 Finally, that you are able to see me and hear me, this course is entitled basic electrical circuits, welcome to the course I am Mahgen Rakhishanapura from the department of electrical engineering at IIT Madras. What we will do in this course is to learn about ways of analyzing circuits, ok. So, it is not about any particular circuit or any particular gadget, but a general technique for analyzing any circuits which you can expand to any new circuit that you may come across, ok. As I mentioned earlier, please feel free to interrupt the lecture by raising your hand and I will also try to be systematic and give you time, let us say every few minutes every 10 minutes or so, so that we can have fuller doubts here, ok. Here is a presentation that sort of outlines what we will be seeing in this course, ok. In fact, it turns out that in this semester, I am also teaching a course at IIT Madras entitled Electrical and Magnetic Circuits. What I will be talking about in this online course will be only the electrical circuits part of it, ok. Now, what are electrical circuits? Electrical circuits are interconnections of electrical components and basically they every electronic or electrical gadget that you see forms an electrical circuit, ok. And magnetic circuits just as a point of information are interconnections of magnetic components and I think all of you would be familiar with transformers and motors, they form magnetic circuits. In this online course, our focus will be on electrical circuits and they are absolutely everywhere around us, you will be able to see electrical circuits we are probably using so many electrical circuits in your day to day life, ok. So, just as an example, the laptop on which I am making this presentation, your mobile phone, music player, the headphones that I am wearing, all of these things form electrical circuits, ok. In this picture, you can see an example of mobile phone which is opened up and it has a number of complicated circuits inside. You build up the circuits hierarchically from simple elements to more complex circuits and they are put together to make a bigger circuit and so on. So, finally, you end up with a very large circuit, ok. As I was saying, a mobile phone is a circuit as you see a music player and so on. And here I have shown a very large, physically very large circuit on the left side. It is a transformer that is used to bring power to your homes and that is also a transformer. And on the right side is another transformer. The one on the left side is probably has a bigger, even bigger than this room in which I am sitting. And one on the right side is a couple of millimeters, they are both transformers, ok. The main point I want to drive home is that circuits themselves come in all shapes and sizes, but there are some methods of analysis that are applicable to all circuits and that is what we will be discussing in this course. So, as I said, this course is about analysis techniques applicable to all circuits and it is not about any particular circuit and it turns out that if you look at electrical engineering curriculum in any university, this turns out to be one of the most important courses, ok. Mainly because it lays a foundation for a number of courses that you will encounter in your electrical engineering curriculum such as networks and systems where you will analyze circuits using more advanced techniques such as Laplace transforms. And some of you may want to do courses in analog circuits. The things that you learn in this course, the methods of circuit analysis are absolutely essential for that course. And also some of you may be studying in detail electrical machines. Again the analysis methods learned in this course will be useful for that. And it turns out that also if you want to get a job in electrical engineering and a lot of electrical engineering companies the interviews will start with some basic electrical circuit questions, ok. So, it is by and large a very useful course for your further studies as well as your career and so on, ok. Now, what are the topics that we will go through? First we will have a discussion on electrical quantities and elements. Some of you would be already familiar with this, ok. I think all of you will have some notion of what a voltage is, what a current is, what a resistor is and so on. And also you would have studied both in high school and later some basics of electrostatics and electromagnetics, ok. And the things that we deal with voltages and currents are related to what we study in electromagnetics such as fields and charges, ok. But we will not deal with, we will not go down to the level of fields and charges but we will stay with voltages and currents. So, in the initial part of this course I will also tell you how these things are related to each other, ok. Then after we discuss electrical quantities and elements we will see how to analyze circuits. Again at some level for very simple circuits you would be familiar with this. But we will see how to scale it up for large circuits which could be arbitrarily large, ok. Now it turns out that there are also certain theorems, certain general theorems about circuits which are very useful in analyzing circuits in representing circuits and so on. We will discuss those things. Then we will talk about what are known as 1 and 2 port networks. It will be very clear