09/09/2015Waves. Waves revision Watch a “Mexican Wave”

19/04/23

WavesWaves

19/04/23Waves revisionWaves revision

Watch a “Mexican Wave”

19/04/23Some 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)

19/04/23Transverse 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?

19/04/23

Oscillating SystemsOscillating SystemsDesign an experiment that determines what the period of oscillation depends on for these two oscillating systems:

T = 2π lg

T = 2πmk

19/04/23

Displacement-time graphsDisplacement-time graphsConsider a pendulum bob:

Let’s draw a graph of displacement against time:

Displacement

Time

Equilibrium position “Sinusoidal”

19/04/23

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”

19/04/23

Phase DifferencePhase Difference

What is the phase difference between each of these waves?

19/04/23

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

19/04/23

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

19/04/23

Electromagnetic RadiationElectromagnetic RadiationE-M radiation is basically a movement of energy in the form of a wave. Some examples:

19/04/23The 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

19/04/23The 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

19/04/23

Water WavesWater WavesQ. Design an experiment that explores the relationship between the depth of water and the speed of a wave in that water.

19/04/23

Reflection revisionReflection revisionReflection from a mirror:

Incident ray

Normal

Reflected ray

Angle of incidence

Angle of reflection

Mirror

19/04/23

Refraction RevisionRefraction Revision

19/04/23

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

19/04/23

RefractionRefraction

19/04/23

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=

19/04/23Questions 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

19/04/23

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.

19/04/23Measuring 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

19/04/23Finding 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

19/04/23Uses 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

19/04/23

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:

19/04/23

PolarisationPolarisation

19/04/23Polarisation and Polarisation and MicrowavesMicrowaves

Describe an experiment that demonstrates that microwaves are polarised.

19/04/23Sugar 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.

19/04/23Using polarized light to see Using polarized light to see stressstress

19/04/23

Pulse-Echo techniquesPulse-Echo techniquesIn pulse-echo techniques sound is reflected from an object to measure the distance to that object:

19/04/23Pulse-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?

19/04/23

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

19/04/23

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.

19/04/23

Ultrasound vs X RaysUltrasound vs X Rays

1) Why are X Rays better than ultrasound?

2) Why is ultrasound better than X Rays?

19/04/23

The Doppler EffectThe Doppler Effect

19/04/23

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”

19/04/23

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.

19/04/23

CoherenceCoherence

These waves have the same frequency and the same constant phase difference, so they are “coherent”

19/04/23

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”:

19/04/23

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.

19/04/23Superposition of Sound Superposition of Sound WavesWaves

19/04/23

Path DifferencePath DifferenceConstructive interference

Destructive interference

Max

1st Max

1st Max

Min

Min

2nd Max

19/04/23Young’s Double Slit Young’s Double Slit ExperimentExperiment

Screen

D

O

A

x

s

λ

λs

x

D= λ

xs

D=

19/04/23Interference Patterns from 2 Interference Patterns from 2 slitsslits

Intensity

Distance

19/04/23

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)

19/04/23

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

19/04/23Stationary (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:

19/04/23Stationary (Standing) Stationary (Standing) WavesWaves

3 nodes 2 antinodes

5 nodes 4 antinodes

19/04/23

HarmonicsHarmonics

Fundamental frequency f0, λ=2l

First overtone, second harmonic, f=2f0, λ=l

Third overtone, fourth harmonic, f=4f0, λ=l/2

l

19/04/23

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

19/04/23

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

19/04/23

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

19/04/23DiffractionDiffraction

More diffraction if the size of the gap is similar to the wavelength

More diffraction if wavelength is increased (or frequency decreased)

19/04/23Interference Patterns from 2 Interference Patterns from 2 slitsslits

Intensity

Distance

19/04/23Interference Patterns from 1 Interference Patterns from 1 slitslit

Intensity

Distance

19/04/23Sound 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.

19/04/23Diffraction 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…

19/04/23Diffraction depends on Diffraction depends on frequency…frequency…

A low frequency (long wavelength) wave will get diffracted more, so the

house can receive it…

19/04/23

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?

19/04/23

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?

19/04/23

ElectricityElectricity

19/04/23

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-

19/04/23

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:

+ -

19/04/23

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

19/04/23

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

19/04/23DC 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

19/04/23

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)

19/04/23

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:

+ -

+-

+

+-

-

-+

+

+

-

-

+

+

+-

-

-

19/04/23

Static ElectricityStatic Electricity

++

+ --

-

--

---

-

19/04/23

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

19/04/23

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?

