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Electricity
26 January 2015

18:54

Charges
• Static electricity
○ Electric charge
 Protons
□ Positive
 Electrons
□ Negative
○ Electrically neutral
 Protons = electrons
○ Negatively charged
 More electrons
○ Positively charged
 More protons
○ Easier to add/remove electrons
 Object negative
□ Electrons added
 Positive
□ Electrons taken away
• Charging by contact
○ Small charges
 Rubbing material against each other
□ Electrons removed
 Friction
 Plastic pen against jumper
□ Lifts small piece of paper
○ STS
 Cleaning
□ Mirrors
□ TV screen
□ Not with dry cloth
 Charge builds
 Dust settles
 Flour mills
□ Charge build
 Cause explosion
○ Charge is measurable in coulombs
 Coulomb
□ Large charge
 Millicoloumbs
□ Often used
• Charging through induction
○ Charged without any direct contact
 Induction
○ Gold-leaf electroscope
 Demonstrates induction
+++++

--------

Gold leaves

Electricity Page 1

Gold leaves

+

Neutral

+

The leaves separate as
they carry a + charge

• Distribution of charge
○ Electric charge
 Spreads out
○ Connected to earth
 Spreads out a lot
□ Disappears
□ Earthing
○ Metal object
 Charge flows on outside
 Curved/spherical
□ Evenly spread charge
○ Point effect
 Wherever an object is less curved, and particular sharp points, there will be a build of charge
...

○ Point discharge
 Point effect
□ Leads to discharge
□ Air
 Becomes ionised
◊ Charged
◊ Negative charges attach to point
 Cancel positive
– Lightning conductors
 Purposes
 Path for lightning Earthing
 Discharge air
 Opposite of point discharge
• Van de Graff generator
○ Used
 Build up static charge
○ Charge
 Transferred
□ Rotating belt
 Friction
 Point effect
□ To metal dome
 Belt
□ Small charge
 Metal
□ Large charge

Electric fields
• Area around a charge where its felt
• Drawing
○ Path a positive charge would take

Electricity Page 2

+

-

+

_

+

• Electric field strength

Electricity Page 3

• Electric field strength
○ Coulombs law
 Derive
□ Electric field strength
○ STS
 Photocopying
□ Rotating drum
 Charged
□ Image
 Copied onto drum
□ Light
 Discharges parts white
□ Toner ink
 Charged
 Attracted
◊ Remainder
□ Modern electronic equipment
 Low voltages
 Working with
◊ Earth prior
• Potential difference
○ Drives electric charge from one point to another
○ Created
 Factors
□ Presence
 Charges
□ Shape of material
○ Measured
 Measuring work done from one point to another
○ Unit
 Volt
○ Earth
 Measured against
 Zero potential (0V)

Capacitance
• Ability to hold charge
• Unit
○ Farad
• Parallel plate capacitor
○ Store electric charge
○ Demonstrated
 Experiment
• Factors determine capacitance of capacitor
○ Common area
○ Distance between plates
○ Material between plates
○ Factors
 Demonstrated
□ Electroscope
□ Plates drawn apart
 Leaves collapse
□ Charge inversely proportional to distance between
□ Reduce area and change material
 Formula
◊
○ STS
 Flash photography
□ Charge capacitor
 Discharges through light bulb
 Tuning radios

V

Electric current
Electricity Page 4

 Discharges through light bulb
 Tuning radios

V

Electric current
• Symbols

Battery (a combination of cells)

Switch

X
Resistor
Galvanometer

• Electric current
○ Flow of charge
• Current
○ 1 amp/ ampere
 Flow of 1 coulomb per second
• Electric circuit
○ Current
 Shown
□ Positive to negative
□ Historical reasons
 Actually
□ Electrons
 Negative to positive
• Voltage
○ When applied to circuit
 Emf
□ Electromotive force
 Source
□ Cell
 Several = battery
 Higher voltage
□ Electrical mains
□ Thermocouple
• Voltage-current graphs
○ Standard circuit
 Electrons through metal
 Ohms law
 Graph
□ Current against voltage
 Straight line through origin
○ Other situations
 Current flows
 Ohms law not obeyed

Electricity Page 5

Lamp

I

I

V
Filament bulb
• Current carried by electrons
• At higher voltages
○ Increased heat
 Increased resistance
□ Limits current