what I mean later, ok. One port means you have one set of terminals where you can apply voltage or apply current. Two ports means there are two such ways of terminals where you can do the same and so on, ok. And there are ways of transforming between multiple ways of representing these circuits we will also study those things, ok. Now one of the other interesting things that we will study is the op amp not in great detail but as an ideal op amp it forms a basic network element. And from that you can make a number of interesting circuits. In fact some of you who may have had building circuits as a hobby would have already done this, would have already used op amps. What we will do in this course is to lay a proper foundation for that and then if you want to design new op amp circuits how to go about doing that and how to analyze complicated op amp circuits those things we will deal with, ok. Now it turns out that essentially circuit analysis consists of you look at the circuit based on the circuit you come up with the number of equations and then you solve the equations, ok. Now if your circuit has only resistors then you will end up with a set of algebraic equations and you have to solve that I think you already know how to do that. It turns out that you can also make interesting circuits when you have capacitors and inductors. In those cases you will end up with what are known as differential equations and some of you may know how to solve it. What we will do is go through the treatment of differential equations the particular kind of differential equations that is constant coefficient linear differential equations that we will use in this course we will deal with that in some detail so that you are familiar with the kind of solutions that can be present, ok. Now finally we will look at polyphase circuits at least some of you would be familiar with 3 phase power transmission and so on. So we will look at some of those things and see why those things are important and see how to analyze those circuits, ok. Now in those online version of the course we will not be dealing with magnetic circuits but you can look at other resources to get some knowledge about those things, ok. Now as far as the goals of this course are concerned it is very simple you learn circuit analysis and learn how to do it well, ok. And the way to do it well is to practice, practice and practice problem solving. Now you practice problem solving for many different reasons sometimes you do it for competitive exams where you solve the same kind of problem many times so the next time the same type of problem comes up you do not have to think about it. Now here it is a little different, ok. The reason for practicing solving a lot of problems is to be confident enough of solving any other problem it may be of the same type, it may be of a slightly modified type or even a completely different type, ok. Any problem that you have to solve you have to be able to approach it with confidence and then solve it. So that is why you have to solve the number of different types of problems, ok. And also more importantly when you solve any problem you have to understand every step of problem solving, ok. It is not a test of speed but you have to know why you are doing what you are doing. So whenever you solve any problem please make it a habit to understand every step and then move on to the next step, ok. And the sort of secondary goal is to learn about linearity. What I mean by this will become clear but a large number of circuits that we will analyze will turn out to be linear. What it means is that you apply certain stimulus you will get some response, you apply another stimulus you will get a different response and you combine the two stimuli the response turns out to be the combination of the original responses, ok. Now this simplifies analysis of grade D it turns out that you do not have to analyze the same circuit many times. You analyze it for one set of inputs you will know the answer for many other types of inputs, ok. In fact any other set of inputs. So you have to become comfortable with this the implications of linearity how to recognize linearity and exploit it while analyzing circuits, ok. Now here are some resources that you can use first of all as I think was already mentioned to you these lectures these online sessions will be recorded and they will be made available to you. In addition to that you can make note of a URL that I will give you. In our group we record our lectures and you can view those lectures and one of the courses that we have taught is this electrical and magnetic circuits which are some overlap with the course that I am teaching now but is at a quicker pace. So you can view those lectures. You of course are familiar with NPTEL I think that is how you came to this course so NPTEL lectures are also very useful on specific topics. And the VLSI group home for IIT Madras this is also something that you can use to further your knowledge of circuits, ok. So with that background perhaps we can get started. I am going to share the journal now, ok. I mentioned some resources. I am going to write down the URLs here. This has recorded lectures on various circuits related courses and we can also see, ok. And finally of course all of you know about NPTEL, ok. So with that background we can get started with our