Current Electricity and Elastic Properties of Solids

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Current Electricity and Elastic Properties of
Solids
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Current

• What is it in simple terms
• What is it measured with ?
• And how do you use it?
• What are its units?
• What is its definition?
• What is the defining equation?

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Current

• Current is the flow of charge from ve to -ve
• Current is measured with an ammeter
• The ammeter is placed in series with the circuit
• The unit is the AMPERE (amp) A
• An amp is one coulomb of charge passing a point
  in one second
• I ?Q/?t
• (Current is the rate of change of charge)

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Charge

• What is it measured in?
• What is the charge on the electron?

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Charge

• This is measured in coulombs (C).
• The charge on one electron is 1.6 x 10-19C.
• One amp is approximately 6 x 1018 electrons
  passing one point in one second.

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Potential Difference

• What is the common name?
• What is it in simple terms?
• What is it measured in?
• What is it measured with?
• How is it measured?
• How is it related to energy?
• What is the definition?

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Potential Difference (VOLTAGE)

• It is the push
• It is measured in volts (V)
• Using a voltmeter
• Connected across something
• The higher the voltage across something the
  greater the energy loss
• One volt is one joule per coulomb
• What is this in equation format?

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Voltage

• One volt is one joule per coulomb
• V W / Q (E QV)
• Voltage Energy / Charge

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Resistance

• What is it in simple terms?
• What is the definition?
• What is it in equation form?
• What is it measured in?

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Resistance

• A measure of how hard it is for electricity to
  pass through something?
• Resistance is the ratio of the voltage across
  something divided by the current flowing through
  it.
• R V / I (V I x R)
• Resistance is measured in OHMS (O)

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Voltage current characteristics

• You need to know the shapes of a -
• Ohmic conductor (resistor)
• Semiconductor Diode
• And Filament Lamp
• So can you remember them and the scales?

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Ohmic Conductor
Current/A
Small resistance
Big resistance
Voltage/V
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Filament Lamp
Current/A
Small resistance
Big resistance
Why does the resistance increase?
Voltage/V
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Filament Lamp
Current/A
Big resistance High current
Small resistance Low current
The resistance increases as the current increases
because the power loss creates a rise in
temperature which makes it more difficult for the
electrons to move.
Voltage/V
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Semiconductor Diode
Current/A
Small resistance
Voltage/V
Approx 0.6V
Very big resistance
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Ohms Law

• What is it ?
• What has to remain constant for ohms law to apply?

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Ohms Law

• The resistance of a metallic conductor remains
  constant provided the temperature remains
  constant.
• OR current is proportional to the applied voltage
  provided the temperature remains constant.
• V I x R

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Non Ohmic conductors?

• Eh?
• Ok what doesn't obey ohms law?
• And what are the uses?

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Thermistors

• The resistance of a thermistor decreases as it
  gets hotter (opposite to a filament lamp or
  ordinary resistor)
• A thermistor can be used as a temperature sensor!

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Circuits!!

• Dont Panic!
• There are some simple rules but you have to learn
  them!
• Read on -

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Current and voltage

• Come on you must know what they are by now

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Current is a FLOW of charge
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Voltage is a measure of the energy lost or gained
when one coulomb of charge moves
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Series and parallel

• What is the difference and how does it effect
  current and voltage?

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Series

• The circuit has one loop only.
• The electricity can only go one way it cannot
  split in a series circuit.
• So what about current and voltage?

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Series

• The current is the .in a series circuit
• The energy and shared out around the
  circuit.
• The across all of the resistances . up to
  the supply (battery) voltage.

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Series

• The current is the same at all points in a series
  circuit
• The energy and voltage is shared out around the
  circuit.
• The voltage across all of the resistances adds up
  to the supply (battery) voltage.

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Parallel circuits

• There is more than one way around the circuit.
• The current HAS to split up
• So how does it work??

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Parallel

• When the current reaches a junction it will
  split.
• The total current entering a junction will be
  equal to the total current leaving the junction.
• This is simply charge conservation.
• How about voltage?

