waves
DESCRIPTION
Waves. Waves revision. Watch a “Mexican Wave”. 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:. - PowerPoint PPT PresentationTRANSCRIPT
21/04/23
WavesWaves
21/04/23Waves revisionWaves revision
Watch a “Mexican Wave”
21/04/23Some definitions…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)
21/04/23Transverse vs. longitudinal Transverse vs. longitudinal waveswaves
Transverse waves are when the displacement is at right angles to the direction of the wave…
Longitudinal waves are when the displacement is parallel to the direction of the wave…
Dis
pla
cem
en
tDirection
Direction
Displacement
Where are the compressions and rarefactions?
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Oscillating SystemsOscillating SystemsDesign an experiment that determines what the period of oscillation depends on for these two oscillating systems:
T = 2π lg
T = 2πmk
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Displacement-time graphsDisplacement-time graphsConsider a pendulum bob:
Let’s draw a graph of displacement against time:
Displacement
Time
Equilibrium position “Sinusoidal”
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Phase DifferencePhase DifferenceThere 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”
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Phase DifferencePhase Difference
What is the phase difference between each of these waves?
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The Wave EquationThe Wave Equation
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
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1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?
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?
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?
4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?
Some example wave equation Some example wave equation questionsquestions
0.2m
0.5m
0.6ms-1
3x108ms-
1
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Electromagnetic WavesElectromagnetic Waves
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Electromagnetic RadiationElectromagnetic RadiationE-M radiation is basically a movement of energy in the form of a wave. Some examples:
21/04/23The Electromagnetic The Electromagnetic SpectrumSpectrum
Gamma rays
X-rays Ultra violet Visible light
Infra red Microwaves
Radio/TV
Each type of radiation shown in the electromagnetic spectrum has a different wavelength and a different frequency:
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
High frequency, _____ wavelength
Low frequency, _____ (high) wavelength
γ
21/04/23The Electromagnetic The Electromagnetic SpectrumSpectrum
Type of radiation Uses Dangers
Gamma rays
X rays
Ultra violet
Visible light
Infra red
Microwaves
TV/radio
Treating cancer, sterilisation
Medical
Sun beds
Seeing things
Remote controls, heat transfer
Satellites, phones
Communications
Cell mutation
Cell mutation
Skin cancer
None (unless you look at the sun)
Sunburn
Very few
Very few
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Water WavesWater WavesQ. Design an experiment that explores the relationship between the depth of water and the speed of a wave in that water.
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Reflection revisionReflection revisionReflection from a mirror:
Incident ray
Normal
Reflected ray
Angle of incidence
Angle of reflection
Mirror
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Refraction RevisionRefraction Revision
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Refraction through a glass Refraction through a glass blockblock
Light slows down and bends towards the normal due to
entering a more dense medium
Light speeds up and bends away from the normal due to entering a less dense
medium
Light slows down but is not bent, due to
entering along the normal
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RefractionRefraction
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Refractive IndexRefractive IndexThe Refractive Index of a material is a measure of the factor by which the material will slow down light:
Refractive index =
Speed in medium 1Speed in medium 2
1μ2 = v1
v2
Willebrord Snellius, 1580-1626
Using some interesting maths I turned this relationship into Snell’s Law:
1μ2 =sinθ1
sinθ2
sin i
sin r=
21/04/23Questions on the Refractive Questions on the Refractive IndexIndex
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.
2) Calculate the angles θW and θG for light incident at 40O to the air-water boundary:
Air
Water
Glass
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More Questions…More Questions…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.
21/04/23Measuring the Refractive Measuring the Refractive IndexIndex
1μ2 =sinθ1
sinθ2
sin i
sin r=
Using Snell’s Law we can measure the refractive index of a material:
From this equation a graph of sin i against sin r will have a gradient of the refractive index:
Sin i
Sin r
21/04/23Finding the Critical Angle…Finding the Critical Angle…
1) Ray gets refracted
4) Ray gets internally reflected3) Ray still gets refracted (just!)
2) Ray still gets refracted
THE CRITICAL ANGLE
21/04/23Uses of Total Internal Uses of Total Internal ReflectionReflection
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
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PolarisationPolarisationConsider 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:
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PolarisationPolarisation
21/04/23Polarisation and Polarisation and MicrowavesMicrowaves
Describe an experiment that demonstrates that microwaves are polarised.
