Hi. It’s Mr. Andersen and this AP Physics
essentials video 87. It is on Kirchhoff’s Loop Rule which is a powerful tool to look
at circuits. And when combined with Kirchhoff’s Junction Rule, which we will get to in a few
videos, it really makes analysis of complex circuits possible. And so the way it is written
is the sum of all the voltage in a loop is equal to 0. And so if we were to write that
out V4, so that would be the voltage of the battery, minus V1 minus V2 minus V3 is equal
to zero. So the sum of all of the voltages is equal to zero. Now how does that work?
Well remember the battery is a voltage lift. It is giving charge, potential energy. And
then we are losing that energy through this resistor, this resistor and that resistor.
And so the sum of all of the voltage differences is zero. The lift minus the drop minus the
drop minus the drop is equal to zero. Now conceptually a better way to think of that
is like a roller coaster. When you are on a roller coaster, when you start there is
going to be a lift. So that is going to lift you up to the top of the roller coaster. Now
the cars have potential energy which is converted into kinetic energy. And if they play it right,
you are going to get right back to the beginning again with no energy left. And so Kirchhoff’s
Loop Rule is really just the conservation of energy in a loop or in a simple circuit.
So the voltage or potential difference around that whole loop is going to be equal to zero.
So we could look at for example a battery and a resistor in a simple loop. The voltage
lift plus the voltage drop is going to sum to zero. Now how do you figure out the voltage
of a resistor? Remember we simply use Ohm’a Law. And that is all you have to know about
Kirchhoff’s Loop Rule in Physics 1. In the Physics 2 we are going to add capacitors and
then also parallel circuits to it. And so if we think back to that roller coaster, as
we store energy in this sphere, it is just like storing energy in the charge across a
battery. And when we let it go we could lose some of that energy. We could gain some back.
We could have another battery. We could lose some. Gain some. Lose some. And so you can
have a really complex circuit and we can solve it using Kirchhoff’s Loop Rule. So think
of it more like this. So we have a battery which is like the lift in a circuit. It is
giving those charge or potential energy or potential difference. And then they are losing
that energy, they come back to the battery again and they are gaining charge. This is
a pretty simple model. Charge is going to be distributed through this whole thing. But
it is a good way to think of what voltage is. And that is why we cannot just measure
the voltage through something. It has to be across something. For example, across a battery
or across a light bulb. And so voltage is equal to the work done by the charge as it
moves. And so if we were to move, for example, one coulomb of charge we could do one joule
of work. That is what a volt is. And so let’s make that usable. Let’s not just short out
our battery. If we put a light bulb here, as that charge moves through it, if it is
a 1.5 volt battery, we are going to be able to generate 1.5 joules of heat and light coming
out of that light bulb. And so if we look at a circuit like this, Kirchhoff’s Loop
Rule lots of time is written like this. The summation of the voltage is equal to zero.
So the first thing you have to figure out is which way is the current flowing? And then
just basically current we will say is flowing from the positive to the negative. So you
can think about going through this loop in a clockwise fashion. To use Kirchhoff’s
Loop Rule you have to start at some point and be able to return to that same point by
tracing out the circuit. And so we are going to say the sum of our voltage is equal to
zero. So you would write it out like this. We are going to start with a battery. The
battery, since it is a lift, we are going to give that a positive value. So positive
V1 minus V2 minus V3, because we are losing that potential difference in each of these
resistors here is equal to 0. And so we could solve for V1. V1 is equal to V2 plus V3. So
let’s do a simple problem. Let’s say we have a 9 volt battery. We have 10 ohm and
5 ohm resistor right here. And then we have a current going in that direction like that.
So first thing we have to figure out is, well, what is the current going to be in this circuit?
So we have learned earlier that we could just add these two resistances together. So that
is going to be a 15 ohm resistance on this series circuit. So we are going to put 15
ohms right here. What is our voltage? That is given as 9 volts. And so we could solve
for current. It is going to be 0.6 amps. So now we just go around and we can use Kirchhoff’s
Loop Rule. So if we look at this resistor right here, what is its voltage going to be?