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Parallel

• The voltage across each branch is the same.
• Now apply these rules to the following circuits-

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Parallel circuits
What is the voltage across each resistor if they
are all the same value? Why? Which resistor(s)
has the most current? Why?
12v
1
2
3
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Parallel circuits
Resistor 1 has 12 v across it ( the same as the
battery) Resistor 2 and 3 together form one
branch and get a total of 12 v across them but
as they are in series with each other they have
6 v across each.
12v
1
2
3
The branch with resistor 1 in only has one
resistor so this resistance is smaller than the
other branch. This means that resistor 1 will
have the most current through it
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Adding resistors together

• If they are in a line just add them together!!
• If they are in parallel use the following
  equation-
• 1/RT 1/R1 1/R2 1/R3
• Dont forget that you should always get a
  resistance that is lower than the lowest single
  resistor.
• If two resistors are the same value then when
  they are in parallel the new resistance will be
  exactly half of one of them.

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Ok How about some simple energy/power equations?

• Can you remember them all?

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Energy/Power

• P I x V
• But E P x t
• So E I x V x t (OR ITV!)
• P I2 x R
• And not in the specification but useful-
• P V2 / R
• But what do they tell us?

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Applications of these equations

• P I x V
• This tells us the power lost in a component (e.g.
  resistor) if the voltage across it is V and the
  current through it is I (tricky stuff eh?)
• E I x V x t
• Guess what! it tells us the energy given out by a
  component (e.g. resistor) if the voltage across
  it is V and the current through it is I and it
  flows for a time t!

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The Potential Divider

• So what does that potential word mean again?
• What units is it measured in?

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The Potential Divider

• The potential divider divides a supply voltage so
  that it is lower.
• Can you remember the circuit?

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The Potential Divider
R1
Vin
R2
Vout
So what is the equation then?
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The Potential Divider
R1
Vin
R2
Vout
Vin Vout x R2 / (R1 R2)
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The Potential Divider made simple!

• Ok in simple terms the voltage is just shared
  between the two resistors.
• If the bottom resistor is bigger then the output
  voltage will be
• If the top resistor is small then the output
  voltage will be.
• So the potential divider circuit is simply a
  circuit based on the of the resistors.

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The Potential Divider made simple!

• Ok in simple terms the voltage is just shared
  between the two resistors.
• If the bottom resistor is bigger then the output
  voltage will be big
• If the top resistor is small then the output
  voltage will be small
• So the potential divider circuit is simply a
  circuit based on the ratios of the resistors.

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Now for a Few Simple Examples

• Use the equation
• Or ratios
• But check to see if the answer is sensible!!

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The Potential Divider
R1 100O
Vin 12V
R2 200O
Vout ?
Vin Vout x R2 / (R1 R2)
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The Potential Divider
R1 100O
Vin 36V
R2 500O
Vout ?
Vin Vout x R2 / (R1 R2)
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The Potential Divider
R1 100O
Vin 12V
R2 ? O
Vout 9V
Vin Vout x R2 / (R1 R2)
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The Potential Divider
R1 100O
R3 200O
Vin 12V
R2 200O
Vout ?
Vin Vout x R2 / (R1 R2)
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Electromotive Force

• What is it?
• What does the symbol look like?
• What are its units?
• So what is it like?
• What sort of things have Electromotive force?

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Electromotive Force

• What is it? Supply voltage
• What does the symbol look like? e
• What are its units? Volts
• So what is it like? Supply voltage!
• What sort of things have Electromotive
  force? Cells, batteries, power packs, generators
  etc.

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Internal Resistance

• What is it?
• What does the symbol look like?
• What are its units?
• So where does it come from?
• What sort of things have internal resistance?

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Internal Resistance

• What is it? Resistance inherent in any emf
  (electromotive force) supply
• What does the symbol look like? r
• What are its units? Ohms
• So where does it come from? Resistance of the
  material that makes up the emf supply
• What sort of things have internal resistance?
  Cells, batteries, power packs, generators etc.

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How are e and internal resistance related?

• What is the equation?
• What does terminal pd mean?
• When the current is zero what happens?

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How are e and internal resistance related?

• What is the equation?
• e I ( R r )
• internal resistance
• Emf current circuit resistance
• What does terminal pd mean?
• The voltage across the battery/cell
• When the current is zero what happens?
• The terminal pd the emf!
• Carry on for diagram!

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Internal resistance
Terminal Pd
V
e
r
I
R
When I 0 The terminal pd e
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Alternating Currents
Current/A
A
B
C
Time/s
What do A,B,C represent?
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Alternating Currents
Current/A
A
B
C
Time/s
Still dont know? Pick from peak, rms and peak to
peak.
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Alternating Currents
Current/A
peak
peak to peak
rms
Time/s
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Alternating Voltages
Voltage/V
A
B
C
Time/s
What do A,B,C represent?
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Alternating Voltages
Voltage/V
A
B
C
Time/s
Still dont know? Pick from peak, rms and peak to
peak.
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Alternating Voltage
Voltage/V
peak
peak to peak
rms
Time/s
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In simple terms

• How do rms and peak values relate i.e. which is
  bigger?
• What is the multiplication factor?