course. Electrical circuits are interconnections of electrical components and they manipulate voltages and currents in some weight, ok. Now I think all of you have heard of voltages and currents. I would like some responses from the participants. What is the voltage? Perhaps we can type it into the chat window. Ok, I have got a number of responses here. I have got a number of responses and basically they kind of fall into two classes. You say that either the voltage is a potential difference or it is related to some force that causes current or that causes electrons to flow, ok. Now both of these are of course quite correct and I will elaborate on these things. And similarly I would like some responses on what is the current? What is an electrical current? Ok, again I have got a number of responses which say that a current is basically flow of charges, ok. And some of you say electrons which is quite correct of course, ok. And some of you also said that it is the rate of change of charges or rate of flow of charges and these things are quite correct, ok. And in the definition for the voltage some of you also related it to the electric field which is quite correct as well, ok. Now I think all of you know that all of you have at least heard of Maxwell's equations. So it relates electric fields and magnetic fields and charges, ok. So you have charges that can create electric fields and charges can move under the influence of electric field they can move under the influence of a magnetic field and so on, ok. Now of course those are the basic equations which govern everything in electromagnetics including our circuits, ok. If you also recall from electromagnetics usually it is quite difficult to solve the problems usually you end up having to do a lot of mathematics. But in circuit things are a lot simpler the reason I will explain shortly, ok. We are also dealing with electric fields and magnetic fields and flow of charges under the influence of either the electric field or the magnetic field. But there are some conditions that make our life a lot simpler we can do things lot more easily. And our primary variables will be voltages and currents and these will be related to the fields, ok. But what we usually deal with are not the electric field or the magnetic field but voltages and currents, ok. Now first let me take an electric current and electric current usually denoted by I is the rate of flow of charge across some surface, ok. So you could have some surface I am showing some pipe like thing and you could have charges flowing this way and the rate of change of charge across the surface is the electric current through the surface, ok. Alright couple of things I think all of you know that it is electrons that do the flowing it is the electrons that flow and electrons are negative charge. So what we are looking at what is defined as the electric current is the flow of positive charges, ok. It is really the negative of the flow of electrons. Now as far as we are concerned it is perfectly alright to think of positive charges are flowing although it is electrons that are flowing and the direction of flow of positive charges will be exactly opposite to the direction of flow of electrons which are really the things that are flowing, ok. It is ok for our purposes to think of currents as rate of flow of positive charges through some surface, ok. And also generally a very useful analogy for electric current is fluid flow, ok. So instead of charges that are flowing you can think of fluids that are flowing in pipes and so on and for a number of cases which involve general rules about currents this fluid flow analogy works quite well, ok. Now in our particular case we will not be looking at charges flowing in arbitrary surfaces we will be looking at currents that are confined to a wire and a wire is a very good conductor in fact we will think of them as ideal conductors which offer no resistance at all to the flow of current. So we will be looking at currents that are confined to wires. Now this is one of the aspects that make our analysis quite simple, ok. If you have charges in fields somewhere it is not very easy to calculate the effect of fields on charges exactly how they move and so on but we will be looking only at electric currents in a wire or through some elements. So our job is a lot simpler, ok. So you may have some wire like that and you could have a current flowing from A to B, ok. Now as I said many times this really consists of electrons flowing from B to A but we can think of it as positive charges flowing from A to B, ok if the current is in this direction, ok. And we also do not worry about exactly how the charges are distributed across the surface of the wire we will be only concerned with the total current flowing through the wire, ok. And I think many of you know this already the electric current has units of ampere, ok and this corresponds to carrying a charge of one coulomb in one second, ok. So if one coulomb of positive charge flows from A to B in one second that constitutes a current of one ampere from A to B, ok. So here I have shown a wire from A to B and I draw an arrow from A towards B and I mark one ampere and that is what this means, ok. One coulomb of positive charge flowing this way. Now I could also show the exact same situation What is the chat deletion you think it is good