Well we just use Ohm’s Law again. We know that resistance is 10. We know that the current
is 0.6. And so it is going to have a voltage of 6 volts. What is the other one going to
be? It is going to be 3 volts. And so you can see that addition of this 9 volts minus
6 volts minus 3 volts is equal to 0. And so to think about that, and this model really
works for me, think of that same circuit drawn like a roller coaster. So we could say the
battery is right here. And so how much potential difference do we have or potential do we have
at the beginning? 0 volts. But we are lifting it to 9 volts as we go through the battery.
We are giving it potential energy, that charge has potential energy. As it moves through
the wire that 9 volts is not going to change throughout here until we get our next resistor.
And so this is a 10 ohm resistor. If it starts at 9 volts what is it going to be as it gets
to the bottom of that? It is going to be 3 volts. So we are going to have a voltage drop
of 6 volts. And then that goes to 3 volts and back down to 0 volts on the second resistor
that is going to be inside. Now if we do a simulation of that, this is a phet simulation,
I have that same circuit drawn. So it is going to be 9 volt potential difference across it.
We could look at the amps and that is going to be 0.6 amps. Again we just added those
resistance and it is going to be the same, you know current through every part of that
circuit. And then the next thing we can do is just verify that those voltages are correct.
So if we look across the first one it is going to be 6 volts across that first resistor.
And then if we were to look across the second resistor, using our voltmeter again, we have
to check it across that element, it is going to be 3 volts right here. But what would happen
if we now make it a parallel circuit. So if we are going to build a parallel circuit on
the other side, and let’s just put a 10 ohm resistor over there. So if you think back
to that roller coaster analogy again, what is going to happen as we move through that
other circuit? Well we had potential energy right here. We have 9 volts of potential energy
here. We are going to have 0 volts of potential energy when we get back to here. And so what
is going to be the voltage drop across that? It better be 9 voltage drop, 9 volts of voltage
potential difference and it is going to be 0.9 amps. So we could check that using our
ammeter and then using our voltmeter. So we get a 9 voltage drop across there. Now as
you move into Physics II you have to understand what is going on with not only resistors but
capacitors. And capacitors, remember, will store charge along plates. And so now we have
a simple circuit. I have drawn the electrons moving in the circuit in this time. And so
we have a 0.9 amp. So we have movement right there. If we were to move across this 1 resistor,
the voltage drop is going to be 9 volts. But now what I am going to do is I am going to
add a capacitor. So we are going to split the junction right here and we are going to
put a capacitor right here. And watch what happens to the charge. The charge eventually
stops. And so let me discharge that capacitor. And so it stops. And so we could even look
at what is happening to the current. You can see the current is dropping to 0. So there
is no flow. But now throughout the whole circuit there is no flow. But now let’s look at
the voltage. And so with the resistors we would expect across this one to be that whole
9 voltage, but it is not. It is 0 volts. And so where is the potential difference? It is
going to be across the capacitor itself. And so when you are using Kirchhoff’s Loop Rule
with capacitors you can think of a capacitor just like a battery. That is where to voltage
is going to be. Now let’s put two capacitors that are going to be in series. And so if
we look at the voltage across each of those, since they are the same capacitance, it is
going to be 4.5 volts on each one. But if we change the capacitance of that next capacitor,
so let’s give this higher capacitance, so it is a larger capacitance, I have moved it
up to 0.20 farads. So now we find the voltage on the bottom part is 3 volts, on the bottom
capacitor. On the top one it is going to be 6 volts. So that is that inverse relationship
when we are looking at capacitors. And that is because we are storing that charge along
that plate. And so did you learn to construct or interpret a graph of energy changes. Again
think of it like a roller coaster. Could you apply the conservation of energy that shows
how the Kirchhoff’s Loop Rule works? And so again it is the voltage lift is equal to
the sum of all the voltage drops. Could you apply this to solve a simple problem? Could
you then start to study capacitors, and we call those steady state circuits. What does
steady state mean? Well, when you just hook it up it is going to be transient, so we see
a little bit of charge still moving. But eventually it becomes a steady state. And so understanding
how a capacitor works inside a circuit like that. And then could you tie this to the potential
energy? The ability of that charge to do work? I hope so. And I hope that was helpful.