21/04/23Sugar Solution and Polarised Sugar Solution and Polarised LightLight
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.
21/04/23Using polarized light to see Using polarized light to see stressstress
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Pulse-Echo techniquesPulse-Echo techniquesIn pulse-echo techniques sound is reflected from an object to measure the distance to that object:
21/04/23Pulse-Echo techniques - Pulse-Echo techniques - UltrasoundUltrasound
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
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?
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The Maths of Pulse-EchoThe Maths of Pulse-EchoConsider shouting at a wall:
The speed of sound is given by:
x
v = 2x/t
Therefore x = vt/2
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The Maths of Pulse-EchoThe Maths of Pulse-EchoThe echo takes 0.8 seconds to return and the speed of sound in water is 1500ms-1. How deep is the water?
t/μs25
50
75
100 125 150 175 200
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.
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Ultrasound vs X RaysUltrasound vs X Rays
1) Why are X Rays better than ultrasound?
2) Why is ultrasound better than X Rays?
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The Doppler EffectThe Doppler Effect
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Phase Difference RevisionPhase Difference RevisionPhase 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”
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CoherenceCoherenceTwo 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.
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CoherenceCoherence
These waves have the same frequency and the same constant phase difference, so they are “coherent”
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SuperpositionSuperpositionSuperposition is seen when two waves of the same type cross. It is defined as “the vector sum of the two displacements of each wave”:
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Superposition patternsSuperposition patternsConsider 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.
21/04/23Superposition of Sound Superposition of Sound WavesWaves
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Path DifferencePath DifferenceConstructive interference
Destructive interference
Max
1st Max
1st Max
Min
Min
2nd Max
21/04/23Young’s Double Slit Young’s Double Slit ExperimentExperiment
Screen
D
O
A
x
s
λ
λs
x
D= λ
xs
D=
21/04/23Interference Patterns from 2 Interference Patterns from 2 slitsslits
Intensity
Distance
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InterferometersInterferometersTask: 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)
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How CD Players workHow CD Players workCDs are made of millions of small bumps etched onto a silvery surface using a laser. Here’s how they work:
Silvery surface
λ/4
Path difference between these two waves = 0, therefore constructive interference
Path difference between these two waves = λ/2, therefore destructive interference
21/04/23Stationary (Standing) Stationary (Standing) WavesWaves
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:
21/04/23Stationary (Standing) Stationary (Standing) WavesWaves
3 nodes 2 antinodes
5 nodes 4 antinodes
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HarmonicsHarmonics
Fundamental frequency f0, λ=2l
First overtone, second harmonic, f=2f0, λ=l
Third overtone, fourth harmonic, f=4f0, λ=l/2
l
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Wind InstrumentsWind InstrumentsWind instruments are basically instruments that form standing waves using air.
Consider waves in an open pipe. They will always form an antinode at an open end:
L
L=λ/2, f=f0
L=λ, f=2f0
L=3λ/2, f=3f0
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Now consider a closed pipe, which will form a node at the closed end:
L
L=λ/4, f=f0
L=3λ/4, f=3f0 L=5λ/4, f=5f0
Wind InstrumentsWind Instruments
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Example QuestionsExample QuestionsA 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
21/04/23DiffractionDiffraction
More diffraction if the size of the gap is similar to the wavelength
More diffraction if wavelength is increased (or frequency decreased)
21/04/23Interference Patterns from 2 Interference Patterns from 2 slitsslits
Intensity
Distance
21/04/23Interference Patterns from 1 Interference Patterns from 1 slitslit
Intensity
Distance
21/04/23Sound can also be diffracted…Sound can also be diffracted…
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.
21/04/23Diffraction depends on Diffraction depends on frequency…frequency…
A high frequency (short wavelength) wave doesn’t get diffracted much – the house won’t be able to receive
it…
21/04/23Diffraction depends on Diffraction depends on frequency…frequency…
A low frequency (long wavelength) wave will get diffracted more, so the
house can receive it…
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Image ResolutionImage ResolutionConsider 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
Distance
Q. What will happen if the objects move
closer together?
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Electron DiffractionElectron DiffractionElectron 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
mv1) 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?