about that? Yeah, but I did not get anything exposed here. Over here on full screen, ok. No, I mean I was saying other things. Yeah, it is ok, ok. So I believe things were interrupted for a little while what I was saying was that a current of one ampere means that a charge of one coulomb is carried over the duration of I mean a charge of one coulomb is carried in one second, ok. Now when I have a wire from A to B as I have shown here, ok and mark an arrow from A towards B and write one ampere that means that a positive charge of one coulomb has gone from A to B in one second, ok. Now the exact same situation can be depicted by having a wire with an arrow drawn from B towards A and with minus one ampere marked on it, ok. Now this is something that you have to get comfortable with you can depict the current, the same current as positive one ampere going from this side to that side or negative one ampere going from that side to this side. The reason this is important, this looks rather trivial the reason this is important is that when you solve for circuits when you start solving circuit you do not know which way the currents are, ok. You have to assign some variables I and mark the directions of currents and I could come out either positive or negative and in later cases we will see that it could even be time varying, ok. Now for you to interpret these results correctly you should become very familiar with the convention, ok. What I want to emphasize is that just because I have drawn an arrow from B to A does not mean that current is actually flowing in that direction it could be the negative applied also, ok. Value could be come out either, value could come out either positive or negative, ok. So that is about currents. So any questions, anything that is confusing about the definition of currents and the convention of the sign we will be talking about currents through wires, ok. Ok, there were a few questions. First one was what is a coulomb, ok. Coulomb is the unit of charge, ok. You perhaps know that electron has a charge of minus 1.6 times 10 to the minus 19 coulombs, ok. So roughly speaking you need 10 billion billion electrons to be flowing to have 1 ampere of current in 1 second, ok. You should have 10 billion billion electrons flowing in 1 second to have 1 ampere of current. So that is the unit of charge. Now there was another question which was about the current flows only on the surface of the conductor or not. Now we will not worry about that, ok. Now it turns out that at low frequencies current flows uniformly through the surface of the wire and as you go to higher frequencies it tends to go towards the surface uniformly through the cross section of the wire at low frequencies. And as you go to higher frequencies it will be only towards the surface of the wire. But for us those leaders are not important at all we will be looking at the total current flowing through the wire, ok. And there was another question on the flow of current through coils. Now whether it is a coil or not current will flow through the wire, ok. As you are probably asking about what happens due to that current there will be magnetic fields but we will not be talking about it at this juncture, ok. And someone else asked whether any random movement of electrons becomes a current, yes it does, ok. In fact electrons are moving randomly all the time and there is a big field of study on noise which is the electric current due to random movement of electrons, ok. As long as the temperature is above absolute 0 this will keep happening. Now there was another question on the positive charge why we take it that way. So this is something historical. I think historically people did experiments with electric currents on all kinds of things when it was not known that electrons are the, electrons are what? Carry current, ok. So they just decided the direction of current as the direction of flow of positive charges and it should also be noted that in certain chemical experiments it could be some positively charged ions that are actually flowing, ok. When we have wires it is only negatively charged electrons that are flowing but that is not the case in every situation. So it is some arbitrary thing and that is the historical convention and we will stick to that, ok. There are also questions on AC and DC and so on. So those things we will not worry about, ok. That is just has to do with how the current changes over time, ok. So that is not something fundamental and so that is about those things. And also for us all conductors are perfect, ok. So the conductor itself will not have any influence on the current, ok. So this is an idealization and many of the wires that we use which are made of copper come fairly close to this ideal level, ok. So again we will not worry about the effect of wires at this point, ok. Now let us now let us move on to the other electrical quantity which is the voltage or potential difference, ok. Now what is this? I think again an analogy could be made with gravitational field, ok. You know that if you have gravitational field, this is the, I am showing only a small area so I am showing it as flat and you know that there is gravitational field in this direction, ok. Now if I place a mass M in a gravitational field what will it do? Obviously it will fall in some way towards the earth, ok. In fact the gravitational