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Electricity
Unit 3
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8.1 Electricity3.1 Introduction3.2 Electricity fundamentals
2.1 Particles and laws2.2 Electricity generation2.3 Electricity magnitudes
3.3 Circuits3.1 Ohm’s law. Electric Power3.2 Elements and Symbols3.3 Circuit associations. Calculations3.4 Basic circuits 3.5 Electric Measurements
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Indicador Prueba Valor
Comprensión del concepto de corriente eléctrica y su base física. Diferenciación entre corriente continua y alterna.
Ex El 2
Interpretación de esquemas de circuitos sencillos de corriente continua
Poster 2
Cálculos en circuitos de corriente continua basados en la ley de Ohm
ex el 4
Conocimiento de la función de cada componente eléctrico y de su simbología
Ex El 2
Formulación y resolución de problemas Ex El 2
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3.1 Introduction
What would happen if we didn’t have electricity?
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3.1 Introduction
However, we have to remember that we can decrease the amount of energy that we waste everyday, helping our sustainable
development.
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3.1 Introduction
What are we going to learn today?
The electric current and its physic principles
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3.1 Introduction
So, what is electricity?The concept of electricity includes all
the phenomena related to electric charges
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3.2.1 Particles and laws
Matter can be electrically charged when the charge distribution is upset
For example, you can change the charge distribution of a pen by rubbing it against your hair. Then you can attract some pieces of paper 8
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3.2.1 Particles and laws
Matter is formed by atoms, which contain smaller particles inside with electric charges:
The electrons and protons
Atom
Electron
Proton
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3.2.1 Particles and lawsElectrons and protons have negative and
positive charges respectively .These charges create forces between them
that can be attraction or repulsion forces according to the value of the charge:
Equal charges: repulsionDifferent charges: attraction
attraction repulsion repulsion 10
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3.2.1 Particles and laws
The use of electricity needs a flow of electrons, the electric current
c
The electric current is the displacement of the electrical charges through the matter
c
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3.2.1 Particles and laws
In solid metals such as wires, the positive charge carriers are immobile, and only the negatively charged electrons can flow.
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All the flowing charges are assumed to have positive polarity, and this flow is called conventional current.
3.2.1 Particles and laws
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3.2.1 Particles and laws
Because the electron carries negatives charges, the electron motion in a metal is in the direction opposite to that of conventional (or electric) current.
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3.2.2 Electricity generation
What are we going to learn next?Explain how the electricity can be created.
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Exercise 3.2.2a :
Explain how the electricity can be created. Describe all elements needed in a common electric generator.
3.2.2 Electricity generation
Solution
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3.2.2 Electricity generationLong time ago… Hans Christian Oersted
discovered that a electric current can disturb a compass
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3.2.2 Electricity generation
Since the compass only is disturbed with a magnet, Volta concluded that an electric current creates a artificial magnetic
Natural magnet
Artificialmagnet
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3.2.2 Electricity generation
The magnet is stronger if we use a spiral instead of a simple circuit.
Therefore electric magnets are formed by several spirals connected to a battery 19
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Using Volta experiment, Mr Michael Faraday discovered that an electric current can be created when a magnet is moving close to an electric circuit or vice versa
3.2.2 Electricity generation
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In conclusion, if we want to create an artificial electric current, we need:
Mechanical energy
to move the circuit or the
magnet
3.2.2 Electricity generation
Closed circuit
Artificial magnet
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This is the diagram of an industrial electric generator
3.2.2 Electricity generation
Artificial magnet
Closed circuit
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The electricity is created when the mechanical energy moves the closed circuit inside the artificial magnet
3.2.2 Electricity generation
Electric engine video Electric generator and Engine video
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When we have all elements together, we find that we create an alternate electric current due to the movement of the circuit inside the magnetic field.
3.2.2 Electricity generation
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Exercise 3.2.2b :
1. Explain the difference between the AC and the DC.
2. Indicate what type of current do we use in this electrical devices: Torch, Bedroom lamp, TV, Mobil phone, Fridge.
3. Draw the diagram of a mobile phone power supply.
4. Find the input and output current in your mobile phone power supply.
3.2.2 Exercise 3.2.2b Electricity generation
solution25
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3.2.2 Electricity generation
What are we going to learn next?Difference between the direct and the alternate current
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The difference between AC and DC is :AC is an alternating current (the amount of
electrons) that flows in both directions and DC is direct current that flows in only one direction
AC changes its Voltage value from +A to –A (+ and – represent the direction) and the DC has a constant Voltage value
3.2.2 Electricity generation
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But, most electric at devices like an iPhone, need a Direct Current that keeps its magnitude and direction constant
3.2.2 Electricity generation
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If we apply an AC to an electrical device like a light bulb, we obtain a light pulse as you see in a bike dynamo:
3.2.2 Electricity generation
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3.2.2 Electricity generation
In order to obtain a direct current we use powers supplies that include different elements that transforms AC into DC.
AC DC
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3.2.2 Electricity generationThese are the elements of a Power supply that
that transforms AC into DC: transformer, rectifier, smoothing and regulator.
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3.2.2 Electricity generationThese are the elements of a Power supply that
that transforms AC into DC: transformer, rectifier, smoothing and regulator.
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3.2.2 Electricity generationThese are the elements of a Power supply that
that transforms AC into DC: transformer, rectifier, smoothing and regulator.
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3.3.1 CIRCUITS
What are we going to learn next?
Analysis of the direct current circuits.
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3.3.1 Exercise 3.3.1:Electricity magnitudes
Exercise 3.3.1:Define Voltage, Intensity and
Resistance and its units
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3.3.1 Electricity magnitudes
To better understand the concept of the electric current, we can think of it as a stream where the drops are the electric charges
We use the water power from the drops’ movement to create energy
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3.3.1 Electricity magnitudes
In order to understand electricity, we have to first know the main electric magnitudes:
VOLTAGE
INTENSITYResistance
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3.3.1 Electricity magnitudes
The electrons need energy to be able to move through a material. This is the Voltage
We define the Voltage as the energy per charge unit that makes them flow through a material. This magnitude is measured in Volts (V).