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ElectricityElectricity
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Electric CurrentElectric CurrentElectric current is a flow of negatively charged particles (i.e. electrons). We call them “charge carriers”
Note that electrons go from negative to positive-+ e-
e-
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Conventional CurrentConventional CurrentAs 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:
+ -
21/04/23
Basic ideas…Basic ideas…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
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More basic ideas…More basic ideas…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
21/04/23DC and ACDC and AC
DC stands for “Direct Current” – the current only flows in one direction:
AC stands for “Alternating Current” – the electrons change direction 50 times every second (frequency = 50Hz)
1/50th s
240V
V
V
Time
T
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Charge and CurrentCharge and CurrentRecall the structure of an atom:
ELECTRON – negatively charged
PROTON – positively 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)
21/04/23
Static ElectricityStatic ElectricityStatic electricity is when charge “builds up” on an object and then stays “static”. How the charge builds up depends on what materials are used:
+ -
+-
+
+-
-
-+
+
+
-
-
+
+
+-
-
-
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Static ElectricityStatic Electricity
++
+ --
-
--
---
-
21/04/23
Measuring ChargeMeasuring Charge
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
21/04/23
Calculating Charge (Q)Calculating Charge (Q)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 chargeI = 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?
21/04/23
Current in a series circuitCurrent in a series circuit
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.
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Current in a parallel circuitCurrent in a parallel circuit
A PARALLEL circuit is one where the current has a “choice of routes”
Here comes the current…
And the rest will go down here…
Half of the current will go down here (assuming the bulbs are the same)…
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Current in a parallel circuitCurrent in a parallel circuit
If the current here is 6 amps
The current here will be…
The current here will be…
The current here will be…
And the current here will be…
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Some example questions…Some example questions…
3A
6A
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Kirchoff’s First LawKirchoff’s First Law
6A
For example:
If the current through here is
4A...…and the current through here is
2A…
… then the current here
will be 6A
Gustav Kirchoff (1824-
1887)
“The sum of the currents leaving a point is the same as the sum of the currents
entering that point.”
21/04/23
VoltageVoltageEarlier on we said that current is when electrons move:
-+ e-
e-“Voltage” is the force that pushes the electrons. For 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.
21/04/23
Voltage in a series circuitVoltage in a series circuit
V
V V
If the voltage across the battery is 6V…
…and these bulbs are all identical…
…what will the voltage across each bulb be? 2V
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Voltage in a series circuitVoltage in a series circuit
V
V
If the voltage across the battery is 6V…
…what will the voltage across two bulbs be?
4V
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Voltage in a parallel circuitVoltage in a parallel circuit
If the voltage across the batteries is 4V…
What is the voltage here?
And here?
V
V4V
4V
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SummarySummary
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”
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An example question:An example question:
V1
V2
6V
3A
A1
A2
V3
A3
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Another example question:Another example question:
V1
V2
10V3A
A1
A2
V3
A3
21/04/23Electromotive force and Electromotive force and p.d.p.d.
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…
Is equal to the sum of the p.d.s
Definition of EMF – “the total work done by a cell per coulomb of charge”
21/04/23
Kirchoff’s Second LawKirchoff’s Second Law
For example:
The voltage across each bulb will be
1V
If the e.m.f of the batteries
is 3V
Gustav Kirchoff (1824-
1887)
“Around any closed loop, the sum of the e.m.f.s is equal to the sum of the p.d.s.”
21/04/23
Voltage at a pointVoltage at a point
Take this point as being 0V
The voltage here is 1.5V
The voltage here is 3V
The voltage here is 4.5V
The voltage here is 6V
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Voltage-position graphsVoltage-position graphs6V
5.9V
0.1V
4.5V
1.5V
0V
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Work doneWork doneDefinition of a volt:
The voltage between two points is the work done per coulomb travelling between the two points
Voltage = work done
charge
V = W
Q
We can see that 1V = 1JC-1
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Example QuestionsExample Questions
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?
21/04/23
Electrical PowerElectrical Power
Voltage = work done
chargeW = QV1) Recall:
2) Also, recall that power = rate of doing work
Power = work done
time
P = W
T
3) ThereforePower = charge x voltage
time
P = Q x V
T
4) But I = Q
T
so Power = current x voltage
P = IV or V2/R or I2R
21/04/23Using voltmeters and Using voltmeters and ammetersammeters
V
A
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.
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Georg Simon Ohm 1789-1854
ResistanceResistance
Resistance is anything that will RESIST a current. It is
measured in Ohms, a unit named after me.
