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.