Energy
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3.3.1 Electricity magnitudes
The higher the Voltage is, the more energy the electric charges will have to keep on moving.
Lower voltage
Higher voltage
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3.3.1 Electricity magnitudes
Intensity is the amount of charges that goes through a conductor per time unit. It is measured in Ampere (A)
Lower intensity
Higher intensity
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3.3.1 Electricity magnitudes
We can see that the stream will have more strength if there is more water in the tank. It’s similar to what happened to the electricity
Less water pressure
More water pressure
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3.3.1 Electricity magnitudes
Electric resistance is the opposition to the movement of the charges through a conductor. It is measured in Ohms ()
Lower Resistance
Higher Resistance
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3.3.1 Electricity magnitudesExercise 3Which one of these lamps will give light?
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3.3.1 Electricity magnitudes
Exercise 4Will this lamp turn on?
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3.3.1 Electricity magnitudes
The electric current always goes through the route with less resistance, like water
Here we have the resistance needed to create light
No resistance 45
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3.3.2 Ohm’s law. Electric Power
What are we going to learn next?
Magnitudes analysis using the Ohm’s Law.
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3.3.2 Exercise 3.3.2a Ohm’s law. Electric Power
Exercise 3.3.2a:Justify how the Intensity will be if: We have a low voltage V We have a low Resistance R
Solution47
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3.3.2 Ohm’s law. Electric Power
Ohm’s law links the three electric magnitudes as is shown:
R
VI
V= Voltage (voltsV)I= Intensity (ampereA)R= Resistance (ohm )
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3.3.2 Ohm’s law. Electric Power
Intensity is directly proportional to voltage:
If the voltage is high, the charges will have a lot of energy. Therefore the Intensity will be high too
R
VI
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3.3.2 Ohm’s law. Electric Power
Intensity is inversely proportional to Resistance
If there is a high Resistance, the intensity will be low.
R
VI The charges will cross the
material slowly
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3.3.2 Exercise 3.3.2.b Ohm’s law. Electric Power
Exercise 3.3.2.b:Calculate the value
of the intensity in these cases:
R
VI
V (V) R () I (A)
2 14
2 2
20 2
12 6
252 64
1000 20
Solution
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3.3.2 c Exercise Ohm’s law. Electric Power
We have a fan connected to the domestic electric supply. The amperimeter indicate a 0,52A on the circuit. 1.What’s is the resistance of the fan?2.What’s the power measured in KwCalculate the Intensity that flaws in a electrical engine of 1,2 Kw installed in my washing machine. What
would be the Intensity and the power if we have 380V at home.Extra data: house electrical supply 230V, 50Hz
Solution52
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3.3.2 D Exercise Ohm’s law. Electric Power
A) Calculate the Intensity that flaws in a electrical engine of 1,2 Kw installed in my washing machine.
B) B)What would be the Intensity and the power if we have 380V at home.Extra data: house electrical supply 230V, 50Hz
Solution53
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3.3.2 Ohm’s law. Electric Power
Power is defined as the work consumed per time unit, and it’s measured in watt W
t
WP
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3.3.2 Ohm’s law. Electric Power
If we apply the Ohm’s law, we obtain a new formula that explains the power of an electrical device
VIt
VQ
t
WP
t
QI
VQWQ
WV
VIP 55
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3.3.2 Ohm’s law. Electric PowerFrom this expression we can derivate
in other two using the Ohm’s Law
R
VI
IRV
VIP
RIP 2
R
VP
2
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3.3.2 Ohm’s law. Electric Power
There is a bulb lamp of 100w connected to 220V electric grid. Calculate:
Intensity throw the lamp.Power of the lamp.Calculate the Kwh that the electricity
meter will show after 20 hours.Indicate the price of the electricity
consumed if the price is 0,90€/Kwh
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3.3.2 Ohm’s law. Electric Power
There is a bulb lamp of 100w connected to 220V electric grid. Calculate:
Intensity throw the lamp.
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3.3.2 Ohm’s law. Electric Power
There is a bulb lamp of 100w connected to 220V electric grid. Calculate:
Power of the lamp.As is says in the wording it is 100WP=100WCalculate the Kwh that the electricity
meter will show after 20 hours.P=100W=0,1kWPKWh=0,1x20h=2Kwh
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3.3.2 Ohm’s law. Electric PowerIndicate the price of the electricity consumed if the
price is 0,90€/Kwh
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3.3.2 Ohm’s law. Electric Power
Electrical companies measure our electrical consume in Kwh with a electricity meter situated in the basement of a building.
hPmedPowerConsu 61
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3.3.3 Elements and Symbols
What are we going to learn next?
Electric components and their applications.
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3.3.3 Elements and symbolsAn electric circuit is a group of elements that allows us
to control electric current through some sort of material
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3.3.3 Elements and symbols
The essential elements in a circuit are:Generator: it creates an electric current
supplying voltage to the circuit. They can be:Batteries: they supply electric current but only for a
short time.Power supplies: they give a constant and continuous
electric current.
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3.3.3 Elements and symbolsThe essential elements in a circuit are:Control elements: we can manipulate
the electricity through the circuit.Switch: they keep the ON or OFF positions.
For example, the switch lights at the bathroom
Push button: The On position only works while you are pressing the button. For example the door bell.
Diverter switch: it is used to switch a light on or off from different points in the same room, as you have in your bedroom
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3.3.3 Elements and symbolsControl elements:
Change Direction diverter switch: We use this element to invert the direction of the electric current through a component.
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3.3.3 Elements and symbolsControl elements:
Relay: It is an electrically operated switch. Thanks to that we can control a circuit from a remote control applying just electricity
An electrical magnet attracts the switch that closes the circuit
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3.3.3 Elements and symbolsSafityIt is used to control high electrical volt
devices, because we don’t touch the main circuit
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3.3.3 Elements and symbolsReceptors: they are the elements that
transform the electric energy into other ones that are more interesting for us. For example:
Incandescent lights: when the electric current goes through the lamp filament it gets really hot and starts emitting light.
Engine: the electricity creates a magnetic field that moves the metal elements of the engine
Resistance: we use it to decrease the intensity of a circuit
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3.3.3 Elements and symbols
Conductor: all the elements have to be connected to a material that transmits the electric charges.
