ELECTRICAL NETWORKS
WHAT DO YOU HAVE TO KNOW
TO FACE THIS TOPIC?
Resistance
Current
OHM's LAW
Potential difference
or
voltage
ELECTRIC CIRCUITS
An ELECTRIC NETWORK is a collection of electric components (resistors, conductors,
inductors, voltage and current generators) connected to each other in any possible way.
An ELECTRIC CIRCUIT is a special type of network that has a CLOSED LOOP giving a
return path for the current.
A NODE is a point on a circuit where two or more circuit elements meet.
Each part between two nodes is called BRANCH
ARE YOU ABLE TO IDENTIFY NODES, BRANCHES AND CLOOSED LOOPS IN THE
ELECTRICALE CIRCUIT SHOWN IN FIG.1?
TRY AND THEN CLICK ON THE
BUTTON TO CHECK THE SOLUTION.
CLOSED
LOOP
FIG.1
BRANCH
NODE
ARE YOU SURE THAT YOU HAVE FOUND ALL CLOSED LOOPS?
CHECK YOUR SOLUTION BY MOVING THE BLACK BOXES
KIRCHHOFF'S FIRST RULE
OR
KIRCHHOFF'S CURRENT RULE
AT ANY NODE IN AN ELECTRICAL CIRCUIT, THE SUM OF CURRENTS FLOWING INTO
THAT NODE IS EQUAL TO THE SUM OF CURRENTS FLOWING OUT OF THAT NODE
fig.1
NODE B : I1, I2 and I3 flow out of the node
I1+I3+I2=0
NODE C : I2 e I5 flow into the node while I4 flows out
I2 + I5 = I4
Now are you able to write the equation for the B node in fig.2?
------------------------------------
MOVE THIS BLACK BOX TO CHECK
YOUR EQUATION
I4 + I7 + I6 + I8 = 0
fig.2
KIRCHHOFF'S SECOND RULE
KIRCHHOFF'S VOLTAGE LAW
THE SUM OF THE ELECTRICAL POTENTIAL DIFFERENCES, CONSIDERED IN THE
SAME DIRECTION, AROUND ANY CLOSED LOOP CIRCUIT IS ZERO
Example: for the red closed loop the kirchhoff's voltage rule say:
VAB+VBE+VEF+VFA=0
And for the yellow closed loop, how does the equation became?
Click the
button to check if your solution is correct
VBC+VCD+VDE+VEB=0
EXERCISES
1) Assume the branches of the fig. 1a and 1b are parts of a more complex electric
circuit. Obtain the currents indicated by "?" by applying Kirchhoff's first rule.
fig. 1b
fig. 1a
Solution
2) By applying the Kirchhoff's second rule in the circuits on fig. 2a and 2b,
obtain the potential difference between the point D and the point C (VDC ) and
then, by applying the Ohm's law determine the currents indicated by "?"
fig. 2a
fig. 2b
Solution
end of lesson
NOW LET'S LISTEN TO THE ENGLISH EXPLANATION
Potential difference
Movie
DIDN'T YOU UNDERSTAND SOMETHING?
LET'S READ THE TEXT
So what's potential difference? Potential difference is what we use to generate current. It's like
a reward for current. The bigger the potential difference, the more current will flow.
So potential difference is used to get us to make current do whatever we want it to do. It's a
wonderful wonderful wonderful thing and it's used to drive essentially every circuit. So what is
the nice source of potential difference? Well, batteries serve as a constant source of potential
difference. When I have a battery that says one and a half volts on it, it means that the potential
difference between the negative side and the positive side is one and a half volts. And always
is one and a half volts. So if I connect that to a circuit, it will drive the current through the circuit
and once the current gets to the other side, it just bumps it up to the top again because it's got
to keep that same potential difference, one and a half volts.
So, they drive the circuits by forcing the current to flow and that's potential difference.
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The electric current
Movie
DIDN'T YOU UNDERSTAND SOMETHING?
LET'S TRY TO READ THE TEXT
So what is electric current? Electric current is the rate of charge flow. So electric current is
something that happens when I have charge moving through a conductor or whatever.
Whenever I've got charge moving, I've got an electric current. So current is equal to charge
passing by a given point divided by how long it too that charge to pass by that given point. It's
given by the symbol i and the unit, of course SI units, what's charge? Coulombs. What's time?
