Welcome back to electronics.
This is Dr. Ferri.
This particular lesson, is a review of Kirchhoff's laws.
In a previous lesson, we reviewed, linear circuit components such as resistors and
capacitors, and conductors.
In this one, we're going to, go through more detail of Kirchoff's Current Law, or
KCL, Kirchoff's Voltage Law (KVL).
Kirchoff's Voltage Law (KVL) states
that the sum of voltages around any closed loop is zero.
Now we show an example of a closed loop here.
And in order to ply, apply this, we would have to know what these, these voltage is.
So, suppose this is, V sub D.
V sub A.
V sub G.
And these are all measured in, volts and this is V sub H.
So, I want to do, I, I sum up the voltages around here.
Now, if I'm summing the voltage from this point, to this point, so I'm looking at
the voltage potential, I actually gain voltage, from this point to this point.
But, when I do a voltage Kirchhoff's Voltage Law.
I want to make sure that I'm always consistent with,
the way I use the polarities.
So I use a little trick in doing this.
I use a trick and say, if I'm going to be summing in this direction,
if I come to plus sign first I add it.
If I come to plus sign here first I add it.
In all these cases I've come to a plus sign first,
if I go around in this direction.
So I'm going to add these on.
If I were to come to, a minus sign first, I would subtract it.
That's just, my trick in making sure I get the polarity right.
So starting at this point, I would have V sub H plus V sub D plus V sub A.
Plus V sub G, all have to sum to zero.
And that's going to be true of any loop.
It'll be true of this loop.
Any loop, any closed loop.
Now, I'm going to have you do a KVL quiz here.
So, looking at this circuit, I want you to find VH.
Now, coming back to the solution here.
Find VH I want to do a KVL.
Well, I can do a KVL around this loop, but I don't know what this voltage drop is.
So let me do a KVL around this loop right here.
And the way I do a KVL is,
in the direction I go, if I hit a plus sign first, I add it.
If I hit a minus sign here as in this case I would subtract it.
Now it's not strictly physical,
because actually I'm losing potential as I go from here to here.
But it's just a trick that I use to keep my polarities, correct.
So, going around here starting with, plus VH and then I get to the minus two.
Over here I get a plus, minus one and around here I get
a minus 5 and then plus 4 equals 0.
So, when I add these up.
Let's say I'm going to have a, a minus 8 plus 4.
In other words solving for it I get a, 4 volts.
Now let's look at KVL and Parallel circuits.
So I got.
These two elements, that are parallel to one another and
that's the only thing in this circuit.
So, if I do a KVL around here, and this is V sub A, and this is V sub B,
going around here, I would have, in this direction, V sub A.
Minus V sub B, because I hit that minus sign first, is equal to 0.
In other words, V sub A is equal to V sub B.
And that is true, any time we've
got two elements, that are in parallel with one another, they're going to have
the same voltage drop, as long as you've defined them with the same polarity.
So any two elements that are parallel with one another,
have the same voltage across them.
Now this a, a numerical example,
an actual circuit example with resisters in there of a caveat.
And I'd like to be able to, solve this.
And do for example a Kirchoff's Voltage Law across this.
So let me, let me write this.
There's lots of, loops I could do.
And do this loop right here.
I can do this loop up here.
So let me write Kirchoff's Voltage Law around here.
So I would like to be able to, write, so I'm going to do it around here.
I'll need to be able to, mention or, or write an expression for
the voltage drop across this resistor.
Now, by the convention we show that resistance goes into
the plus side in order for us to be able to use Ohm's Law.
So we'll call that V sub one.
So, if I want to go around here I hit the minus sign first, minus 10.
Plus this voltage drop here, V sub 1, plus V 0.
And, that's all I've got on this loop is equal to 0.
So V sub 1 is equal to i sub 1 times 20.
V sub zero is equal to i sub 2 times 10.
And this is by Ohm's Law.
So now I got an expression.
That I can use to solve for, for these variable here in terms of the currents.
I can also do a loop around this way.
Suppose, I do this loop around here so in this case I hit the plus sign first.
So it's plus 2, minus v 0 'cause I hit that minus sign and
then plus voltage drop.
Well remember the current goes into the plus side.
Plus I 3 5 is equal to zero.
So I have another expression and v zero again.
Is equal to i2 times 10.
So what we've been showing here is how to write KVL's for a particular circuit,
an actual circuit, that we're making use of Ohm's Law for that.
Kirchhoff's Current Law says that the current entering a node equals the current
leaving a node.
For example, suppose I've got this current.
This is a node right here and this is a node because everything here is connected.
So this is a node there and call this of A and this I'll call
of B, of E, and.
I sub d.
So, if I do KCL at this node I would sum up everything entering and that would be
i sub b plus i sub d is equal to the sum of what's leaving, i sub a plus i sub e.
And that's true for any node.
So, I 've got a node over here.
And in note over here and note over here.
It's true at every note.
So in this particular case we look at for
example if we draw the current if I've changed the directions so
now this one I'm showing this way this way this way now it's entry is word i sub A.
Plus I sub B, what's leaving is I sub D plus I sub E.
So if I change the arrow, the reference of my current,
I have to just be careful that I'm consistent with it.
Now, if I have two elements in series with one another, then all the current-
this is a node between them-
the current entering has to equal the current leaving.
So, if this is i sub A, and this is i sub B, then the current
that enters this node, i sub A, has to equal the current that leaves this node.
So that means that any current that flows through an elements that are in
series with one another, is the same current.
So, this current is all the same because they're in series.
Let's look at a KCL for a particular numerical example a,
a circuit, real circuit.
And I'm going to look at this node right here.
And I want to look at all the currents entering and leaving.
And let me define this as being.
The one that maybe I'm trying to solve for i.
So, let me look at the currents entering.
We have i1 is equal to i3 plus i2 plus i.
And that's, that's just how to do the KCL at this node.
In summary, we've introduced the Kirchhoff's voltage line,
Kirchhoff's current law.
We've applied them, the Kirchhoff's voltage law to parallel elements and
found that two elements in parallel have the same voltage across them.
We've applied the KCL to series elements and saw that any two elements that were in
series had the same current going through them.
And then we also solved a simple circuit using Kirchhoff's laws.
In our next lesson we'll do a review of impedance methods.