Welcome back. 
Let's do some more linear circuits. 
Last time we talked about this idea of 
resistance and looking at individual 
elements. 
Now we're going to start putting them 
together, and we're going to be 
discussing Kirchhoff's Laws. 
So we're going introduce Kirchhoff's 
Current Law and Kirchhoff's Voltage Law, 
and then we'll use it to solve a very 
simple circuit. 
So as I mentioned before in our previous 
lesson we introduced Ohm's law. 
We introduced this idea of resistance and 
then we calculated it. 
And then we found this way of relating 
the voltages and currents within devices. 
So now we're going to look at between 
devices in a system perspective. 
After we've covered this, were going to 
then be able to start talking about 
resistors as actual devices that are 
intended to exhibit Ohm's Law. 
So the objectives of this lesson are to 
first of all have you be able what 
Kirchoff's current law and Voltage law 
are, and describe this voltage 
relationship parallel elements. 
And current relationship of series 
elements as well as to use Kirhhoff's Law 
to find unknown values in a simple 
circut. 
Kirchoff's Voltage Law basically states 
it is, that you make your way around any 
closed path in a circuit summing up your 
voltages. 
Now the sum has to be zero. 
And this is because if you start in one 
place [INAUDIBLE] And you take a trip 
around and then you come back to where 
you started. 
You can't have gained or lost any, kind 
of, electrical elevation. 
So as an example, if I have this pathway 
here, I can sum up all of my various 
voltages. 
VA, VG, VH and VD. 
Because this makes a closed circuit and 
then when I get back to the beginning. 
The total sum of the voltage has to be 
zero. 
And you can go in any direction you want, 
this one happens to be clockwise, but I 
can also do it counterclockwise. 
Or in this case just flip the signs 
rather. 
And so now instead of having the arrows 
go from the pluses to the minuses; now 
they go from the minuses to the pluses. 
So if I sum up the a, the c, the f, the 
h, and the e, they still all have to 
equal 0. 
And this would be equivalent to, if I 
instead changed the direction. 
The E, the H, the F, the C, and the A. 
You see that these are 2 equivalent ways 
of going around and looking at the 
circle. 
So if I look at parallel circuts. 
And they make a nice little loop here. 
If I do my Kirchhoff's law, I see that VA 
minus VB has to be equal to 0. 
And this is because general trend is 
you're following the arrow. 
You can either choose to use the first 
sign that you see or the second sign that 
you see. 
So here I used the first sign. 
So I used plus vA and minus vB. 
When I do that, I could actually put the 
vB on the other side, and I discover that 
anytime you have two parallel elements, 
Which is to say two elements that connect 
the same two nodes that they have to have 
the same voltage across them due to 
Kirchhoff's current, or Kirchhoff's 
voltage law. 
For Kirchhoff's current law we're going 
to be looking at the currents. 
And Kirchhoff's current law states that 
the sum of all the currents going into a 
node must equal the sum of the currents 
going out of the node. 
And remember we've already kind of 
discussed nodes as being the set of 
interconnected wires. 
So if I color the blue node here and I 
give some ref instructions I get the 
equation that ia plus ib must equal id 
plus ie because ia and ib are going in id 
and e are going out. 
I'll look at another node this orange 
node. 
I see that IB plus IF, the two going out 
must equal IC, the one going in. 
Let's look at physical descriptions to 
why Kirchhoff's Current Law is so 
important. 
What if I had this system, where I have a 
one mili amp. 
Current source and I have two nodes 
separated by this one centimeter of 
distance and I have current that's now 
flowing through the system and Kirkov's 
current law does not hold but that means 
that I'm going to be building up charge 
here as I'm pushing You know pulling 
electrons, and pushing electrons through. 
So this is going to get a charge at a 
rate of ten to the negative third times T 
cololms, so T being in seconds. 
But on the other note, these, this charge 
has to come from somewhere. 
It's coming from Q 2. 
So we get negative ten to the third times 
T cololms. 