Seconds. So we got coulomb per second. One coulomb per second is called one ampere or
amp, alright. So the current gives the number of coulombs of charge passing a given point in
one second. So if for example my current is 3 amps, then that means that every second, 3
coulombs of charge pass by my given point. Alright.
There's the convention that essentially everybody uses for current. And that is that current is
taken to be in the direction of positive charge flow. Now we use this convention despite the
fact that in almost every situation, electrons are usually going the other way. But it's kind of
easier for us to talk about positive quantities and you know what, Ben Franklin was good but
he didn't know everything. So he assigned the electron negative charge instead of positive. Oh
well, you deal with what you're given.
Alright. So potential difference is what causes current to flow. If I've got a high potential over
here and a low potential over here, then my current is going to go this way because positive
charge wants to go away from the high potential and towards the low potential. So that's the
way that we can make current flow, is we can make one side of a conductor at a high potential
and the other side at a low potential. So we always flow from high to low.
And that's current.
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OHM'S LAW
This law expresses a relation between the potential difference across a wire and the current flowing
into it.
Ohm's law states that the current through a conductor between two points is directly
proportional to the potential difference across the two points.
Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical
equation that describes this relationship:
where I is the current through the conductor in units of amperes,
V is the potential difference measured across the conductor in units of volts,
and R is the resistance of the conductor in units of ohms.
Note: if we call A and B teh two ends of the wire and we take V as the potential difference between
A and B (where A is the positive terminal) the current found with Ohm's law is the one flowing from
A to B.
RESISTANCE
The electrical resistance R is not only a characteristic of the conductor’s material but depends on the shape of it.
The electrical resistance of a uniform conductor is given in terms of resistivity by:
where L is the length of the conductor in SI units of meters, S is the cross-sectional area in units of squared meters, and ρ is the resistivity in
units of ohm·meters.
The resistivity depends only on the conductor’s material. Resistivity is a measure indicating how strongly a material opposes the flow of electric
current.
Good conductors have low resistivity, while poor conductors (insulators) have resistivities that can be 20 orders of magnitude larger
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POTENTIAL DIFFERENCE
Before we can talk about poten al difference, one needs to understand what is electric poten al and what is an electric field.
The charges come in two types: posi ve charge and nega ve charge. Alike charges repel each other and unlike charges a ract each
other. They exert this force of a rac on or repulsion through an electric field that surrounds the charge. Any charge that comes in
vicinity of another charge experiences a force of repulsion or a rac on.
Consider a posi ve test charge placed in an electric field. An a rac ve force is exerted on it by the electric field center. That is why
forcing this charge away from the electric field center requires work to be done. That work increases its electric poten al energy!
More the amount of charge, more will be the work required to force the charge away.
Thus electric poten al energy of the charge increases as we go away from the charge center of the field.
Electric poten al is the energy required to transport a unit electrical charge to a specific posi on in an electrical field. Every point in an
electrical field has a different electric poten al which is a func on of distance from the charge source of the field.
What is Poten al Difference?
Now, understanding electric poten al difference is simpler. The electric poten al difference between two points, is the energy
required to transport a unit charge between those two points. It could also be defined as the change in the poten al energy that
occurs due to transport of a unit charge from one point to the other.
Electric current flows from a point of high electric poten al to a point which has a lower electric poten al. Current flows between two
points that have a poten al difference so as to balance this inequality.
Example: Two terminals of any ba ery have a poten al difference between them, which is measured in volts. When you connect any
circuit between the two terminals of the ba ery, charge flows from one terminal to the other to equalize the charge imbalance and
con nues ll the poten al difference between them is maintained.
Electric poten al difference is measured in volts. One volt is defined as one joule per coulomb.
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English lesson
THE RESISTANCE
The electrical resistance of an electrical element is the opposition to the passage of an
electric current through that element.
The inverse quantity is electrical conductance,.
The SI unit of electrical resistance is the ohm (Ω).
The Ohm is defined as a resistance between two points of a conductor when a constant
potential difference of 1 Volt, applied to these points, produces in the conductor a current of 1
ampere
Can you calculate the resistance value using the resistors color codes?
Valori numerici
Moltiplicatore
Tolleranza
Example:
A resistor has the following colours: brown,
black, orange and gold.
Which are the possible values of it?
resistance?
Da 9500 Ohm a 10500 Ohm
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?
?
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fig. 2a
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