hello and welcome to another lesson which we will talk about notes and loops so the objective here or objectives are nodes and loops those are the two items that we will talk about in this lesson so what's a node basically a node is a connection of two or more circuit elements so what is circuit elements i'll talk about circuit elements resistors power supplies like voltage supply current supply and of course later on we will see that we we will deal with capacitors and inductors so let's look at an example of showing how we can determine the number of nodes in a circuit so we have this circuit with power supply v resistor r1 r2 and then another resistor in parallel like that that's r3 so the question here is we want to determine how many nodes does the circuit have so if we look here we will of course one mistake usually students will do is they consider a wire like this as a node so like here the between r1 and r3 they might say there is a node here well why this is just a wire it's not an element a wire is not considered a circuit element so so a wire is not considered a circuit element hmm and as i said circuit elements are resistors power supplies whether it is voltage or current supply also like we said we will learn later about capacitors inductors and so forth there's other elements like um diodes transistors and things but they're not going to be covered in in this course so in this course you will only be covering resistors um capacities of course [Music] capacitors inductors and so forth these are the only ones so here let's look at this go back and look at the circuit so it's a connection a node is a connection of two or more circuit elements so here the power supply is a circuit element resistor is a circuit element so then this here will be considered as a node in this point here now again you cannot say there's a one here in the middle in the middle there because this is just the wire so that the element is r1 and just like you consider like you can cut this wire and just make it you can make the connection at this point instead so a wire is not a circuit element and hence it cannot be used as a node so there is one note here between the voltage and r1 now if we look that we have r2 and r1 so this is a point where they connect together and we see that also r3 is connected to this one so again do not make that mistake of thinking at this because just the way it's drawn here as uh like an uh straight i mean uh right angle that you will think oh this is just another note no again this is a wire and it cannot be considered as a node otherwise you will be considering this wire and this resistor the wire is not a circuit element okay so that's there is that one there what else we have we have another connecting elements we have r2 with the power supply so we can say at this point they meet and so forth this is where they both of them meet and also we see that r3 also connecting at this point a lot of times we will um kind of like when we uh draw notes like that so just like we put a dot like this between the two a dot like that between other resistors and then this is the bottom one this is connects the negative part of the power supply with the resistors r2 and r3 this is most of the time we would consider this as the reference element so this whole point where i draw the circle this whole point is just one this whole thing is just one point one node and this is like a lot of times we would consider this like the reference node or sometimes we'll just call it like the ground node so that's that's where all the resistors are grounded well not all of them in this case the the way in the circuit on the r2 r3 what the power supply are uh grounded are one as not it's connected to r2 and hence it is not uh with that so so this circuit of course we can redraw the circuit as having a easier way so here are how many notes we have we have uh three notes so then we have all right so that's if we want to redraw the circuit we can withdraw the circuit just maybe to drive the point and show as the following so we have the first circuit element the power supply that's v then we have r1 then we have r2 and then we have here like that r3 so this is r2 and this is our three so you can see now this is the junction in which they the three meets r1 r2 and r3 so basically a node is a junction bit point between two circuit elements and that's what they are so don't worry about and of course i could have actually withdrawn the bottom one let me see just to show r1 and r2 or 3 just like that just to show that this is also the reference uh what we usually consider as a reference this is also like a one this is one note here one note here one note here so that's how we can actually uh draw the circuit okay um like that okay so just to draw but why we don't use this circuit or this one here it just because we want to do analysis we want to try try to draw it like we had in the first place here so if we want to make any notations for current for voltage then we have enough room otherwise and this this one here we don't have enough room on hands that's why we don't uh why that's why we don't do that all right so let's do an example another example on that so another example we want to also find how many nodes so we have this circuit with this resistor like that another resistor like this connect it and call this vx this is r1 r2 and then we're connecting these two resistors like that so this is r3 and r4 so this is like v this is could be any anything could be k let's say vx something like that and so then the question is how am again how many nodes oh that's the circuit have how many nodes well same thing here we have to look at the way when we have from the definition two circuit elements together two or more if they are connected at a junction then they are considered as connected uh having one node so in this one here we see that r3 and the voltage source they connect here and this point here is really the same point as this one why because this is just a wire so again we i could have just redrawn this to be at this point here and and then instead of being at that point so really this whole thing here is one point so it's just the same just like this is how it is connected so this we have here one node okay so this is one not here then we have another two circuit elements r1 and r2 and they're connected at this point and also actually they are connected with r4 so there's r our r1 r2 and rs4 are connected at uh this point so this is the junction in which they the three circuit elements they meet so that's two here of course then we have the reference one and again this is good the whole these this is just wires all of them are coming to the same point so this is just one junction in which the three the negative of the power supply with the negative of the current supply and the resistor two are connected together and they form what we call like we said the reference node and most of the time like i said we consider this as the ground node what else we have we look of course this is here coming r3 and then we have r3 and r4 so these are two circuit elements so they are connected somewhere here so that's another junction so we see here that we actually have um four uh no it's one two three four [Music] now of course uh most of the software's now that we have if it's a full version it will um cover any number of nodes so you could have 100 nodes and and it will cover them it will simulate but free versions a lot of times depending on that uh software the company that is making it free they they put a limit so maybe 10 notes 15 notes whatever that company or whoever's putting it out as a free or the free version of it could be limited to a number of notes 10 15 20 whatever that number but for our purposes really the number of notes that we will be using is going to be way much less than the number of notes we are allowed to simulate for the free version or we can use the simulate for the free version so we don't you don't have to worry about that for the purpose of this course the number of nodes are going to be much less so there is no issue here okay so this is about nodes let's go to the next one which is the loops loops by definition it's a closed path containing two or more circuit elements so so it's just like a path that starts at one point it can cover at least it should cover two elements and of course most of the time it will cover more than two elements so an example will be would be um let's look at this circuit here we have the power supply v we have a resistor another one and then we have another one like that so this is r1 r2 and r3 so then from the definition of loops it's a closed path containing two or more circuit elements so if you want to define that loop we will start at any point anywhere we want to end the circuit and then we'll go in a closed path so here let's say if we start here so this is where we start in this path and until we get to this point this is the end of that pass so this is like the closed path where we get to that point so this is a closed path that we have here so that's one loop so you can see it's a closed bath containing in this case containing three elements so we could say this is like lube one another one week after we can see here in this we have two circuit elements and again wherever we start we can start from this point and again so you will see that this is another closed loop so we can say loop two of course there is another one a lot of times we don't use but sometimes it could be beneficial for some circuit analysis in which we want to maybe we have elements we can find easily if we draw the third loop which is what we call the outer loop most of the time so if we start from here and then this loop will continue in this fashion and then until it closes up back here so that's another loop we call that outer loop loop three so that's the three loops that we have um a lot of times we of course don't draw it like this we will just use the arrows to do that so if i want to redraw this circuit i can draw it as like this r1 r2 r3 and this is the voltage source so a lot of times we will just say this is the we'll just go like this of course if you start drawing the loops for our circuit analysis we will see either we draw them and like a clockwise or counter clockwise so we'd like to keep it for our convenience easier to keep it that way going so this is like loop one this is loop two and then uh and here this is like this that will be loop um three so we will usually use the arrows like that to say that this is the direction of these two so that will give the arrow here just to say we're going clockwise of course we can withdraw going counterclockwise it's preferable that we do all of them either clockwise or counter-clockwise you know don't mix and match you might get into kind of like confusion so so that's that's all for this uh lesson on the next lesson we uh it will talk about how uh to use nodes and loops in and for circuit analysis okay thank you for listening and take care