The circuit has to be CLOSED in order to allow the electricity to circulate around it from the positive to the negative pole.
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3.3.3 Elements and symbols
Protection elements: they keep all the circuit elements safe from high voltage rises that can destroy the receptors.Fuse: the first one will blow, cutting
the circuit in case of a voltage rise. They are easily replaced
Circuit breaker: they are used in new electrical installations, at home or at factories. If there is a voltage rise, you don’t have to replace them, only reload them. 71
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3.3.3 Elements and symbols
Electric symbols are used to represent electric circuits with drawings that replace the real circuit elements.
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3.3.3 Elements and symbols
Exercise: Draw the following circuit using electric symbols
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3.3.3 Elements and symbols
Exercise: Draw the following circuit using electric symbols
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3.3.3 Elements and symbols
Exercise: Draw the following circuit using electric symbols
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3.3.3 Elements and symbols
Generator
Battery
Battery association
Conductors:
When two conductors are crossed without any contact we indicate it with a curve
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3.3.3 Elements and symbols
Control elements
Push button
Switch
Diverter switch
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3.3.3 Elements and symbols
Protection elements
Fuse
Receptors:
Lamp
Resistances: they have two symbols
Engines
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3.3.4 Circuit associations
The behaviour of electrical elements depends on how they connect to each other.
There are three possible configurations :
SeriesParallelMixed
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3.3.4 Circuit associationsSERIES circuit
The series circuit connects the electrical elements one behind the other.
In this way, there is only one connection point between elements 1 & 2 are connected only by A2 & 3 are connected only by B 80
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3.3.4 Circuit associationsPARALLEL association
In this association, all the elements are connected by two points.
So, 1, 2 & 3 are connected by A and B
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3.3.4 Circuit associationsMIXED association
Mixed association has elements associated in parallel and in series.
1, 2 & 3 are in parallel and all of them are in series with 4
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3.3.4 Circuit associations
But what happens to receptors when they are connected in series or parallel associations?
Series and parallel association change the value of intensity and voltage through receptors.
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3.3.4 Circuit associationsVoltage
Series Parallel
Voltage is distributed between elements, that is the reason why they have less energy for each lamp, so the light is lower in each lamp.
Voltage is the same in all elements, so all the lamps have the same energy and the light is higher.
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Intensity
Series Parallel
All the lamps are in line, so they create a high resistance, that is the reason why the intensity is lower but the battery will have a longer life.
All lamps are separated so they create a low resistance, that is the reason why the intensity through the lamps is higher, but the battery will have a shorter life
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Circuit
Series Parallel
If there is any cut along the conductor, the electric current will not be able to go from the positive to the negative pole.
If there is any cut along the conductor, the electric current can go through any other way
CUT
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If there is any cut in series association, the water can’t go further. But in parallel association there will be no problem.
cut
3.3.4 Circuit associations
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3.3.4 Circuit associationsExercises
Which of these elements are associated with series, parallel or mixed circuits? Name the connection points with letters.
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3.3.4 Circuit associationsExercises
Which of these elements are associated with series, parallel or mixed circuits. Name the connection points with letters
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3.3.4 Circuit associationsExercises
Which of these elements are associated with series, parallel or mixed circuits?. Name the connection points with letters.
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3.3.4 Circuit associations. Calculations
Calculate in each case the resistance equivalent Rt
Solution91
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3.3.4 Circuit associations. Calculations
Calculate in each case the resistance equivalent Rt
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3.3.4 Circuit associations. Calculations
SERIES circuit In this association we find that:
VT=V1+ V2+V3
RT=R1+R2+R3
IT=I1= I2=I3 ET=E1+ E2+E3RTET
IT
VT
ET=VT
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3.3.4 Circuit associations. Calculations
RTET
IT
VTI1
I2 I3
V1
V2 V394
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3.3.4 Circuit associations. Calculations
SERIES circuit
INTENSITY= EQUAL IT=I1=I2=I3
RTET
IT
VT
ET=VT
I1
I2 I3
IT IT
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3.3.4 Circuit associations. Calculations
SERIES circuit
VOLTAGE= DIVED VT=V1+ V2+V3
RTET
IT
VT
ET=VT
IT IT
V1
V2V3
VT
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3.3.4 Series Exercise Circuit associations. Calculations
Calculate in each case the resistance equivalent Rt, It and Vt. Calculate the I and V in each Resistance
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3.3.4 Circuit associations. Calculations
Calculate in each case the resistance equivalent Rt, It and Vt. Calculate the I and V in each Resistance
RT= 1ºR1= 0,5 Ω R2= 6,3 Ω R3= 6/5 Ω
IT= 2º I1= 2º I2= 2º I3= 2º
VT= 220VV1= 3º V2= 4º V3=5º
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and
Vt. Calculate the I and V in each Resistance
85
63,6
2
1321
t
t
t
R
R
RRRR
RT= 8 Ω R1= 0,5 Ω R2= 6,3 Ω R3= 6/5 Ω
IT= 27,5 A I1= I2= I3=
VT= 220V V1= V2= V3=
5,278
220
T
T
T
TT
I
I
R
VI
1º
2º
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and
Vt. Calculate the I and V in each Resistance
RT= 8 Ω R1= 0,5 Ω R2= 6,3 Ω R3= 6/5 Ω
IT= 27,5 A I1= 27,5 A I2= 27,5 A I3= 27,5 A
VT= 220V V1= V2= V3=
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and
Vt. Calculate the I and V in each Resistance
RT= 8 Ω R1= 0,5 Ω R2= 6,3 Ω R3= 6/5 Ω
IT= 27,5 A I1= 27,5 A I2= 27,5 A I3= 27,5 A
