ejc - stem · created in a second coil of wire. self induction ... if a transformer has 50 turns on...
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20kV to 25kV
400kV
275kV / 400kV
132kV
400V 3-phase
230V (50Hz)
Generated by large power stations
Stepped up at power station
Bulk transmission over long distances
Distribution to towns and cities & industry
Light industry and commercial
Domestic supply
The National GridThe purpose of the National Grid is to transmit electricity across the
country with as little loss as possible.
11kV / 33kVDistribution to towns & cities and industry
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Drax Power Station
Output power: 4 Gigawatts
Output current: 19,000 Amperes
Output voltage: 23,500 Volts
Provides 7% of the country’s electricity requirements.
One of the 660 Megawatt
alternators in the turbine
room of the power station.
EJC
Magnetism
Soft IronUsed in relays and transformers.
A relay is a device that contains a
solenoid (coil of wire) and is used to
activate a number of switches.
Steel, nickel & cobaltUsed to make permanent magnets
such as magnetic welding clamps.
CopperCopper is not strongly magnetic.
Copper is used in electrical cables.
EJC
Capacitor voltage ratings
Capacitors in parallelIf two capacitors are connected in
parallel then the maximum
working voltage is the lowest
value.
If two 10V capacitors are
connected in parallel then the
working voltage is 10V.
Working voltageA capacitor can be damaged if the
voltage applied to it is greater than the
working voltage.
If two capacitors have a working voltage
of 10V each then the overall voltage
rating is 20V.
Electrolytic capacitorsElectrolytic capacitors must be
connected to a d.c supply and in the
correct polarity. If the capacitor is
connected in reverse polarity then it can
become damaged.
+
+
10V
10V
10V10V
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Capacitors in series
When all capacitance
values are the sameIf three identical capacitors are
connected in series then you can
easily calculate the total capacitance
by dividing the capacitance by the
number of capacitors in the circuit.
Example
If three 10uF capacitors are
connected in series:
10 ÷ 3 = 3.3 µF
10uF
10uF
10uF
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Capacitors in series
100uF
200uF
300uF
The standard methodYou can calculate the total
capacitance of any series circuit using
this formula:
1
𝐶𝑇=
1
𝐶1+
1
𝐶2+
1
𝐶3+⋯
1
𝐶𝑇=
1
100+
1
200+
1
300= 0.0183
𝐶𝑇 =1
0.0183= 54.5µF
Example
If 100uF, 200uF and 300uF capacitors are connected in series:
You can use this formula for any
number of capacitors.
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Capacitors in parallel
Just add them up!If capacitors are connected in parallel then to calculate
the total capacitance you simply add the values up.
Example
If three 10uF capacitors are connected in parallel:
10 +10 +10 = 30uF
10uF 10uF 10uF
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Resistors in parallel
100Ω 100Ω 100Ω
When all resistance values are the
sameIf three identical resistors are connected in parallel
then you can easily calculate the total resistance by
dividing the resistance by the number of resistors in
the circuit.
Example
If three 100Ω resistors are connected in parallel:
100 ÷ 3 = 33.3 ΩEJC
Resistors in parallel
100Ω 200Ω 300Ω
The standard methodYou can calculate the total resistance of any parallel circuit
using this formula:
1
𝑅𝑇
=1
𝑅1
+1
𝑅2
+1
𝑅3
+⋯
1
𝑅𝑇
=1
100+
1
200+
1
300= 0.0183
𝑅𝑇 =1
0.0183= 54.5 Ω
Example
If 100 ohm, 200 Ohm and 300 Ohm resistors are connected in
parallel:
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Resistors in series
100Ω
Just add them up!If resistors are connected in series
then to calculate the total resistance
you simply add the values up.
100Ω
100Ω
Example
If three 100Ω resistors are connected in
parallel:
100+100+100 = 300 Ω
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RC Timing
Charging CapacitorsWhen a capacitor is connected in
series with a resistor it takes a
certain amount of time to charge up.
It charges quickly at first and
then slows down as it reaches
maximum.
The time it takes the capacitor
potential difference (pd) to reach
63% of the supply voltage is
calculated with:
T = C x R
Example
Resistor = 1K
Capacitor = 200µF
T = 200x10-6 x 1000
T = 0.2 SecondsWhich is the same as 200mS
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Charge in Capacitors
Capacitor ChargeWhen a capacitor is connected to a
supply it develops a charge as
electrons build up on the plates.
To calculate the charge stored in the
capacitor you can use this formula:
Example
Supply voltage = 1000V
Capacitor = 100nF
Q = 100x10-9 x 1000
0.0001 Coulombs
Which is the same as100µC
Charge = Capacitance x Voltage
Q = C x V
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Induction
Mutual InductionThis is where one coil of wire is
energised and causes a voltage to be
created in a second coil of wire.
Self InductionThis is where a voltage is induced
which opposes the initial flow of
current.
Dynamic InductionThis is where a voltage is created in
a length of wire when it is moved
within a magnetic field.
Generators apply this.
Motor EffectA conductor that carries a current will move at right angles to
the magnetic field.
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Heating elementsDevices that are designed to produce heat need a high current
to flow through a length of wire. For a high current to flow the
wire must have a low resistance. This is because I = V ÷ R.
LOW RESITANCE = HIGH CURRENT = LOTS OF HEAT!
Producing Heat
Incandescent lampsIncandescent lamps work by allowing a current to flow
through a tungsten filament.
HIGHER RESITANCE
=
LOWER CURRENT
=
LESS HEAT
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Stepping up & downA transformer is used to step-up or step-down voltages. They
are used in electronic equipment to produced a low voltage
from the mains voltage of 230V.