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• Peak is bigger than rms
• By a factor of ?2

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What about the equations?

• How do rms and peak values relate?

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Rms and peak

• Irms I0 / ?2
• Root mean square current Peak current
• Vrms V0 / ?2
• Root mean square voltage Peak voltage

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The oscilloscope

• What does it display?
• The vertical axis is controlled by the ?
• The horizontal axis is controlled by the ?

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The oscilloscope

• What does it display?
• Voltages ac and dc
• The vertical axis is controlled by the ?
• Y gain
• The horizontal axis is controlled by the ? Time
  base
• What is it used for?

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The oscilloscope

• It is used to measure voltage
• It can also be used to measure the time period
  and frequency of ac voltages
• And to measure time intervals
• As well as to simply see the shape of a waveform!
• How do you use it??

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The oscilloscope

• Before you can do anything you must write down
  what the and the are.
• And make sure you put the units down!!

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The oscilloscope

• Before you can do anything you must- write down
  what the time base and the y - gain is.
• And make sure you put the units down!!
• (milliseconds!)
• E.g. Time base is 3ms per division.
• Y Gain is 5V per division.

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Look at the following and work out what you can!
The time base is 5ms per div and the y gain is 3V
per div
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You should write each calculation out carefully
e.g.-

• The peak value of the wave is 1.5 divisions
• The y gain is 3V per division
• So the peak voltage is 1.5 x 3 4.5V
• There are 4 waves fitting in 8 divisions
• So each wave fits into 8/4 2 divisions
• The time base is 5ms per division
• So the time for one wave is 5 x 2 10ms
• The frequency is simply 1/the time period
• f 1/10 x 10-3 100Hz

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Now have a go at another one!
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Look at the following and work out what you can!
The time base is 6µs per div and the y gain is 8V
per div
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You should write each calculation out carefully
e.g.-

• The peak value of the wave is 1.5 divisions
• The y gain is 8V per division
• So the peak voltage is 1.5 x 8 12V
• There are 4 waves fitting in 16 divisions
• So each wave fits into 16/4 4 divisions
• The time base is 6µs per division
• So the time for one wave is 4 x 6 24µs
• The frequency is simply 1/the time period
• f 1/24 x 10-6 4.16 x 10 4Hz

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Look at the following and work out what you can!
The time base is 9ms per div and the y gain is
0.1V per div
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You should write each calculation out carefully
e.g.-

• The peak value of the wave is 3 divisions
• The y gain is 0.1V per division
• So the peak voltage is 3 x 0.1 0.3V
• There are 4 waves fitting in 8 divisions
• So each wave fits into 8/4 2 divisions
• The time base is 9ms per division
• So the time for one wave is 9 x 2 18ms
• The frequency is simply 1/the time period
• f 1/18 x 10-3 55.6Hz

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Now for Some Elastic Behaviour

• What does Tensile force mean?
• What does Tensile extension mean?

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Now for Some Elastic Behaviour

• What does Tensile force mean?
• Force applied that will stretch something (as
  opposed to compressive force that squashes
  things!)
• What does Tensile extension mean?
• Extension produced by Tensile force!
• For materials that obey Hooks Law how are force
  and extension related?

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Are you Hooked Yet?

• A material that obeys Hookes law has an
  extension that is directly proportional to the
  applied load.

Tensile Force / N
Hookes Law region
Extension / m
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Hookes law Equation

• What is it?
• Ps. its not in the specification but seems to be
  required and helps understanding!!
• It is the equation with a spring in it!

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Hookes Law Equation

• For a material obeying Hookes law-
• Force is proportional to extension
• F k x e
• Force Spring constant extension

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• What are the units for k?
• What does a big k mean?

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• What are the units for k?
• N/m Nm-1
• What does a big k mean?
• A stiff spring!!

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Energy in stretched object?

• What is the energy stored in a stretched object
  when the force is F and the extension is e AND it
  obeys Hookes law?

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Energy in stretched object?

• The energy stored in a stretched object when the
  force is F and the extension is e AND it obeys
  Hookes law is -
• E ½ F e
• Now derive it!

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Average force

• If a material obeys Hookes law the final force
  will be greater than the average force.
• What is the average force if the final force is F?