V
Metal
• Current carried by
electrons

I

I

V
Vacuum
• Cathode warmed
• Higher voltages
○ Electrons move
across vacuum

V
Gases
• Current carried by
ions
• Higher voltages
○ No more ions
created
○ Current limited

I

I

V
Electrolysis (inactive
electrodes)
• Current carried by ions

Resistance
• Ohm laws
○ Gives definition for resistance
• Resistance and temperature
○ Resistance
 Depends on temperature
 Variation
□ Not same for all materials

Electricity Page 6

V
Electrolysis (active
electrodes)
• Current carried by ions

Metals (resistance increase with temperature)

Resistance Ω

Temperature oC

Semiconductors (resistance decreases with temperature)

Resistance Ω

Temperature oC

• Resistivity
○ Resistance
 Varies
□ Length l
 Longer the greater resistance
□ Cross sectional area A
 The wider the lower the resistance
□ Material
 Property of material
◊ Resistivity p
 Formula
□
• Resistors in series

R1
a

○ Add all resistance up
○ Add all voltage
• Resistors in parallel

Electricity Page 7

R2

R3

b

○ Add all voltage
• Resistors in parallel

R2

R3
(b) Parallel

○ Total current
 Add
○ Resistance
 Add all
 1 over resistance
• Potential divider
○ Longer resistor
 Larger resistance
○ Current flows
 Resistor
 Resistance
□ Proportionally reduced

10Ω

5Ω
2
...
Set up the apparatus as shown in the diagram
...

2
...
Allow a current of 0
...

3
...
Calculate the change in temperature ∆T
...
Repeat the above procedure for increasing values of the current I
...
Take several readings
...

Joule's law actually states that Pα I2, where P is the power, but:

If mass and time are kept constant, as is the case here, we can say that P α ∆T
Therefore, if ∆T α I2, we can conlude that P α I2

∆T/oC

Electricity Page 20

I2/A2

A straight line graph through the origin verifies that

, i
...


To measure the resistivity of the material of a wire
Apparatus

Ω

Ohmmeter

Nichrome wire

Crocodile clips

l

Metre stick

Method
1
...
Ensure that the resistance of the leads when the crocodile
clips are connected together is zero
...
Note the resistance, R, for a particular length, l, of wire
...
Increase the distance between the crocodile clips
...

4
...
Use the micrometer to find the diameter of the wire at
different points, taking the zero error into account
...

5
...

Conclusion
For each set of results, calculate the resistivity using the formula:
, (where A = πr2)
...


Accuracy
• Kinks in the wire will affect the measurement of both length and cross-sectional area
...


Electricity Page 21

To investigate the variation of the resistance of a metallic conductor with temperature
Apparatus
Ω

Ohmmeter

Glycerol-filled boiling
tube

Thermometer

Metallic conductor

Water-filled beaker

Heat source (hot plate)

Method
1
...

2
...

3
...

4
...

5
...


Conclusion
Plot the graph of resistance against temperature
...

• It is important to use as accurate a thermometer as possible
...


To investigate the variation of a thermistor with temperature
Apparatus
Ohmmeter

Ω

Glycerol-filled boiling
tube

Thermometer
Thermistor

Water-filled beaker

Heat source (hot plate)

Method
1
...

2
...

3
...

4
...

5
...

Conclusion
Plot the graph of resistance against temperature

R/Ω

T/oC

Accuracy
• It is important to slowly heat the water to avoid a situation where the water will be much hotter than the
Electricity Page 23

• It is important to slowly heat the water to avoid a situation where the water will be much hotter than the
thermistor
...


To investigate the variation of current (I) with p
...
(V) for a metallic conductor etc
...
)

Method
1
...
c
...
Move the slider along the resistor to obtain different values for the voltage V and hence the current I
...
Obtain a number of values for V and I and plot a graph of I against V
...
Repeat, replacing the wire with these various devices
...
Add some semolina to a shallow dish of oil
...
Attach electrodes as shown in the diagram
...


To show the distribution of charge on an object
Apparatus
+
+

+

+

+

Proof plane
+

+

Gold-leaf electroscope

Method 1
1
...

2
...
(i
...
touch it)
3
...