VT= 220V V1= 13,75V V2= 173,25V V3= 33V
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3.3.4 Circuit associationsPARALLEL association
VT=V1= V2=V3
IT=I1+ I2+I3 ET=E1+ E2+E3
321
1111
RRRRT
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3.3.4 Circuit associations
VT=V123=V1= V2=V3
IT=I123=I1+ I2+I3103
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3.3.4 Circuit associationsPARALLEL association
INTENSITY= DIVEDIT=I1+I2+I3
I3
I2
I1
IT104
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3.3.4 Circuit associationsPARALLEL association
INTENSITY= DIVEDIT=I1+I2+I3
I3
I2
I1
IT105
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3.3.4 Circuit associationsPARALLEL association
VOLTAGE: IQUALVT=V1= V2=V3
V1
V2
V3VT 106
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3.3.4 Circuit associationsPARALLEL association
V1
V2
V3 VT
RT= R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= I1= I2= I3=
VT= 20V V1= V2= V3=
RT= R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= I1= I2= I3=
VT= 220V V1= V2= V3=
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3.3.4 Circuit associationsPARALLEL association
V1
V2
V3 VT
RT= R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= I1= I2= I3=
VT= 20V V1= V2= V3=
RT= 1ºR1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= 2º I1= 3º I2= 4º I3= 5º
VT= 220VV1= 20V V2= 20V V3=20V
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3.3.4 Circuit associationsPARALLEL EXERCISE
V1
V2
V3VT
RT=2,11Ω R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= I1= I2= I3=
VT= 20V V1= V2= V3=
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3.3.4 Circuit associationsPARALLEL EXERCISE
V1
V2
V3VT
RT=2,11Ω R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT= I1= I2= I3=
VT= 20V V1= V2= V3=
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3.3.4 Circuit associationsPARALLEL EXERCISE
V1
V2
V3VT
RT=2,11Ω R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT=9,48A I1= I2= I3=
VT= 20V V1= V2= V3=
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3.3.4 Circuit associations VOLTAGE: IQUAL
VT=V1= V2=V3
VT=20
V1
V2
V3VT
RT=2,11Ω R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT=9,48A I1= I2= I3=
VT= 20V V1=20V V2=20V V3=20V
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3.3.4 Circuit associationsPARALLEL EXERCISE
V1
V2
V3VT
RT=2,11Ω R1= 6 Ω R2= 18 Ω R3= 4 Ω
IT=9,48A I1=3,33A I2=1,11A I3=5A
VT= 20V V1=20V V2=20V V3=20V
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3.3.4 Circuit associationsMIXED association
We have to convert the parallel associations into series in order to obtain Vt, It and Rt. T
1ºVt, It and Rt2º
V4, I4 and V123
3ºI1, I2 , I3 and
V123
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3.3.4 Circuit associationsMIXED association
IT=I123=I4 series association
I123=I1+ I2+I3 parallel association
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3.3.4 Circuit associationsMIXED association
IT=I123=I4 series association
I123=I1+ I2+I3 parallel association
I1
I2
I1116
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3.3.4 Circuit associationsMIXED association
I123=I1+ I2+I3, but they don’t have to be equal, it depends on the R in each path.I1
I2
I1117
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3.3.4 Circuit associations
VT=V123+V4 series association
V123=V1= V2=V3 parallel association
V1
VT=V123+V4 V2
V3118
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3.3.4 Circuit associations
VT=V123+V4 series association
IT=I123=I4 series association
V123=V1= V2=V3 parallel association
I123=I1+ I2+I3 parallel association
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3.3.4 Circuit associations
1ºVt, It and Rt
2ºV4, I4 and
V123
3º I1, I2 , I3 and
V1
VT=V123+V4 series association
V123=V1= V2=V3 parallel association
I123=I1+ I2+I3 parallel association
IT=I123=I4 series association
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3.3.4 Ex 1 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
RT= 1ºR1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 2º I1= 5º I2= 6º I3=2º
VT= 20VV1= 4º V2= 4º V3=3º
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3.3.4 Circuit associations. Calculations
RT= 6 Ω
IT=
VT= 20V
1º
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RT= 6 Ω R1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 10/3 A I1= I2= I3=
VT= 20V V1= V2= V2= 2º
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RT= 6 Ω R1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 10/3 A I1= I2= I3= 10/3 A
VT= 20V V1= V2= V3=
I1
I2
I3I1-2
I3
2º
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RT= 6 Ω R1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 10/3 A I1= I2= I3= 10/3 A
VT= 20V V1= V2= V3= 5V
3º
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RT= 6 Ω R1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 10/3 A I1= I2= I3= 10/3 A
VT= 20V V1= 15V V2= 15V
V3= 5V
Two ways to calculate V1 and V2
4º
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RT= 6 Ω R1= 6 Ω R2= 18 Ω R3= 3/2 Ω
IT= 10/3 A I1= 2,5 A I2= 5/6 A I3= 10/3 A
VT= 20V V1= 15v V2= 15V V2= 5 V
AIR
VI
AIR
VI
6
5
6
5
18
15
5,22
5
6
15
12
22
11
11
5º6º
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3.3.4 Circuit associations
1ºVt, It and Rt
2ºV4, I4 and
V123
3º I1, I2 , I3 and
V1
VT=V123+V4 series association
V123=V1= V2=V3 parallel association
I123=I1+ I2+I3 parallel association
IT=I123=I4 series association
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3.3.4 Ex 2 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
RT= R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= I1= I2= I3= I4=
VT= 220V V1= V2=
V3 V4=
4 Ω
4 Ω
8 Ω12 Ω
220V
sol
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3.3.4 Circuit associations. Calculations
E represents the electrometric force that is the Total Voltage that provides a electric source like a battery or a power supply,
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3.3.4 Circuit associations
Exercise 3.3.4. Try to make a cheat sheet with all the formulas needed to solve electric circuits. It has to be no bigger than 25cm2.
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
SolSol132
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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3.3.4 Circuit associations. Calculations
Calculate in each case the resistance equivalent Rt, It and Vt. Calculate the I and V in each Resistance
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3.3.4 Circuit associationsExercise:
Which of these lamps have more lightness?
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3.3.4 Circuit associationsExercise:
Which of these assemblies generates electricity?
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3.3.4 Circuit associationsExercise:
What happen in this exercise if we activate:
1. 1 and 7
2. 1 and 8
3. 1,2 and 3
4. 1,2,3,4,5,6 and 7
5. 1,4,6 and 7
What do you have to activate to switch on…?