The resistance of a component can be calculated using Ohm’s Law:
Resistance = Voltage (in V)
(in ) Current (in A)
V
RI
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An example question:An example question:
V
A
1) What is the resistance across this bulb?
2) Assuming all the bulbs are the same what is the total resistance in this circuit?
Voltmeter reads 10V
Ammeter reads 2A
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More examples…More examples…
12V
3A
3A
6V
4V
2A
1A
2V
What is the resistance of these bulbs?
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ResistanceResistance
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
21/04/23
Resistors in SeriesResistors in Series
V1
V2
R1
R2
VT
I
VT = V1 + V2
VT = IRT
But V1 = IR1 and V2 = IR2
IRT = IR1 + IR2
“In a series circuit current stays the same but voltage splits up”
RT = R1 + R2
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Resistors in ParallelResistors in ParallelIT
R1 R2
I1 I2
IT
V
“In a parallel circuit voltage stays the same but current splits up”
IT = I1 + I2
IT = V
RT
V = V + V
RT R1 R2
1 = 1 + 1
RT R1 R2
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Example questionsExample questionsCalculate the equivalent resistance:
1)
3)
2)
4)
10Ω
10Ω
40Ω
20Ω
20Ω
100Ω
100Ω
20Ω
100Ω 50Ω
50Ω
21/04/23
Power through a resistorPower through a resistor
Recall: 1) P = IV 2) V = IR
Putting these two equations together gives us: 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.
21/04/23
Carrier DensityCarrier DensityConsider a copper atom:
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.
The diameter of a copper atom is about 0.25nm
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)
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Some questions…Some questions…
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.
21/04/23
Drift SpeedDrift Speed
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.
Definition: Drift speed is the speed with which electrons will move down a wire. How do we work it
out?
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
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Example questionsExample questions1) 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.
21/04/23
Battery Bulb
This seems slow…This seems slow…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:
When an electron is pushed in it knocks on the others so that electrons “come out” at the other end. Simple really…
21/04/23
Comparing Drift SpeedsComparing Drift SpeedsConsider 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
21/04/23
ResistivityResistivityThe 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?
21/04/23
Electron DriftElectron DriftWhat happens inside a conducting material? The following model of a metal wire could help:
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.
IonsElectrons
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Electron DriftElectron DriftNow apply a voltage:
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.
IonsElectronsNegative Positive
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Understanding ResistanceUnderstanding Resistance1) Increase length
2) Increase area
3) Decrease resistivity
Resistance = resistivity x length
area
R = ρL
A
Therefore
21/04/23
Understanding CurrentUnderstanding CurrentRecall the equation:
I = nAqv
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 ____ _____.
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
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Potential DividersPotential Dividers
0V
VIN
VOUT
0V
R1
R2
(R1 + R2)
VIN x(R2)VOUT
The Potential Divider equation:
21/04/23Some example questionsSome example questions
0V
12V
VOUT
0V
100
100
0V
1.5V
VOUT
0V
50
45
0V
50V
VOUT
0V
10
75
0V
3V
VOUT
0V
75
25
21/04/23Practical applicationsPractical applications
0V
Vin
VOUT
Here’s a potential divider that is used to control light-activated switches…
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
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An exampleAn example
A
15Ω
A
A
6V
Calculate the missing values (from June 2006)
0.24A
R
4Ω V
? ?
?
?
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More examplesMore examples
?
20Ω
?
A
18V
0.5A
?
10Ω
?
18V
10Ω 40
Ω
10
Ω
? ?
?
?
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Current-Voltage GraphsCurrent-Voltage Graphs
Voltage on powerpack/V
Current/A Voltage/V
1210…0…-10-12
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Two simple components:Two simple components:
2) Thermistor – resistance DECREASES when temperature INCREASES (“negative temperature coefficient”)
1) Light dependant resistor – resistance DECREASES when light intensity INCREASES
Resistance
Amount of light
Resistance
Temperature
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Current-voltage graphsCurrent-voltage graphs
I
V
Consider a resistor:
Current increases in proportion to voltage
R
V
Resistance stays constant
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Current-voltage graphsCurrent-voltage graphs
I
V
Now consider a bulb:
R
V
Resistance increases as the bulb gets
hotter
As voltage increases the bulb gets hotter
and resistance increases – “non-Ohmic
behaviour”
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Current-voltage graphsCurrent-voltage graphs
I
V
Now consider a diode:
I
V
Resistance decreases as the (“negative-
temperature-coefficient”) thermistor gets hotter
A diode only lets current go in the “forward” direction
Now consider a thermistor:
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Internal ResistanceInternal Resistance
-+
V The voltage across the terminals of a battery is
called the “terminal p.d.”
