Welcome to the introduction to electronics.
I'm Dr. Ferri and this lesson will be a review of circuit elements, and
actually the next few lessons will be a review
of basic circuit type principles that you're expected to
know before you come into an electronics class, so they cover linear circuit
principles, so if you want to review these lessons, you're welcome to do it.
If you want to skip them because you're very familiar with circuit elements,
linear circuit elements, then you're free to do that as well.
In this lesson, we will review resistors, capacitors, and inductors, and
their current voltage characteristics, as well as looking at sources and nodes.
So let's look at these passive elements.
A resistor, a capacitor, and an inductor.
In each of these cases.
We show by convention that the current is going into the plat, the positive side
of the voltage, and with that sort of convention we get the equation.
So this equation corresponds to this convention where this arrow is
flowing into the positive side.
And this particular equation is called Ohm's Law.
The voltage is equal to current times the resistance.
The resistance is measured in ohms.
And the symbol is.
And omega. Now if I go on to a capacitor,
capacitor is an energy storing device.
And it has, it is governed by this differential
relationship between the current through the capacitor and the voltage across it.
And note again that the convention is to show the current going into
the plus side of the voltage and then we get this equation.
The, the units on capacitors are farads and
usually we'll, we'll be looking at units that are in 10 to the minus 6 farads
or represented as micro farads.
Those are common, more commonly seen.
Then we get to inductors.
Inductors are also energy storing devices and
the current voltage relationship is this.
Notice that now we're taking the derivative of the current to give us
the voltage.
The common units are henries.
Which we represent as H.
And it's oftentimes, we'll look at, ten to
the minus three, or millihenries.
So the range that we often look at is again, millihenries.
And notice again that the, by convention that the current is going into
the positive side of the voltage in order to get this equation.
These are called passive elements,
because they don't require a power supply just for that element.
There are other elements that we will see in electronics that we'll
call active elements that require a power supply to make them work,
to make them give their characteristics.
Now let's look at the basic series and
parallel connections of resistors, inductors, and capacitors.
The series resistors, you just sum them up.
So the total resistance from this point here to this point here
is the sum of the two things.
And inductors work the same way.
The total inductance between this point.
And this point is the sum of the two individual inductances.
And again, this would be in Ohms, and Inductors would be in Henrys.
Now the parallel connection's a little bit different.
Parallel connections,
meaning that the resistors are connected together at one end and
again at the other end, whereas in series they're connected only between them.
The resistance, total resistance between this and this, so it's equivalent
resistance across everything, is the inverse of the sum of the inverses.
Now if I only have 2 resistors I can simplify this.
So if R3 is equal to 0 and I only have R1 in parallel with R2.
So that represents the fact that R3 is equal to 0 and
I've only got two resistors in parallel.
Then that would be equal to R1 times R2 over R1 plus R2.
And we can get that by setting R3 to equal to 0 here or dropping that off of here.
And then just simplifying this form.
So, then we've got the same relationship for
inductors in parallel, this, this relationship here.
So, we would also say L1 in parallel with L2, L1 times L2 over L1 plus L2.
Now capacitors are little bit different.
They operate at, in a different way.
The series capacitors has a same equation that we use
before when we were looking at parallel resistors or any parallel inductors.
So.
Capacitors in series, you use this relationship.
Capacitors in parallel are easier.
The equivalent capacitance between this point and
this point is just the sum of the individual capacitances.
So, connections and sources.
When we look at a schematic, we'll see a ground.
It's very commonly used and the ground looks like this.
It's a reference for zero volts.
When we look at linear circuits with DC voltages maybe batteries supplying it,
we often times pick a ground and say that's our reference node.
And reference node meaning that we're going to say the voltage with respect to
anything else any other point in that circuit.
Is the potential, with respect to that Ground Node.
And so, it's just a reference node.
And when we get to electronic circuits,
it usually has a little bit more meaning to it.
Because we often times,
power these electronic circuits with AC or wall power, you know?
You plug it into the wall.
And when you plug it into the wall, we're connected to a power system.
In that power system, the power that comes into your house.
Usually is grounded, meaning that there's a connection down to the ground and
to the real ground, to Earth.
And so when the power supplies are connected to the wall and then they're
connected to your circuit, often times we are required to ground our circuit.
So in that case, the ground often times has a more physical meaning to it,
really relating to the ground, the true ground.
A Node is anything that has the same potential,
that's connected electrically together.
So, every point on here, is the same node.
Now, I might have different current going through these branches, leaving this node.
But the voltage everywhere on this node, is the same.
With respect to Ground.
Our Voltage Source, we have Independent Sources for both the Voltage Source and
the Current Sources.
Independent Sources will show as circles.
The volt, the units on a Voltage Source are going to be in volt.
Units on a Current Source are going to be in amps.
Oftentimes.
We supplied them with smaller amps, maybe milliamps.
Dependent sources have the little, the little tri, diamond shape.
Now the difference between the independent source and the dependent source is
that the independent source doesn't depend on the rest of the circuit.
It's going to be.
It's going to be independent, no matter what you do to the rest of the circuit,
you define a function for that independent source.
Now dependent source, there's a dependence on some other part of it.
For example, I might have this voltage supply, gives me a voltage, but
it might be dependent on current in one of my branches, or I might have.
A dependent current source which might be
dependent on a current in one of my branches.
It might be, be dependent on a voltage at one of my nodes.
So, these two are dependent on something else that's happening in the circuit.
This right here.
Is independent of what's going on in the circuit.
Now all of these, all voltage sources have the units of volts, and
all current sources have the unit of amps.
Let's look at a common, common connection here.
This is a, a circuit schematic.
We've got a independent.
Voltage source.
An independent currant source.
We've got our ground right here.
We've got our resistors.
This case, we don't have any capacitors or inductors.
We've got some nodes here.
These are all connected together.
That's one node.
That's another node.
Here's a node right here.
And then we've got some nodes that only connect to resistors.
So this resistor, this is a series combination because the resis,
they're connected right in the middle.
I don't see any other obvious connections.
These two are not series.
Because they're connected in the middle, but
they're also got something coming off of it.
So that means they're not in series.
And similarly, these for example, they're not in series nor are they in parallel.
To be in parallel, they'd have to be connected together at both ends.
So, this particular circuit, we show with this ground and
ground is very commonly shown in electronic circuits.
But they're shown oftentimes in a different way, they're shown this way
because every, everything along this bottom node is connected to ground.
So, I could just separate them out and
just show each point coming down to ground.
So this is equivalent, if I'm trying to do Kirchoff's Voltage Law or
Kirchoff's Current Law.
In this circuit versus this one, I'm going to treat this as if these are all
connected together with a line, just like this is.
So this lesson just gave some summary review of basic circuit components.
In the next lesson we will cover Kirchhoff's Laws.