field could be due to any body and it will always fall from a higher gravitational potential to a lower gravitational potential and let us say this was at a height h2 above earth and the other one was at a height h1 above earth. When it falls from h1 to h2 it gains a potential energy which is mg times h1 minus h2, ok. So it falls from a higher potential to a lower potential and while doing so it gains potential energy, ok. Now similarly if you have an electric field which is usually denoted by that and then you place a charge q it will, this is of course a positive charge q it will fall. I mean here I use the word fall not in the gravitational field but in the electrical field, ok. So it will go from there to there, ok. It will tend to go and if it does that it will also gain a potential energy which is q times let us say the potential this electric potential is denoted by v and if this is v1 v2 it will be v1 minus v2, ok. You see that the gravitational potential energy that is gained is proportional to the mass, ok and the electrical potential energy that is gained will be proportional to the charge. So we leave out this if this charge and mass are property of the body that is falling and the rest of it is the property of the field, ok and that is the potential difference, ok. So the amount of energy gained is equal to the amount of charge times the potential difference between here and there and that is v1 minus v2, ok. Similarly here in the gravitational case the amount of potential energy gained is the mass of the body that is falling times the potential here minus the potential there which is g times h1 minus h2. So what I want to emphasize here is that the potential makes sense only when measured as a difference of values between two points, ok. It is v1 minus v2. If you just say potential at this point is something that is not a very significant thing, ok. So you always have to measure this voltage or potential difference between two points and this is true of circuits as well, ok. Now as usual we are not looking at arbitrary fields that are distributed in space and charges falling in this. They are only looking at electrons moving in wires or charges moving in wires and the fields will be inside the wires, ok. So the potential difference the electrical potential difference is very much like the gravitational potential difference. The gravitational potential difference acts on the mass and the mass that falls in the gravitational field will gain some potential energy. Similarly an electric field electric charge that falls in an electric field will gain some potential energy, ok. So when we are talking about circuits we will not worry about potential energy or electric field we will talk only about the potential difference, ok. Ok it looks like the connection has been broken for some people or the quality has been questionable. So what I will do is I will just pause the camera to conserve the bandwidth and hopefully things will be better. You can give me feedback on whether it is indeed better, ok. What I was saying here is that I was trying to make an analogy between voltages or potential differences Oh yeah Video is off No that is what I mean people said Ok. So the video is off now by the way. What I was saying here was that I was trying to make an analogy between electrical potentials and gravitational potentials that you are familiar with. Here on the left side I have shown the earth and the gravitational field pointing downwards and if you place a mass somewhere it will fall down in the direction of the gravitational field and it will gain potential energy. It will always fall from a region of high potential to a region of low potential. Let us say it falls from a height h1 to a height h2. It gains a potential energy which is m times g gravitational acceleration times h1 minus h2. Analogously in an electric field shown on the right side electric field pointing downwards if you place a charge q somewhere it will fall that is it will move in the direction of the electric field and let us say it falls from one point where I have marked the potential of v1 to another point where I have marked the potential of v2 it gains a potential energy which is q times v1 minus v2 ok. So the amount of potential energy gained is proportional to the charge and it is charge times the potential difference just like the amount of gravitational potential energy gained is mass times some difference and it is the difference between some quantity at the initial point and some quantity at the final point. So what I want to emphasize here is that the voltage or potential difference makes sense only when measured as difference between value set two different points ok. There is not much significance to saying that the potential at particular point is one volt without saying with respect to what that potential is ok or in other words you have to say that the potential difference between point A and point B is something. This is something you have to do in circuits as well as the voltage is always measured between two points ok. So in fact while you are discussing it among yourselves or thinking about it you should always think of two points between which the voltage is measured. Lot of confusion about voltage comes about because you forget that it is measured between two points ok. So any questions about