And then I can use coulombs law, 
remembering that KE is equal to this 
8.987 times 10 to the ninth newton meters 
squared per coulombs squared, and 
plugging in these values, I discover that 
the strength of the attractive force 
between These two points is equal to 
89.87 times t squared meganewtons. 
And so let's see what's going on here. 
In the first millisecond I have 20 pounds 
of pressure, or attractive force, pulling 
these two together. 
After one second it's twenty million 
pounds, and then two seconds, eighty 
million pounds, or kilogram. 
They're all listed over here. 
So there's a tremendous amount of force 
that's going to be pulling these things 
together. 
And it's this electromagnetic force that 
motivates Kirchoff's law and why it's so 
important. 
If I place two devices in series in this 
configuration, it's possible for us to 
find another relation, similar to like we 
did with the parallel circuits. 
And when we say series, that means that 
there's two devices connected to each 
other, but there's nothing else 
connecting in that middle area. 
Because they're in series, the currents I 
a must equal i b because of Kirchhoff's 
Current Law. 
The current flowing in to that center 
node, here, has to be equal to the 
current flowing out. 
Now we're going to solve a simple 
problem. 
We have a few nodes and from the things 
we have learned so far, we know that P is 
equal to i times v. 
We also have Kirchhoff's Current Law and 
Kirchhoff's Voltage Law. 
So let's find the unknown values. 
First of all, at A, we have one amp of 
current flowing through it, and we have 
three watts. 
The arrow goes from the plus to the 
minus, which means that, because p equals 
i times v, this must be 3 volts. 
Now I can use Korkov's Voltage Law, and 
make this big loop around the outside 
here, so I get minus 3 volts plus vB plus 
5 is equal to 0. 
As long as the vB is minus 2 volts. 
Using Kirchoff's current law we see that, 
since we have 1 amp of current flowing 
this way, and A and B are in series but 
the arrows now point in opposite 
directions. 
This current must be minus one m. 
D and C are two devices that are in 
parallel with each other and so 
Kirchoff's voltage law states that they 
have to have the same voltage. 
That's 5 volts. 
We also know the power in c is five watts 
the arrow goes from the plus to the minus 
so p equals i times b. 
That means that the current flowing 
through here must be one ampere. 
Because we have minus one ampere coming 
here and one ampere going out here that 
would be the same as having. 
One ampere flowing this way. 
And Kurcoff's current law states that the 
sum of that, that, and that have to be 
zero, which means that this current is 
minus two amps. 
So finally the two unknown powers pb Is 
now equal two [UNKNOWN] plus to the 
minus, so minus two plus minus one...two 
watts...and Pd we have they are going 
from the plus to the minus so that equals 
I times V, 5 times -2 is -10 watts And if 
I add all of these up, 3 plus 5, plus 2, 
plus -10, is 0, which means we have 
conservation of power, and that gives us 
some confidence that our answer is 
correct. 
Finally remembering that if they're 
positive powers, we say that they're 
consuming power, and negative that 
they're Generating. 
This is a source, and the others are 
consuming power. 
And so we've been able to solve all of 
the voltages, currents, and powers, for 
this simple example. 
So to summarize, we've covered Kirkov's 
current law, voltage law. 
We applied Kirkov's voltage law, to show 
that parallel elements have the same 
voltage. 
And use Kirchhoff's Current Law to 
identify that series elements have the 
same currents. 
We gave an interesting justification for 
Kirchhoff's Current Law. 
And then solved a simple circuit by using 
Kirchhoff's Laws and, as well as, the 
Power Law that we learned before. 
In our next lesson we'll be introducing 
resistors, that are devices that are 
specifically intended. 
To exhibit Ohm's Law and inhibit current 
flow. 
And then we'll apply Ohm's Law and 
Kirchhoff's laws together to some 
resistor circuits. 
As always, if you've had any questions on 
this material, go to the forums. 
I look forward to seeing you there and 
seeing you in our next lesson. 
Until then.