1. A and B
2. A, B and C
3. A, B , C and M
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3.3.4 Circuit associations
Draw the electric circuit of a car that has :
1.2 front lamps
2.2 Back lamps
3.A forward and backward engine that stops automatically when it crash with a object
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3.3.4 Circuit associations
Why are these assemblies no correct?
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3.3.6 Electric Measurements. Polimeter
Ohmmeter: It measures the resistance and the continuity of a circuit or component.
Resistance control
If there is no resistance that means that there is a shortcircuit If there is a maximum resistance that means that the cricuit is open
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3.3.6 Electric Measurement. Polimeter
4K7
• In order to get a precise lecture we have to choose the correct range of measurement.
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3.3.6 Electric Measurements. PolimeterVoltimeterVoltimeter
AplicationAplication: If we want to measure the voltage present in a component we have to conect the electrodes in parallel
V
Voltage in a component 144
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If we want to measure the voltage of battery we have to place the control in the Direct Current and in the proper scale
3.3.6 Electric Measurements. Polimeter
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Amperimeter: In order to be able to measure the current we have to place the electrodes BETWEEN the circuitr or in sereies
A
CONTROL DE CONSUMO
3.3.6 Electric Measurements. Polimeter
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4K7
Amperimeter: we chose the position according to the scale of the current.
3.3.6 Electric Measurements. Polimeter
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3.3.4 Circuit associations
Exercise:
According to this assembly, chose the correct answer:
The I through the lamp is 2,3 AThe voltage between the lamp is
2,3 VThe resistance of the lamp is 2,3
Ω
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A closed
B open
A open
B closed
A closed
B closed
Engine
lamp 1
lamp 2
Point out in the table if the engine and lamps works for the following situations
3.3.4 Circuit associations
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Exercise 3.2.2a :Explain how the electricity can be created. Describe all elements needed in a common electric generator.
Thanks to the discoveries made by Faraday and Oesterd, we know that when a closed circuit moves inside a magnetic field an electric current is created inside the circuit.
Therefore, nowadays we use an artificial magnet (made with a electric current that flows through a spiral that has a iron bar inside), closed circuit (spirals) and mechanical energy to create electricity. The closed circuit is moved thanks to the mechanical energy inside the artificial magnet. Thanks to the energy of the magnetic field created by the magnet the electrons from the circuit start to move creating the electric current.
3.2.2 Electricity generation
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1. Explain the difference between the AC and the DC.
The difference between AC and DC is that AC is an alternating current (the amount of electrons) that flows in both directions and DC is direct current that flows in only one direction; Also, AC changes its Voltage value from +A to –A (+ and – represent the direction) and the DC has a constant Voltage value
3.2.2 Sol Exercise 3.2.2b Electricity generation
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Exercise 3.2.2b :
2.-Indicate what type of current do we use in this electrical devices: Torch, Bedroom lamp, TV, Mobil phone, Fridge.
3.2.2 Electricity generation
AC power is what fuels our homes. The wires outside of our house are connected at two ends to AC 152
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Exercise 3.2.2b :
2.-Indicate what type of current do we use in this electrical devices: Torch, Bedroom lamp, TV, Mobil phone, Fridge.
3.2.2 Electricity generation
DC is found in batteries and solar cells and it used for most of our electric devices. We need to convert the AC into DC in most of electric devices using power suplies
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Exercise 3.2.2b :
2.-Indicate what type of current do we use in this electrical devices: Torch, Bedroom lamp, TV, Mobil phone, Fridge.
3.2.2 Electricity generation
AC DCTV TORCHFridge PhoneBedroom lamp
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AC DC
3. Draw the diagram of a mobile phone power supply.
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Exercise 3.2.2b :
4.Find the input and output current in your mobile phone power supply.
3.2.2 Electricity generation
Input; 100-240 VOutput: 5,3 V
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3.3.1 Exercise 3.3.1:SolutionElectricity magnitudes
Exercise 3.3.1:Define Voltage, Intensity and Resistance and
its unitsSimbol Name Definition Unit
V VoltageVoltage Is the energy per
charge unit that makes them flow through a material
Volts (V)
I IntensityIntensity is the amount of
charges that goes through a conductor per time unit
Ampere (A)
R Resistance
Electric resistance is the opposition to the movement of
the charges through a conductor.
ohm (Ω)
BAck
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3.3.2 a Exercise Ohm’s law. Electric Power
Intensity is directly proportional to voltage:
If the voltage is Low, the charges will have less energy to move. Therefore the Intensity will be low too
R
VI
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3.3.2 a Exercise Ohm’s law. Electric Power
Intensity is inversely proportional to Resistance
If there is Low Resistance, the intensity will be High because there is less opostion to the movement of electrons.
R
VI The charges will cross the
material slowly
exercise
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3.3.2 Exercise 3.3.2.b Ohm’s law. Electric Power
Exercise 3.3.2.b:Calculate the value
of the intensity in these cases:
R
VI
V (V) R () I (A)
2 14 0,14A
2 1 2
20 2 10A
72 V 12 6
252 64 3,94 A
1000 20 50A
exercise
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V (V) R () I (A)
2 2
2 4
3.32 b Solution Ohm’s law Calculations with Ohm’s law 5º Exercise Solution
1AI 2
2I
R
VI
A5,0I 4
2I
R
VI
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V (V) R () I (A)
2 4
10 5
6.4 Ohm’s law Calculations with Ohm’s law Solution
8VV
24V
IRV
2R5
10R
I
VR
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V (V) R () I (A)
5 10
20 1000
6.4 Ohm’s law Calculations with Ohm’s law Solution
A 0,5I
10
5I
R
VI
20kvV
V00002V
200001V
IRV
exercise
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3.3.2 c Solution Ohm’s law. Electric Power
We have a fan connected to the domestic electric supply. The amperimeter indicate a 0,52A on the circuit. Extra data: house electrical supply 230V, 50Hz
1º Text analysis:
I= 0,52A ; V=230V;
R= ? ; P=?
1.What’s is the resistance of the fan?
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3.3.2 c Solution Ohm’s law. Electric Power
We have a fan connected to the domestic electric supply. The amperimeter indicate a 0,52A on the circuit. Extra data: house electrical supply 230V, 50Hz
1º Text analysis:
I= 0,52A ; V=230V;
I= ? ; P=?