voltage any questions about voltage ok. There are a number of questions one was related to electromotive force and voltage ok. These are basically different terms for the same thing. Electromotive force is a somewhat old term and we use the term voltage now and somebody asked what happens if the field is in opposite direction or if the charge is negative. Now if the field is in opposite direction it will cause a potential in some different way ok. Now as we said as I said earlier we will not worry about fields we will only work with potentials and if the charge is negative whatever happens to the positive charge exactly the opposite will happen to the negative charge. A positive charge falls from higher to lower potential and a negative charge falls from lower to higher potential ok. Now one of the other questions is I said that the potential energy gained is Q times V1 minus V2 so how do we know V1 ok. Now when you talk about potentials in a field you will measure V1 with respect to infinity but it does not matter what it is measured with respect to ok. So if V1 and V2 change by the same amount it does not matter to anything ok. So it is only with the value of V1 minus V2 that matters. Now this will become more clear when we go on to discuss particular elements because we will only be discussing voltage differences across the elements ok. Now there are also number of other questions on interaction between charges and fields that we will not worry about and we do not have to ok. Our goal here is to do circuit analysis. So we can analyze circuits by staying at the level of voltages and currents without going into the fields ok. Now there are some laws that govern voltages and currents in a circuit ok. Now as I said I have not even put on what circuit it is. These are very general laws that apply to any circuit ok. This is you can think of them as basic properties of voltages and currents ok. Now one of these that talks about currents says that if you have a number of branches number of wires connected to a single point such a point is known as a node ok. And these do not have to be just wires there could be some elements right now we will not worry about what they are ok. Now what this says is that if you measure currents flowing out of the node ok. I will choose to measure the current in this direction. I call this I1, I2, I3, I4. So there is a law that says I1 plus I2 plus I3 plus I4 equals 0 ok. Now this has nothing to do with any particular circuit but this is true for any circuit ok. And this I think many of you already would know this is known as k-cops current law ok. So briefly could you tell me the conditions under which this is true is this always true under any circumstances or are there some conditions ok. There are a number of responses I have broadly grouped them into always true and for linear elements circuits and somebody said something about no resistance in the wires and then somebody else said charge conservation or no charge accumulation and so on ok. Now it turns out that of course this is not correct if I mean that is the reason I ask the question. Now this is a kind of funny answer because I have not even put down what circuit it is right I already said that these are critical properties of currents it has absolutely nothing to do with what circuits we apply it to ok. So this is something also important for a different reason I think whoever answered these things are mixing up some different concepts linearity refers to voltage current relationships or different elements. Now the k-cops current law that I am discussing here has nothing to do with what circuit it is ok it is generally true of all circuits or with some conditions as we see and again this also is something similar it has no resistance in the wires again it has absolutely nothing to do with that because you could have wires and you could have elements connected to it which could be resistance ok. Because if you said no resistance at all then such a law or such a theorem would not be very useful ok because it has to be useful for real circuits. Now finally we come to the main point which is that it is charge is conserved that is charge is neither created nor destroyed and more importantly it is not just this that is important there is no local charge accumulation ok that is you have current flowing out of it now if the sum is more than 0 that means that this charge was depleting from this point and if the sum is less than 0 charge is getting accumulated at this point ok neither of it is true so charge is conserved of course and also charge is not accumulated locally in any point ok so this is the reason why this is the assumption under which Kirchhoff's current law is true in fact there are conditions where it is not true if there is time we can discuss those things later but now for a large number of circuits this is true and we can use Kirchhoff's current law safely ok so that is true again as I mentioned earlier very useful analogy for thinking about currents is fluid flow ok so if you have a pipe here and then it branches off into two pipes it is very obvious I mean even without analyzing to most of you intuitively obvious that if there is water flowing here and then it will branch off into two and let us say here at a rate of 10 liters per minute now whatever the rates here are I mean this pipe could be big