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Internal ResistanceInternal Resistance
-+
V This voltage DECREASES when more components
are added…
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Internal ResistanceInternal ResistanceAll 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.
21/04/23Measuring Internal Measuring Internal ResistanceResistance
EMF
Lost volts
Terminal p.d.
From Kirchoff’s 2nd law:
EMF = lost volts + p.d
E = Ir + V
V = E - Ir
V = (-r)I + E
V
I
21/04/23
Short Circuit CurrentShort Circuit Current
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.
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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:
Numerical quizNumerical quiz
10Ω each 20Ω
each
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Numerical quizNumerical quiz6) 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.
21/04/23
Numerical quizNumerical quiz11)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:
0V
12V
VOUT
0V
50
150
0V
20V
VOUT
0V
4
6
21/04/23
The Nature of The Nature of LightLight
W Richards
The Weald School
21/04/23
IntensityIntensityDefinition: “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 =
(in Wm-2)
Power (in W)
Area (in m2)φ =
P
4πr2
An “inverse square law”
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IntroductionIntroductionSome 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.
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Photoelectric EmissionPhotoelectric EmissionConsider a gold-leaf electroscope…
Now charge the top:
5000V
-
+
- - - - ---
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Photoelectric EmissionPhotoelectric EmissionLet’s put a piece of zinc on top:
-
Now shine some UV light onto it:
-
-
-- - --
Ultra-violetUltra-violet light is causing the zinc to emit
electrons – this is “Photoelectric
Emission”.
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Some definitions…Some definitions…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.
21/04/23
Photoelectron EnergyPhotoelectron EnergyPhoton
-Some energy is needed to release the electron (the work function φ)…
…and some energy is given to the electron as kinetic energy.
Photon Energy = work function + kinetic energy of electron
21/04/23
Calculating Photon EnergyCalculating Photon Energy
I think that the energy of a photon is proportional to its frequency, so E=hf,
where h = Planck’s Constant = 6.63x10-34Js.
Photon energy = work function + kinetic energy of electron
hf = φ + 1/2mv2
On the previous slide we said that…
21/04/23Measuring the Energy of a Measuring the Energy of a PhotoelectronPhotoelectron
V
A
-
+
Illuminate the electrode:
Electrons are “stopped” by this voltage
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The “Hill” analogyThe “Hill” analogyTo 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.
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).
Vs
Negative electrode
21/04/23
Photon EnergyPhoton EnergyCombining 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
Photon frequency
Threshold frequency
Gradient = h/Q
21/04/23
Spectra – introductionSpectra – introduction
21/04/23
Source of light “Spectra
”
SpectraSpectra
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helium
Some wavelengths of light are absorbed by
the gas – an “absorption spectrum”.
Absorption SpectraAbsorption Spectra
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SpectraSpectraContinuous spectrum
Absorption spectrum
Emission spectrum
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Emission SpectraEmission SpectraHydrogen
Helium
Sodium
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SpectraSpectraConsider a ball in a hole:
When the ball is here it has its lowest gravitational potential energy.
We can give it potential energy by lifting it up:
If it falls down again it will lose this gpe:
20J
5J
5J
30J
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SpectraSpectraA 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”
21/04/23
SpectraSpectraIf we illuminate the atom we can excite the electron:
0eV
-0.85eV
-1.5eV
-3.4eV
-13.6eV
Q. What wavelength of light would be needed to excite this electron to ionise it?
Light
Energy change = 3.4eV = 5.44x10-
19J.Using E=hc/λ wavelength = 3.66x10-7m(In other words, ultra violet light)
21/04/23
SpectraSpectraAbsorption spectrum
Emission spectrum
Sodium
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Example questionsExample questions1) 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.
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?
0eV
-0.85eV
-1.5eV
-3.4eV
-13.6eV
21/04/23
Electron DiffractionElectron DiffractionElectron 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
mv1) 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?