2º- What’s the power measured in Kw
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3.3.2 c Solution Ohm’s law. Electric Power
Calculate the Intensity that flaws in a electrical engine of 1,2 Kw installed in my washing machine.
Extra data: house electrical supply 230V, 50HzText Analysis:R= ?; V=230V; I= ?; P=1,2kW
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3.3.2 c Solution Ohm’s law. Electric Power
Calculate the Intensity that flaws in a electrical engine of 1,2 Kw installed in my washing machine. What would be the Intensity and the power if we have 380V at home.
Text Analysis:R= ?; V=380V; I= ?; P=1,2kW
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3.3.4 Circuit associationsSolutions
Parallel: 1, 2 and 3 are joined together by A and B
Series: 1 and 2 are joined by A; 2 and 3 are joined by B
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3.3.4 Circuit associationsSolutions
Mixed: Series: 1 and 2 are joined to ASeries: 2 and the 4 & 3 association are joined by B Parallel: 4 and 3 are joined by B and C
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3.3.4 Circuit associationsSolutions: red-series Blue: parallel
SERIES: 1 and 2 are joined by A. 2 & 3 are joined by B3 & 4 are joined by C
MIXED: Series:1 is joined to 2 and 3 by A Parallel: 2 and 3 are joined by A and B Series: 2 and 3 are joined to 4 by C
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3.3.4 Circuit associations. Calculations
85
63,6
2
1321
t
t
t
R
R
RRRR
5,32
7
7
21
28
1
28
7
28
1
4
11
111
21
T
T
T
T
T
R
R
R
R
RRR
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3.3.4 Circuit associations. Calculations
2
9
69
21
2
12
18
1
18
3
18
1
6
11
2
3
2
9111
21
21
21
2121
321321
R
RR
RR
RRRR
RRRRRR
T
T
T
TT
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3.3.4 Circuit associations. Calculations
13
20025
200
1311213
40
1
25
11
111111
21
21
2121
321321
T
t
t
tt
RR
RR
RRRR
RRRRRR
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3.3.4 Circuit associations. Calculations
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3.3.4 Circuit associations. Calculations
1500
1500
11
6000
1
3000
1
6000
11
1111
1500
5001000
543
543
543
543 543
543
21
21
2121
21
R
R
R
RRRR
R
R
R
RRR
R
1000
1000
11
2000
1
2000
11
111
76
76
76
76 76
76
R
R
R
RRR
R
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3.3.4 Circuit associations. Calculations
3000
15001500
5_1
5_1
543215_1
5_1
R
R
RRR
R
3000
20001000
8_6
8_6
8768_6
8_6
R
R
RRR
R
1500
1500
11
3000
1
3000
11
111
8_65_1
T
T
T
T
T
R
R
R
RRR
R
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3.3.4 Circuit associations. Calculations
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3.3.4 Circuit associations. Calculations
20
20
11
100
1
25
11
111
43
43
43
4343
43
R
R
R
RRR
R
120
10020
432
432
432432
432
R
R
RRR
R
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3.3.4 Circuit associations. Calculations
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3.3.4 Circuit associations. Calculations
60
60
11
120
1
120
11
111
5_2
5_2
5_2
54325_2
5_2
R
R
R
RRR
R
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3.3.4 Circuit associations. Calculations
32
32
11
40
1
160
11
111
651
T
T
T
T
T
R
R
R
RRR
R
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
80
552521
t
t
t
R
R
RRR
RT= 80 Ω R1= 25 Ω R2= 55 Ω
IT= 2,75 A I1= I2=
VT= 220V V1= V2=
AI
I
R
VI
T
T
T
TT
75,280
220
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
VVVVSeries
VRIV
VRIV
AIIISeries
t
t
220
25,15175,255
75,6875,225
75,2
21
222
111
21
RT= 80 Ω R1= 25 Ω R2= 55 Ω
IT= 2,75 A I1= 2,75 A I2= 2,75 A
VT= 220V V1= 68,75 V V2= 151,25V
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
13
200R
200
13
40
1
25
1
R
1
R
1
R
1
25ΩR
1213RRR
R
1
R
1
R
1
T
321
21
2121
321
T
T
RT= 200/13 Ω
IT=
VT= 20V
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
1,3AI13200120
1320020
R
VI
T
T
TT
32121T
2121
321T
VVVVV
III
III
circuitMixed
RT= 200/13 Ω
IT= 1,3 A
VT= 20V
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A
A
VT
5,0I
40
20
R
VI
8,0III
25
20
R
VIII
20VVV
3
3
33
2121
21
212121
321
32121T
2121
321T
VVVVV
III
III
circuitMixed
RT=200/13 R1= 13 Ω R2= 12 Ω R3= 40 Ω
IT=1,3A I1= I2= I3=0,5A
VT= 20V V1= V2= V3=20V
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V
V
6,9V
128,0RIV
4,10V
138,0RIV
2
222
1
111
RT= 200/13 Ω R1= 13 Ω R2= 12 Ω R3= 40 Ω
IT= 1,3 A I1= 0,8 A I2= 0,8 A I3= 0,5 A