Electricity Page 27

3
...

4
...

5
...

Conclusion
The charge is evenly distributed over the dome
...

Conclusion
The is no charge (and no electric field) inside a metal conductor

Proof plane
Pear shaped conductor

Gold-leaf
electroscope

Method 3
Repeat the above procedure using a proof plane to investigate at various points on a pear shaped conductor
...
Set up the apparatus as shown
...
Allow the capacitor to build up a charge
...
Disconnect it from the generator and bring a conducting wire from each plate to the bulb
...


The demonstrate the factors on which the capacitance of a capacitor depends
Apparatus
d

Van de Graff generator

+
+
+
+
+
+

-

+++++

Charged capacitor

Material of permittivity ε

Charged electroscope

Method
Set up the apparatus as shown
...
Changing the material between the plates also affects the
capacitance
...

Conclusion
Similary we can show that reducing A, the common area, reduces the capacitance, and varying the material
between the plates affects the capacitance according to the formula:

To demonstrate that a current carrying conductor in a magnetic field experiences a force

Electricity Page 29

Foil

N

S

Magnets
Current

Retort stand

Method
Set up a circuit as shown in the diagram, supporting the foil with a retort stand
...

Conclusion
The direction of the force can be determined by the left hand rule, and its magnitude is given by the formula:

To demonstrate the principle on which the definition of the ampere is based
Apparatus

Switch

Wires move apart

Aluminium foil, suspended from a retort stand

Method
1
...

2
...

Observation
The wires move apart
Conclusion
This indicates that parallel wires conducting a current will experience a force
...

Remember
The ampere is the current that, if maintain in two infinitely long wire of negligible cross section placed one
Electricity Page 30

The ampere is the current that, if maintain in two infinitely long wire of negligible cross section placed one
metre apart in a vacuum would produce between the wires a force of 2x10 -7 newtons per metre length of
wire
...
Set up the circuit as shown
...
Move the magnet towards the coil at varying speed
...

Conclusion
The existence of the current on the galvanometer indicates that the changing magnetic field is creating an emf
as stated in Faraday's Law
...


Remember
Faraday's law of electromagnetic induction states that when there is a change in the magnetic flux linking a
coil, an emf is induced in that coil
...


To demonstrate Lenz's law
Apparatus

String

South

Retort stand

North

Magnet

Aluminium loop

Method
1
...

Electricity Page 31

1
...

2
...

Observation
The loop always moves in the same direction as the magnet
...

Remember
Lenz's law states that the direction of an induced current is such as to oppose the change causing it
...


Insulator
An insulator is a material that tends to restrict the flow of electrons
...


Electric field strength/ electric field intensity
Electric field strength is the force per unit positive charge at a point in an electric field
...


Volt
The potential difference between two points is 1 volt if the work done in moving a charge of
1 coulomb from one point to the other is 1 joule
...


Farad
A body has a capacitance of 1 farad if the addition to the body of 1 coulomb raises the
potential of the body by 1 volt
...


Resistance
The resistance of an object within an electrical circuit is defined as the ratio of the voltage
across it to the current flowing through it
...


Resistivity
The resistivity, ρ, of a material is the resistance of an object of that material, with unit area
and unit length
...


Where: P = power, I = current

Semiconductor
A semiconductor is a material whose resistivity lies between that of a conductor and an
insulator
...


Magnetic flux density
Magnetic flux density (B) is the force experienced by a conductor of length 1m carrying a
current of 1A at right angles to the field
...


Ampere
The ampere is that current which, if maintained in two parallel, infinitely long wires of
negligible cross section placed one metre apart in a vacuum, would produce between the
wires force of 2x10-7 newtons per metre length of the wire
...
The strength of the emf is proportional to the rate of change of the flux
linking the coil
...


Electricity Page 35

Derivations
28 January 2015

21:33

Resistors in a series
This is an example of three resistors connected in a series as shown in the diagram below
...


R3

R2

b

a

Following Ohm's law we can say:

And dividing the equation by :

Resistors in parallel
See the diagram below
...
It is described by the formula:
Electricity Page 36

A force exists on a current carrying conductor in a magnetic field
...

We can say that the current in this case is the quantity of charge passing any point per second (
effective length of the charge in the magentic field is given by

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