Transformers
50
100x 230 = 115VSecondary voltage =
Primary
voltage
(input)
Secondary
voltage
(output)
Example
If a transformer has 50 turns on the primary, 100 turns on
secondary and has a primary voltage of 230V, calculate the
secondary voltage:
Secondary turns
Primary turnsx Primary voltageSecondary voltage =
Primary turns
(copper wire)Secondary turns
(copper wire)
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Effect of self inductionWhen an alternating current flows
through a coil an EMF (electromotive
force, measured in volts) is generated, or
induced in the coil.
The EMF induced is in the opposite
direction to the supply voltage and
opposes a change in current.
The EMF induced can be calculated like
this:
Self Induction
EMF = L x Rate of change
Inductance measured in Henrys
Example
If coil has an inductance of 10 Henrys and the current
changes at a rate of 15 Amps / Second:
EMF = 10 x 15 = 150 V
Amps / Second
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Force created by an electric currentIf a wire (conductor) is placed at right angles to a magnetic
field a force acts on the wire and causes it to move at right
angles to the magnetic field.
The amount force depends on:
• The strength of the magnetic field – known as the flux
density which is measured in Tesla
• The amount of current flowing through the wire
• The length of the wire
Magnetism & Force
F = B x I x l
Flux density
Current
Length of wire
Example
A wire has a length of 50 cm and carries a current of 20 Amps,
is placed in a magnetic field. The magnet field strength is
300mT. The force acting on the wire is:
F = 0.3 x 20 x 0.5 = 3 Newtons
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Capacitor theoryCapacitor structureA capacitor consists of two
metal plates separated by an
insulating material called a
dielectric. A capacitor is
capable of storing electric
charge.
The unit of capacitance is the
Farad and depends upon this
formula:
d
Metal plate
Dielectric
Metal plate
εo εr x A
dC =
Surface
area of the
metal
plates
Distance
between the
metal plates
Permittivity of
free space
(8.85x10-12)
Key factsThe capacitance is the permittivity multiplied by the area,
divided by the distance between the metal plates.
Different insulating materials have different permittivity.
Relative
permittivity
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Cells and Batteries
CellsA cell converts chemical energy
into electrical energy.
BatteriesBatteries are made by
connecting a number of cells
together. Connecting cells in
series increases the voltage,
connecting them in parallel
increases the current it can
supply.
Primary and Secondary CellsPrimary cells and batteries can not be recharged
Secondary cells and batteries can be recharged
A car battery consists of six 2 Volt secondary cells connected
in series.
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Inductive & Capacitive
CircuitsInductive CircuitsIn a circuit that includes a coil such as a motor, the current
flowing through the circuit lags behind the voltage.
Capacitive CircuitsIn a circuit that includes a capacitor the voltage lags behind
the current flowing through the circuit.
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Force, Mass and
AccelerationWhat is force?A force acting on an object causes it to accelerate. You can
work out the force needed to make the object accelerate by
using the formula:
Example
A mass of 1500g is accelerated at 200cm/s2
The force required is:
F = 1.5 x 2
3 Newtons
Force = Mass x Acceleration
F = m x a
2m/s2
1.5kg
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Cells and Batteries
CellsA cell converts chemical energy
into electrical energy.
BatteriesBatteries are made by
connecting a number of cells
together. Connecting cells in
series increases the voltage,
connecting them in parallel
increases the current it can
supply.
Primary and Secondary CellsPrimary cells and batteries cannot be recharged
Secondary cells and batteries can be recharged
A car battery consists of six 2 Volt secondary cells connected
in series.
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SI UnitsBasics
Measurement Abbreviation SI Unit SI Unit
SymbolResistance R Ohm Ω
Resistivity 𝜌 ohm-metre Ω m
Current I Ampere AVoltage
(potential difference,
EMF)
V Volts V
Power P Watts W
Charge Q Coulombs C
Energy E Joule J
a.c circuits
True power P Watts WApparent power S Volt-amp VA (or kVA)Reactive power Q Volt-amp
reactive
VAr (or kVAr)
Power factor p.f or COS ϴ none noneInductance L Henry HCapacitance C Farad FCapacitive
ReactanceXL Ohm Ω
Inductive
ReactanceXC Ohm Ω
Impedance Z Ohm ΩFrequency F Hertz HzPeriodic time τ Second S EJC
Formulae
𝑃 =𝑉2
𝑅
𝑃 = 𝐼 × 𝑉
𝑃 = 𝐼2 × 𝑅
Power
P
I V
Ohm’s Law
V
I R
𝑉 = 𝐼 × 𝑅
Force
F
m a
𝐹 = 𝑚 × 𝑎
Series Resistors
𝑅 =𝜌 𝐿
𝐴
Resistors in Parallel
1
𝑅𝑇=
1
𝑅1+
1
𝑅2+
1
𝑅3…
Capacitors in Series
1
𝐶𝑇=
1
𝐶1+
1
𝐶2+
1
𝐶3…
Resistors in Series
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3…
Capacitors in Parallel
𝐶𝑇 = 𝐶1 + 𝐶2 + 𝐶3…
𝑍 = 𝑅2 + 𝑋2
Impedance
AC Power
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 = 𝑇𝑟𝑢𝑒2 + 𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑒2
Force on a conductor
𝐹 = 𝐵 𝐼 𝑙
Inductive Reactance
𝑋𝐿 = 2 π 𝑓 𝐿
Inductive Reactance
𝑋𝐶 =1
2 π 𝑓 𝐶
Capacitance
𝐶 =ε𝑜 ε𝑟 𝐴
𝑑
Time Constant
τC R
τ = 𝐶 × 𝑅
Charge
Q
C V
𝑄 = 𝐶 × 𝑉
EMF
𝐸 = 𝐿 Δ𝑡
E
L Δt
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