0:13

Now, in this module, we'll be concentrating on

Â developing some analysis tools that you can use to analyze circuits like this.

Â Specifically, we'd like to be able to solve for voltages and

Â currents in a fairly complicated circuit.

Â The other thing that we want to cover is, we want to introduce

Â physical applications, including resistive circuits.

Â 0:37

This first lesson is on Kirchhoff's Voltage Law,

Â and we will be building upon some concepts that we learned in the last module.

Â In particular, Ohm's Law, and

Â the idea of Loops, close paths for the current to flow.

Â 0:52

Kirchhoff's Voltage Law is presented right here.

Â The sum of the voltages around any loop is zero.

Â There's a shorthand notation for it that we show right here.

Â And this is an example of a loop.

Â Now I want to get into an analogy.

Â That is going on a hike in a mountain range.

Â As you go on the hike, you go up and down hills.

Â You're gaining potential and

Â you're losing potential as you're going around that hike.

Â So, as you circle back or loop around back to your starting place,

Â you have no net change of potential, no net change in elevation.

Â It's the same thing as you go around a loop with the voltages.

Â Right here,

Â from this point to this point, you've gained potential, you've gained voltage.

Â And then, from this point to that point, you've lost it.

Â So as you go around this loop and end up back at your starting point right here,

Â you have no net changing potential, no net changing voltage.

Â So let's look at this example.

Â I'm going to start right here and I'm going to go around the loop.

Â And let me go ahead and show it is going around this way.

Â And I'll show the arrow in the clockwise direction.

Â Now you notice from right here to here, I'm gaining potential.

Â And then over here, I'm gaining more potential.

Â And then over here, I'm losing potential, and I'm losing potential again.

Â It's kind of hard for students to remember that when they're gaining and

Â losing potential, you have to be very cognizant about these signs right here.

Â So I've got a little trick that I do.

Â 2:17

And the trick is when I come to a minus sign first, I subtract that term.

Â So I would subtract this term, this term, this one I come to a plus so

Â I add that term.

Â So let me go ahead and write this out.

Â So I have a minus VA minus VB plus VD plus VC is equal to zero.

Â That's my Kirchhoff's Law The fact is, it has to sum to zero.

Â Now I can add another loop here, and

Â the Kirchoff's Voltage Law has to apply for this one as well.

Â And actually I've just added two loops.

Â I add this loop right here, and then I add a loop around the outside.

Â So now I have three loops.

Â 2:58

And the Kirchhoff's Voltage Law has to apply for each one.

Â Let's take a look at this loop right here.

Â If I start right here and go around the loop this way,

Â I get a minus V sub D and I come to the plus sign here, plus V sub e = 0.

Â Now one thing to notice about this is that these two

Â elements are in parallel with one another.

Â And I know that because they share a node at this end and

Â a they share a node at the other end.

Â So what we've got is V sub d is equal to V sub e.

Â Whenever I've got two elements that are in parallel with one another

Â their voltages are the same.

Â I'm going to do a more elaborate example.

Â This time one with numbers and

Â suppose in this particular example, I want to solve for V sub B.

Â So I look at this and say okay, what equation do I need to find?

Â And I look for a loop with V sub B in it.

Â So here's one loop right here.

Â So let me look at this one.

Â There's only three terms in it.

Â So I'm going to go ahead and do Kirchoff's voltage law in this direction.

Â 4:10

So, I get to the V sub b, I get to the plus first.

Â I have a plus V sub b and then I get to the plus here.

Â I have a plus 1 plus, but this is a minus four so

Â plus a minus four is equal to zero.

Â So V sub E is equal to three volts.

Â 4:41

Okay, to solve for V sub A, I can do a Kirchhoff's voltage law around here.

Â So V sub A is equal to 6 volts Now the other thing

Â to note about this is that has got to be true for every other loop.

Â So with these these values V sub A and V sub B being defined and

Â everything else, then I should go back around and

Â if I looked at the KVL around any of these other loops it should still work.

Â They should still sum to zero.

Â Even around this big outer loop.

Â And how many loops do I have here?

Â I've got one two three, and then I've got this loop right here that's four,

Â five, six around here, and then the big one is seven.

Â So I've got seven loops here the KVL holds for each one of those.

Â Let's look a little bit more carefully at components that are in

Â parallel with one another.

Â So in this case we have two sets of parallel components.

Â These resistors, this one right here and

Â this one right here, are in parallel because they share the node at both sides.

Â Similarly, over here, we have these three components here are in parallel because

Â they share this node and this node.

Â Now, what we've said before is that voltages across parallel elements

Â are equal.

Â So that means the voltage across this resistor is the same as the voltage

Â across this resistor.

Â And something to point out here is this voltage source right here

Â is the voltage that is across this resistor and

Â also the voltage that is across this current source.

Â Another example I want to highlight is a voltage lock with

Â a current source in there.

Â Look at this loop right here.

Â 6:20

-10 going around this way plus this current times 100 so I'm using Ohms law.

Â So a 100 times i1 plus 200 times i2 Is equal to zero.

Â So that's one of my equations.

Â Now, if I did Kirchoff's Voltage Law around here, I will go,

Â let's see if I start right here, based on the standard convention,

Â the passive convention on Ohm's Law,

Â if the current is defined as going in this direction,

Â the voltage would be positive, the voltage polarity would be like this.

Â So in other words, I'm going into the negative side of it, -100i1.

Â Same thing over here.

Â This is going to be the +- side because the current's going in this way.

Â So I've got a -300 I 3 plus

Â the voltage drop over the source.

Â I will call V sub I.

Â Now as I said before a common mistake for

Â students to make is thinking that this is zero.

Â It is not zero.

Â I am not sure what it is.

Â It's a variable that I would have to solve for by solving all the other currents and

Â then coming back and solving for that.

Â Another example that I want to cover is a Kirchoff's voltage law

Â with respect to open circuits.

Â So I've got an open circuit here, and

Â suppose I want to solve for V sub ab.

Â V sub ab means the voltage from b to a.

Â So from b to a.

Â 8:02

Now once I've defined it this way, it's a little bit easier to see it,

Â how to apply Kirchhoff's Voltage law for this example.

Â So, if I go around here, I have a minus V sub r2, and

Â then I come up to here and I get a plus

Â V sub ab + V sub R 3 = 0.

Â And if I can solve for V sub R2 through Ohm's law or something else,

Â or if I know what these are, then I can go back and solve for this.

Â So the key here in doing an open loop

Â is there still is a potential to cross that open loop.

Â You just have to define that voltage and apply KVL the standard way.

Â To summarize, in this lesson we've gone over some key concepts.

Â The first is the Kirchhoff's Voltage Law,

Â which is some of the voltages around any loop is zero.

Â Remember, we can have multiple loops in any given circuit.

Â 9:00

Special cases to remember, parallel components have the same voltage, and

Â we looked at this example here.

Â And note again, that a current source does not have zero voltage.

Â And that you can see right here.

Â This particular current source has this voltage drop across it.

Â