Download Waves - The Student Room

02/05/2017
Waves
Waves revision
Watch a “Mexican Wave”
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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)
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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
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Consider a pendulum bob:
Let’s draw a graph of displacement against time:
Equilibrium position
Displacement
“Sinusoidal”
Time
Phase Difference
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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?
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The Wave Equation
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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
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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
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Electromagnetic Radiation
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E-M radiation is basically a movement of energy in the form of
a wave. Some examples:
The Electromagnetic Spectrum
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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
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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
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Refraction through a glass block
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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
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Refractive Index
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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
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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…
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1) Ray gets refracted
3) Ray still gets refracted (just!)
THE CRITICAL
ANGLE
2) Ray still gets refracted
4) Ray gets
internally reflected
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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:
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Polarisation
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Polarisation and Microwaves
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Describe an experiment that demonstrates that microwaves
are polarised.
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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.
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Using polarized light to see stress
Pulse-Echo techniques
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In pulse-echo techniques sound is reflected from an object to
measure the distance to that object:
Pulse-Echo techniques - Ultrasound
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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
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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
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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?
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The Doppler Effect
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Phase Difference Revision
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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
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These waves have the same frequency
and the same constant phase
difference, so they are “coherent”
Superposition
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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
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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
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Path Difference
Constructive
interference
Destructive
interference
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1st Max
Min
Max
Min
1st Max
2nd Max
Young’s Double Slit Experiment
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D
λ
s
O
x
λ
s
=
x
D
λ =
xs
D
A
Screen
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Interference Patterns from 2 slits
Intensity
Distance
Interferometers
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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
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3 nodes
2 antinodes
5 nodes
4 antinodes
Harmonics
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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
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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)
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Interference Patterns from 2 slits
Intensity
Distance
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Interference Patterns from 1 slit
Intensity
Distance
Sound can also be diffracted…
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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…
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A high frequency (short wavelength)
wave doesn’t get diffracted much – the
house won’t be able to receive it…
Diffraction depends on frequency…
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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?
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Electricity
Electric Current
Electric current is a flow of
negatively charged particles
(i.e. electrons). We call
them “charge carriers”
+
e-
-
e-
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Note that
electrons go
from negative
to positive
Conventional Current
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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
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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
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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
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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…
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3A
6A
Kirchoff’s First Law
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“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
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If the voltage
across the
battery is 6V…
…what will the
voltage across
two bulbs be?
V
V
4V
Voltage in a parallel circuit
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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
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Another example question:
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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
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“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
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Voltage-position graphs
6V
5.9V
4.5V
1.5V
0.1V
0V
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Work done
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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…
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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
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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?