Hi. It’s Mr. Andersen. And this is AP Physics essentials video 92. It is on Kirchhoff’s
Junction Rule which when used with Kirchhoff’s Loop Rule can solve very complex circuit problems.
And so it is very simple. It just says the current that we have coming into a junction,
so for example if this is a junction, the current of i2 plus i3 has to equal the current
coming out of the junction. It is an application of the conservation of charge in physics.
Or if we were to use a pipe and water analogy, the flow coming into a junction has to equal
the flow coming out. But the flow could be in this direction or the flow could be in
this direction. The sum of the flows coming in has to equal the sum of the flows coming
out. And so the Kirchhoff’s Junction Rule is an application of the conservation of charge.
And so in Physics I you should be able to solve a simple circuit and the current in
has to equal the current out. So that would be a simple circuit in parallel or series
that has a battery and some resistors. As you move into Physics II you have to be able
to add capacitors in steady stay to that understanding of Kirchhoff’s Junction Rule. And so Kirchhoff’s
Junction Rule again, application of conservation of charge is written like this. The sum of
the currents in has to equal the sum of the currents coming out. And so if we were to
solve a simple problem, if we have this junction right here and I were to give you the currents
i1 and i2, how would you set this up? Well first of all we figure out what is going in,
what is coming out. We can use the arrows for that. So i1 is coming into the junction.
What is coming out? i2 plus i3. So we set it up like this. i1 equals i2 plus i3. And
then I just write in what I know. I know 7 amps and 3 amps. And so I can solve for i3
being 4 amps coming out of the junction. We can even get very complicated problems like
this. And so you may want to pause the video and try to solve this. I am giving you four
currents. And then you have to solve for the one that you do not know. So first of all
write it out. What is the current coming. I would say it is going to be i1 and i4. What
is coming out? i2, i3 and i5. Write in what you know. And then you can solve for what
you do not know. In this case i5 should be equal to 3 amps. And so you should be able
to experiment with this as well. So I am using a phet simulation, a circuit builder. So I
have built a 9 volt circuit. This would be a parallel circuit with a 10 and 20 ohm resistor.
I can use an ammeter to show that it is 1.35 amps into the junction. One of those coming
out is 0.9 amps and so could you figure out what is the other current coming out of that
junction? Well it is simply Kirchhoff’s Junction Rule. It is going to be 0.45 amps.
The sum coming in has to equal the sum that is coming out. You also should be able to
solve that if we have a circuit diagram like this. Generally on a circuit diagram, and
these are going to get complex, when we have multiple batteries. What you do is draw the
current going away from the positive side of the battery. So I would have this i1 going
in this direction. We could also show i3 going away from the battery here. And then I could
say, alright, so here is my junction. And so we are going to have i2 coming out. And
then if you know any of the values in it, so if I know any of the current, then I can
simply solve for the one that I do not know. Now lots of times you can also use Kirchhoff’s
Loop Rule in concert with this to solve more complex problems. But I should get a i2 value
or rather an i3 value of 9 amps. As you move into Physics II you should be able to understand
what is going on with capacitors at steady state. So I have a simple parallel circuit
right here. Two 10 ohm resistors, a 9 volt battery. I could use an ammeter. We have 1.0
amps coming in. One junction is 0.9 and the other is going to be 0.9 as well. I am now
going to turn on the electrons, so you can see what is going on. Remember the charge
moves in the opposite direction to that. I am going to remove one of those resistors
and then put in a capacitor. Watch what happens when I add the capacitor to my circuit. You
could see the electrons move for a second and then they stop. And I could eventually
discharge that. They will move for second and then they stop. So if I look at how much
current is flowing through that branch that has the capacitor, it is 0.0. So we still
have Kirchhoff’s Junction Rule, 0.9 equals 0.9 plus 0. But you can see that that charge
stops. It is acting like a dam inside that water. And so you can think of a capacitor
just like a break in a circuit when we are applying Kirchhoff’s Junction Rule. So if
I put a capacitor here or here, it is going to be a break in that circuit. There is not
going to be any current flowing through that branch of the circuit. And so did you learn
to apply Kirchhoff’s Law? Again current in is equal to current out. Could you design
an investigation. Again I used a phet simulation to do that. Could you use schematics to figure
out where the current is? And then finally, as you move into Physics II, do you understand
how capacitors can act as a break in a circuit? I hope so. And I hope that was helpful.