19/04/23

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.

19/04/23

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)…

19/04/23

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…

19/04/23

Some example questions…Some example questions…

3A

6A

19/04/23

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.”

19/04/23

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.

19/04/23

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

19/04/23

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

19/04/23

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

19/04/23

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”

19/04/23

An example question:An example question:

V1

V2

6V

3A

A1

A2

V3

A3

19/04/23

Another example question:Another example question:

V1

V2

10V3A

A1

A2

V3

A3

19/04/23Electromotive 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”

19/04/23

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.”

19/04/23

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

19/04/23

Voltage-position graphsVoltage-position graphs6V

5.9V

0.1V

4.5V

1.5V

0V

19/04/23

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

19/04/23

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?

19/04/23

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

19/04/23Using 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.

19/04/23

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

19/04/23

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

19/04/23

More examples…More examples…

12V

3A

3A

6V

4V

2A

1A

2V

What is the resistance of these bulbs?

19/04/23

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

19/04/23

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

19/04/23

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

19/04/23

Example questionsExample questionsCalculate the equivalent resistance:

1)

3)

2)

4)

10Ω

10Ω

40Ω

20Ω

20Ω

100Ω

100Ω

20Ω

100Ω 50Ω

50Ω

19/04/23

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.

19/04/23

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)

19/04/23

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.

19/04/23

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

19/04/23

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.

19/04/23

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…

19/04/23

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

19/04/23

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?

19/04/23

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

19/04/23

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

19/04/23

Understanding ResistanceUnderstanding Resistance1) Increase length

2) Increase area

3) Decrease resistivity

Resistance = resistivity x length

area

R = ρL

A

Therefore

19/04/23

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

19/04/23

Potential DividersPotential Dividers

0V

VIN

VOUT

0V

R1

R2

(R1 + R2)

VIN x(R2)VOUT

The Potential Divider equation:

19/04/23Some 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

19/04/23Practical 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

19/04/23

An exampleAn example

A

15Ω

A

A

6V

Calculate the missing values (from June 2006)

0.24A

R

4Ω V

? ?

?

?

19/04/23

More examplesMore examples

?

20Ω

?

A

18V

0.5A

?

10Ω

?

18V

10Ω 40

Ω

10

Ω

? ?

?

?

19/04/23

Current-Voltage GraphsCurrent-Voltage Graphs

Voltage on powerpack/V

Current/A Voltage/V

1210…0…-10-12

19/04/23

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

19/04/23

Current-voltage graphsCurrent-voltage graphs

I

V

Consider a resistor:

Current increases in proportion to voltage

R

V

Resistance stays constant

19/04/23

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”

19/04/23

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:

19/04/23

Internal ResistanceInternal Resistance

-+

V The voltage across the terminals of a battery is

called the “terminal p.d.”

19/04/23

Internal ResistanceInternal Resistance

-+

V This voltage DECREASES when more components

are added…

19/04/23

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.

19/04/23Measuring 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

19/04/23

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.

19/04/23

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

19/04/23

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.

19/04/23

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

19/04/23

The Nature of The Nature of LightLight

W Richards

The Weald School

19/04/23

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”

19/04/23

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.

19/04/23

Photoelectric EmissionPhotoelectric EmissionConsider a gold-leaf electroscope…

Now charge the top:

5000V

-

+

- - - - ---

19/04/23

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”.

19/04/23

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.

19/04/23

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

19/04/23

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…

19/04/23Measuring the Energy of a Measuring the Energy of a PhotoelectronPhotoelectron

V

A

-

+

Illuminate the electrode:

Electrons are “stopped” by this voltage

19/04/23

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

19/04/23

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

19/04/23

Spectra – introductionSpectra – introduction

19/04/23

Source of light “Spectra

”

SpectraSpectra

19/04/23

helium

Some wavelengths of light are absorbed by

the gas – an “absorption spectrum”.

Absorption SpectraAbsorption Spectra

19/04/23

SpectraSpectraContinuous spectrum

Absorption spectrum

Emission spectrum

19/04/23

Emission SpectraEmission SpectraHydrogen

Helium

Sodium

19/04/23

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

19/04/23

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”

19/04/23

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)

19/04/23

SpectraSpectraAbsorption spectrum

Emission spectrum

Sodium

19/04/23

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

19/04/23

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?