VT= 20V V1= 10,4 V V2= 9,6 V V3= 20 V
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
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AIIIInassociatioSeries
AR
VI
VEEEV
RR
RRRR
T
T
TT
TT
TT
T
1
115
15
15205
151023
321
21
321
RT= R1= 3 Ω R2= 2 Ω R3= 10 Ω
IT= I1= I2=
I3=
VT= V1= V2= V3=
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VRIV
VRIV
VRIV
10101
221
331
333
222
111
RT= Ω R1= 3 Ω R2= 2 Ω R3= 10 Ω
IT= 1A I1=1A I2= 1A
I3= 1A
VT= 15V V1= 3V V2= 2V V3=10V
PT= 15W P1= 3W P2= 2W P3=10W
WIVP
WIVP
WIVP
10110
212
313
333
222
111
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3.3.4 sol Ex 2 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
RT= 1º R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 2º I1=2º I2= 7º I3=6º I4=2º
VT= 220V
V1= =3º V2= 5º V3=5º V4=4º
4 Ω
4 Ω
8 Ω12 Ω
220V
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3.3.4 sol Ex 2 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
RT= 1º R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 2º I1=2º I2= 7º I3=6º I4=2º
VT= 220V
V1= =3º V2= 5º V3=5º V4=4º
4 Ω
4 Ω
8 Ω12 Ω
220V
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3.3.4 Circuit associations. Calculations
4 Ω
4 Ω
8 Ω12 Ω
220V
4 Ω 8/3Ω 12 Ω 220V
56/3 Ω 220V
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3.3.4 Circuit associations. Calculations
RT= 6 Ω
IT=
VT= 220V
1º
220V
4 Ω
4 Ω
8 Ω12 Ω
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RT= 18,67Ω R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 11,78 A I1= I2= I3=
VT= 220V V1= V2= V3= V4=
2º
131/8 Ω 220V
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2º
4 Ω
4 Ω
8 Ω12 Ω
220V
RT= 18,67Ω R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 11,78 A I1= 11,78A
I2= I3= I4= 11,78 A
VT= 220V V1= V2= V2=
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3º
RT= 18,67Ω R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 11,78 A I1= 11,78A
I2= I3= I4= 11,78 A
VT= 220V V1= 47,12V V2= V3= V4= 141,36V
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Two ways to calculate V1 and V2
4ºRT= 18,67Ω R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 11,78 A I1= 11,78A
I2= I3= I4= 11,78 A
VT= 220V V1= 47,12V V2=31,52 V
V3=31,52 V
V4= 141,36V
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5º6º
RT= 18,67Ω R1= 4 Ω R2= 4 Ω R3= 8 Ω R4= 12 Ω
IT= 11,78 A I1= 11,78A
I2=7,88A I3=3,94A I4= 11,78 A
VT= 220V V1= 47,12V V2=31,52 V
V3=31,52 V
V4= 141,36V
back201
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
202
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RT=20 Ω R1= 7 Ω R2= 6 Ω R3= 3 Ω R4= 11 Ω
IT= I1= I2=
I3=
I4= 1,5A
VT= 30V V1= V2= V3= V4=
2
6
3
R
1
20ΩR3
1
6
1
R
1
1127RR
1
R
1
R
1
RRRRRRRR
32
32
T32
T3232
4321T4321T
R204
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RT=20 Ω R1= 7 Ω R2= 6 Ω R3= 3 Ω R4= 11 Ω
IT= 1,5A I1= 1,5A I2=
I3=
I4= 1,5A
VT= 30V V1= V2= V3= V4=
A5,1IIII
:
A5,1I
5,120
30
R
VI
43-21T
T
T
TT
nassociatioSeries
A
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RT=20 Ω R1= 7 Ω R2= 6 Ω R3= 3 Ω R4= 11 Ω
IT= 1,5A I1= 1,5A I2=
I3=
I4= 1,5A
VT= 30V V1= 10,5V V2=3V V3=3V V4= 16,5V
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RT=20 Ω R1= 7 Ω R2= 6 Ω R3= 3 Ω R4= 11 Ω
IT= 1,5A I1= 1,5A I2= 0,5A
I3= 1A
I4=1,5A
VT= 30V V1= 10,5V V2=3V V3=3V V4= 16,5V
A
A
1I
3
3
R
VI
5,0I
6
3
R
VI
3
3
33
2
2
22
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RT=20 Ω R1= 7 Ω R2= 6 Ω R3= 3 Ω R5= 11 Ω
IT= 1,5A I1= 1,5A I2= 0,5A
I3= 1A
I5=1,5A
VT= 30V V1= 10,5V V2=3V V3=3V V5= 16,5V
PT= 45V P1=15,75W P2=4,5W P3=3W P5= 24,75W
W
W
W
W
75,24IVP
3IVP
5,4IVP
75,15IVP
444
333
222
111
208
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
209
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RT=19 Ω R1= 8 Ω R2= 6 Ω R3= 10 Ω R4= 5 Ω R4= 5 Ω
IT= I1= I2=
I3=
I4=
I4=
VT= 19V V1= V2= V3= V4= V4=
PT= P1= P2= P3= P4= P4=
5ΩR
5
1
10
1
10
1
R
1
R
1
R
1
R
1
10ΩR
10Ω55R
RRR
R
1
R
1
R
1
RRRR
5-43
5-43
5435-43
54
54
545-4
5-435-43
5-4321T
19ΩR
568R
RRRR
T
T
5-4321T
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RT=19 Ω R1= 8 Ω R2= 6 Ω R3= 10 Ω R4= 5 Ω R5= 5 Ω
IT=1A I1=1A I2=1A
I3=
I4=
I5=
VT= 19V V1= 8V V2=6V V3=5V V4=2,5V V5=2,5V
PT= P1= P2= P3= P4= P5=
545-4
5-435-4-3T
5-4-321T
T
T
TT
III Series
IIII Parallel
1AIIII
1AI
91
91
R
VI
545435-4-3 VVVVV
5VV
51RIV
6VV
61RIV
8VV
81RIV
5-4-3
5-4-35-4-35-4-3
1
222
1
111
212