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Average force

• The average force will be ½ F!!
• How far has this average force moved if the final
  extension is e? e thats a tough one!

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Work done

• The average force will have moved e!!
• So what is the work done?

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Work done

• The work done is the average force x distance
• Work ½ F x e
• So the energy stored in a stretched object
  is- E ½ Fe
• As long as it obeys H.

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Breaking up

• No not you but materials
• What does plastic and elastic mean?

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Plastic and Elastic

• What does plastic and elastic mean?
• Plastic behaviour, the material is permanently
  deformed once stretched.
• Elastic behaviour, the material returns to its
  original length when released.

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Brittle fracture

• Here a material will snap/fracture (often after
  sudden loads) due to the propagation of cracks
  through the material. For example glass shows
  brittle behaviour and will shatter suddenly when
  a crack travels through the glass. When cutting
  glass a crack is deliberately made by scratching
  the glass to encourage a crack to move in the
  desired direction.

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Ductile Behaviour

• Here the material is behaving plastically and
  will deform large amounts before breaking. For
  instance when soft Iron is stretched the wire
  will stretch and a section of it will deform into
  a narrow region just before it breaks.

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Simple stress-strain graphs

• These are a bit like the old force extension
  graphs.
• What will a standard metal look like?
• Think about whether it is proportional and when
  it would snap etc-

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Stress strain curve for metal
Stress /Mpa
C
B
A
What do A,B,C represent?
Strain (NO UNITS!)
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Stress strain curve for metal
Stress /Mpa
Fractures
Yield point
200
Limit of proportionality
Strain (NO UNITS!)
0.005
0.010
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Stress strain curve for Glass
Stress /Mpa
Note very little plastic deformation before it
fractures
Strain (NO UNITS!)
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What would polythene look like?

• Think about the gradient at the start
• Would it feel stiffer than metal ?
• What happens after you have stretched it a bit
  (think of the plastic that holds together cans of
  beer!)
• Would you expect bigger or smaller strains than
  metal?
• Why?

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Stress strain curve for polythene
Stress /Mpa
Polythene can have very large stains before it
finally snaps!
10
2
3
1
4
Strain
100
Now look at the following curves and say which is
the stiffer!
Stress
A
B
Strain
101
Now look at the following curves and say which is
the stiffer!
Stress
A is the stiffer one with the higher young's
modulus
Strain
102
Now look at the following curves and say which is
the most ductile!
Stress
A
B
Strain
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Now look at the following curves and say which is
the most ductile!
Stress
B is the most ductile as it has a much larger
plastic deformation
A
Strain
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Last but not leastYoung's modulus

• What is the symbol?
• What are the units?
• What do you divide by what to get it!?
• What is the equation?

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Last but not leastYoung's modulus

• What is the symbol? E
• What are the units? Pa or N/m2
• What do you divide by what to get it!?
• Stress/strain!
• What is the equation?
• E Tensile stress
• Tensile strain
• How about the equation in symbols?

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Young's Modulus

• E stress/strain
• E F/A e/l
• E Fl
• Ae

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You must know the method for measuring young's
modulus for a wire

• Note the following points-
• Two wires are used and suspended from the same
  point.
• One is the test wire and one is to give a
  constant reference.
• What problem does this eliminate?

108

• The wires are suspended from the same point so
  that if the support drops both wires will drop
  the same amount.
• How is the extension measured?
• How is the length measured?
• How is the diameter of the wire measured?
• How is the load measured?

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Measuring Young's Modulus

• How is the extension measured?
• With a vernier scale attached between the two
  wires
• How is the length measured?
• Using a metre rule!
• How is the diameter of the wire measured?
• Using a micrometer at least three times.
• How is the load measured?
• By knowing the mass/weight of the loads!

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So What Happens to the Results?

• Guess what we plot a graph!!
• So how does this help?
• What can we tell from the graph?

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Stress Strain Graph
Stress
What does the gradient tell us?
Strain
112

• If it is a stress-strain graph the gradient is
  the young's modulus!
• Easy peasy
• If it is a force extension graph its not so easy-

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Force Extension Graph

• The gradient is F/e
• So how can we find out E?
• E Fl/Ae so E (F/e) x l/A
• So E gradient x l/A

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Finally!

• What else does a stress strain graph tell us??

115

• The area under a stress strain graph tell us the
  strain energy stored per unit volume.

116
Hope That Wasn't Too Much of aStrainI was
trying Not toStresstoo Many Points