resistor. 9) A piece of copper wire has a length of 2m, an area of 1mm2 and a resistivity of 1.7x10-8Ωm. Calculate the resistance. 10)Calculate the charge carrier density in this wire if the drift speed is 1mms-1 and the current through it is 2A. Numerical quiz 02/05/2017 11) How many electrons does it take to have a charge of 20C? 12)A bulb dissipates 800W of power. If its resistance is 200Ω calculate the current through it. 13)What is the voltage across this bulb? 14)An electric fire uses 1200C of charge over 2 minutes. What current did it draw? 15)Calculate the following output voltages: 12V 20V 50 150 0V 4 VOUT 0V 6 0V VOUT 0V 02/05/2017 The Nature of Light W Richards The Weald School Intensity 02/05/2017 Definition: “Intensity” means the strength of light arriving at a certain point, and can also be called “Radiation flux density” Energy dissipation Clearly, a wave will get weaker the further it travels. Assuming the wave comes from a point source and travels out equally in all directions we can say: Energy flux = Power (in W) (in Wm-2) Area (in m2) φ= P 4πr2 An “inverse square law” Introduction 02/05/2017 Some basic principles: 1) The wavelength of blue light is around 400nm (4x10-7m) 2) The wavelength of red light is around 650nm (6.5x10-7m) 3) Therefore blue light is higher frequency than red light 4) Light is treated as being a wave. Therefore the amount of energy a light wave contains should depend on its intensity or brightness. Photoelectric Emission 02/05/2017 Consider a gold-leaf electroscope… Now charge the top: 5000V + Photoelectric Emission 02/05/2017 Let’s put a piece of zinc on top: Now shine some UV light onto it: - - - - - - Ultra-violet light is causing the zinc to emit electrons – this is “Photoelectric Emission”. Some definitions… 02/05/2017 For zinc, this effect is only seen when UV light is used, i.e. when the light has a frequency of 1x1015Hz or higher. This is called the “Threshold Frequency” and is generally lower for more reactive metals. Max Planck (1858-1947) proposed that electromagnetic radiation, like light, comes in small packets. The general name for these packets is “quanta”. In the specific case of electromagnetic radiation, a quanta is called a “photon” and its energy depends on its frequency, not how bright it is. The amount of energy needed to release an electron from a metal is called the “work function” and is given the symbol φ. Generally, work functions are lower for more reactive metals. Photoelectron Energy 02/05/2017 …and some energy is given to the electron as kinetic energy. - Some energy is needed to release the electron (the work function φ)… Photon Energy = work function + kinetic energy of electron Calculating Photon Energy 02/05/2017 I think that the energy of a photon is proportional to its frequency, so E=hf, where h = Planck’s Constant = 6.63x10-34Js. On the previous slide we said that… Photon energy = work function + kinetic energy of electron hf = φ + 1/2mv2 02/05/2017 Measuring the Energy of a Photoelectron Illuminate the electrode: Electrons are “stopped” by this voltage A V + The “Hill” analogy 02/05/2017 To help us understand this further, let’s say the electron is like a ball rolling up a hill… The amount of potential energy the electron gains is equal to the amount of kinetic energy it had at the start. Negative electrode Vs - In electric terms, the voltage the electron can work against depends on how much energy it had. Energy of electron = QVs = 1/2 mv2 …where Vs is the “stopping voltage” (i.e. the height of the hill it can go up before coming back down again). Photon Energy 02/05/2017 Combining the previous two slides, we get: Photon energy = work function + kinetic energy of electron hf = φ + QVs Let’s rearrange to give us a straight line graph: Vs = h f – φ Q Q Vs Gradient = h/Q Threshold frequency Photon frequency Spectra – introduction 02/05/2017 Spectra Source of light 02/05/2017 “Spectra” Absorption Spectra helium Some wavelengths of light are absorbed by the gas – an “absorption spectrum”. 02/05/2017 Spectra Continuous spectrum Absorption spectrum Emission spectrum 02/05/2017 Emission Spectra Hydrogen Helium Sodium 02/05/2017 Spectra 02/05/2017 Consider a ball in a hole: When the ball is here it has its lowest gravitational potential energy. 5J We can give it potential energy by lifting it up: If it falls down again it will lose this gpe: 5J 30J 20J Spectra 02/05/2017 A similar thing happens to electrons. We can “excite” them and raise their energy level: 0eV -0.85eV -1.5eV -3.4eV -13.6eV An electron at this energy level would be “free” – it’s been “ionised”. These energy levels are negative because an electron here would have less energy than if its ionised. This is called “The ground state” Spectra 02/05/2017 If we illuminate the atom we can excite the electron: Q. What wavelength of light would be needed to excite this electron to ionise it? 0eV -0.85eV -1.5eV -3.4eV Light Energy change = 3.4eV = 5.44x10-19J. Using E=hc/λ wavelength = 3.66x10-7m -13.6eV (In other words, ultra violet light) Spectra Absorption spectrum Emission spectrum Sodium 02/05/2017 Example questions 1) State the ionisation energy of this atom in eV. 2) Calculate this ionisation energy in joules. 3) Calculate the wavelength of light needed to ionise the atom. 0eV -0.85eV -1.5eV -3.4eV 4) An electron falls from the -1.5eV to the -3.4eV level. What wavelength of light does it emit and what is the colour? 5) Light of frequency 1x1014Hz is incident upon the atom. Will it be able to ionise the atom? -13.6eV 02/05/2017 Electron Diffraction 02/05/2017 Electron diffraction patterns are seen when electrons are passed through graphite crystal. Diffraction is seen because the distance between the atoms is of the same order as the de Broglie wavelength of the electrons. de Broglie wavelength λ = h mv 1) What is the de Broglie wavelength of electrons travelling at around 2x107ms-1 (electron mass = 9.1x10-31kg)? 2) What would happen to the diffraction pattern if the voltage to the electrons (and therefore their speed) was increased?