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RT=19 Ω R1= 8 Ω R2= 6 Ω R3= 10 Ω R4= 5 Ω R5= 5 Ω
IT=1A I1=1A I2=1A
I3=
I4=
I5=
VT= 19V V1= 8V V2=6V V3=5V V4= V5=
PT= P1= P2= P3= P4= P5=
5VV
51RIV
6VV
61RIV
8VV
81RIV
Reach in Voltaje
5-4-3
5-4-35-4-35-4-3
1
222
1
111
V5VV
VVVVV
35-4-3
545435-4-3
213
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RT=19 Ω R1= 8 Ω R2= 6 Ω R3= 10 Ω R4= 5 Ω R5= 5 Ω
IT=1A I1=1A I2=1A
I3=0,5A
I4=0,5A
I5=0,5A
VT= 19V V1= 8V V2=6V V3=5V V4=2,5V V5=2,5V
PT= P1= P2= P3= P4= P5=
5454
5-4
5-454
3
3
33
II0,5AI
10
5
R
VI
0,5AI
10
5
R
VI
parallelin R
in the I thecalculate sLet'
V
V
5,2V
55,0RIV
5,2V
55,0RIV
5
555
4
444
214
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RT=19 Ω R1= 8 Ω R2= 6 Ω R3= 10 Ω R4= 5 Ω R5= 5 Ω
IT=1A I1=1A I2=1A
I3=0,5A
I4=0,5A
I5=0,5A
VT= 19V V1= 8V V2=6V V3=5V V4=2,5V V5=2,5V
PT=19W P1=8W P2=6W P3=2,5W P4=1,25W P5=1,25W
W
W
W
W
W
25,1IVP
25,1IVP
5,2IVP
6IVP
8IVP
444
444
333
222
111
215
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
216
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RT=14 Ω R1= 1 Ω R2= 6 Ω R3= 3 Ω R4= 3 Ω R5= 16 Ω R6= 16 Ω
IT= I1= I2= I3= I4= I5= I6=
VT=28V V1= V2= V3= V4= V5= V6=
PT= P1= P2= P3= P4= P5= P6=
Ω8R
8
1
16
1
16
1
R
1
R
1
R
1
R
1
Ω2R
2
1
3
1
6
1
R
1
R
1
R
1
R
1
RRRRR
5-4
5-4
545-4
32
32
3232
654321T
14R
8321R
RRRRR
T
T
654321T
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RT=14 Ω R1= 1 Ω R2= 6 Ω R3= 3 Ω R4= 3 Ω R5= 16 Ω R6= 16 Ω
IT=2A I1=2A I2= I3= I4=2A I5= I6=
VT=28V V1=2V V2=4V V3= 4V V4=6V V5= 16V V6= 16V
A
A
2II
2II
IIIII
2AI
14
28
R
VI
4T
1T
6-543-21T
T
2
TT
16VV
82RIV
6VV
32RIV
4VV
22RIV
2VV
21RIV
6-5
6-56-56-5
4
444
3-2
3-23-23-2
1
111
V16V
6V1V
VVV
4VV
4VV
VVV
6
5
656-5
3
2
323-2
219
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RT=14 Ω R1= 1 Ω R2= 6 Ω R3= 3 Ω R4= 3 Ω R5= 16 Ω R6= 16 Ω
IT=2A I1=2A I2=2/3A I3=4/3A I4=2A I5=1A I6=1A
VT=28V V1=2V V2=4V V3=4V V4=6V V5=16V V6=16V
PT= P1= P2= P3= P4= P5= P6=
A
A
3
4I
3
4
R
VI
3
2I
6
4
R
VI
2
3
33
2
2
22
A
A
1I
16
16
R
VI
1I
16
16
R
VI
2
6
66
5
5
55
220
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RT=14 Ω R1= 1 Ω R2= 6 Ω R3= 3 Ω R4= 3 Ω R5= 16 Ω R6= 16 Ω
IT=2A I1=2A I2=2/3A I3=4/3A I4=2A I5=1A I6=1A
VT=28V V1=2V V2=4V V3=4V V4=6V V5=16V V6=16V
PT=56W P1=4W P2=8/3W P3=16/3W P4=12W P5=16W P6=16W
W
W
W
W
W
W
WTTT
16IVP
16IVP
12IVP
3/16IVP
3/8IVP
4IVP
56IVP
666
555
444
333
222
111
221
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3.3.4 Circuit associations. CalculationsCalculate in each case the resistance equivalent Rt, It and Vt. Calculate the I
and V in each Resistance
222
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3= I4= I5=
VT=89V V1= V2= V3= V4= V5=
PT= P1= P2= P3= P4= P5=
Ω04,18R53
12667,312R
Ω53
126R
126
53
6
1
9
1
7
1
R
1
R
1
R
1
R
1
R
1
RRRR
T
T
543
5-4-3
5435-4-3
5-4-321T
A
A
93,4I
93,4I
IIII
:elements series In the
4,93AI
18,04
89
R
VI
2
1
5-4-321T
T
T
TT
224
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3= I4= I5=
VT=89V V1=59,16V V2=18,09V V3= V4= V5=
PT= P1= P2= P3= P4= P5=
V72,11V53
12693,4V
RIV
5-4-3
5-4-3
5-4-35-4-35-4-3
5435-4-3
222
111
VVVV
09,1867,393,4RIV
16,591293,4RIV
A
A
225
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3= I4= I5=
VT=89V V1=59,16V V2=18,09V V3=11,72V V4=11,72V V5=11,72V
PT= P1= P2= P3= P4= P5=
11,72VVVVV
V same thehave elements parallel The
11,72VV53
1264,93V
RIV
5435-4-3
5-4-3
5-4-3
5-4-35-4-35-4-3
226
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3=1,67A I4=1,30A I5=1,95A
VT=89V V1=59,16V V2=18,09V V3=11,72V V4=11,72V V5=11,72V
PT= P1= P2= P3= P4= P5=
A
A
A
95,1I
6
11,72
R
VI
30,1I
9
11,72
R
VI
67,1I
7
11,72
R
VI
3
5
55
4
4
44
3
3
33
227
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3=1,67A I4=1,30A I5=1,95A
VT=89V V1=59,16V V2=18,09V V3=11,72V V4=11,72V V5=11,72V
PT=438,77W P1=291,66W P2=89,18W P3=19,57W P4=15,23W P5=22,85W
W
W
W
W
W
WTTT
85,22IVP
23,15IVP
57,19IVP
18,89IVP
66,291IVP
77,438IVP
555
444
333
222
111
228
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229
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RT=18,04 Ω R1= 12 Ω R2= 3,67Ω R3= 7 Ω R4= 9 Ω R5= 6 Ω
IT=4,93A I1=4,93A I2=4,93A I3=1,67A I4=1,30A I5=1,95A
VT=89V V1=59,16V V2=18,09V V3=11,72V V4=11,72V V5=11,72V
PT= P1= P2= P3= P4= P5=
Ω04,18R53
12667,312R
Ω53
126R
126
53
6
1
9
1
7
1
R
1
R
1
R
1
R
1
R
1
RRRRR
T
T
32
5-4-3
5435-4-3
4321T
230