and this could be small and all of that so this is flowing at some rate R1 and this is flowing at some rate R2 you know that R1 plus R2 equals 10 liters per minute ok or if I have to use the convention and for currents I took all the flow to be away from the node so I can also take R1 liters per minute flowing that way R2 liters per minute flowing this way and this way it is minus 10 liters per minute ok it is a slightly weird way of saying it but a useful way when you talk about currents I initially assume that the flow is that way but it turns out that the flow is from left to right so that means from right to left minus 10 liters per minute are flowing ok so minus 10 plus R1 plus R2 will be 0 ok this is something that you intuitively feel is through ok even without knowing a great deal of flow dynamics and so on ok and why does this happen if this was not the case water would be accumulating here or water would be drawn out of here ok if we had a tank here into which water is accumulating this could not this need not be true ok for instance I could have water and then flowing into a tank and then nothing coming out of it whatever is coming here is going into the tank this is analogous to charge accumulation and we assume that such a thing is not happening as long as that is not happening this Kirchhoff's current law is true some of all the current flowing out of a node or equivalently some of all currents flowing into a node will be 0 ok a very useful thing and in fact a necessary thing to solve for circuits similarly there is something that governs voltages in general ok so let us say you have an electrical circuit electrical circuit means that there is some loop of electrical components now we have not even discussed any element but I will take some 2 terminal elements 1, 2, 3 4 and 5 ok and I will measure the voltage across each one like I said voltage is potential difference between 2 points so here I will measure v1 in this direction and here I will measure v2 in this direction please mind the directions in which I am writing this v3 here v4 you see that I am taking all the differences in the same direction and v5 ok again this has nothing to do with the specifics of the circuit and there is a law that says that v1 plus v2 plus v3 plus v4 plus v5 equals 0 and this is known as dead corpse so it appears that the audio was broken what I was talking about was the sum of voltages around the loop being 0 so here I have shown it for this particular circuit v1 plus v2 plus v3 plus v4 plus v5 equals 0 that is sum of voltages around this closed loop is 0 so all the voltages being defined with a consistent polarity you see that they are all in the same direction around the loop and this is known as kickoff voltage law the response I would like from participants is to tell me the conditions under which this is true again I have got a number of responses ok now some of you said that it is true in a closed loop yes of course it is only the closed loop that I am discussing I have written a loop and as I have written on the side sum of voltages around a closed loop equals 0 so my question is is that violated in some condition ok now it turns out that it can be violated if there is significant time varying magnetic field cutting this loop ok so this loop has certain area so this loop can enclose certain time varying magnetic fields if there are time varying magnetic fields in the cutting the loop then the sum of voltages does not have to be 0 ok so again all the practical situations or most of the practical situations that we encounter the time varying magnetic fields cutting this loop will be small enough cutting our loops will be small enough that we can take the sum of voltages to be exactly 0 ok ok so again this turns out to be true in a practice in a lot of cases so we can use the kickoff voltage law also safely ok now there are some people asking questions on what happens if voltages are induced from other loops that is exactly what I am saying that if there are time varying magnetic fields there will be the sum of these things will not be 0 it will be related to the rate of change of magnetic field and the area of the loop so we will not consider those conditions we will only consider the condition where the flux is 0 that is time varying flux cutting time varying magnetic field cutting the loop is 0 ok so we have these two basic laws and kickoff's voltage law and kickoff's current law one relates to voltages in a loop and one relates to currents in a loop and one of the very important things while applying this is to apply it with a consistent polarity ok so here I will show a loop the loop will have some elements but I will not worry about those or maybe I will show it with elements so that there is no confusion so if you look at this what I have done is to go this way ok if I go in a clockwise loop I always have minus first and plus next and so on ok in the direction in this direction ok as long as there is going in the in this direction and then I sum all the voltages it becomes 0 similarly for kickoff's current law at a node the sum of all currents flowing out of a node is 0 so I suggest that right from the beginning you adopt a consistent polarity because if you make a mistake with the polarity of these things obviously you will get the wrong answer ok now one thing I have to mention about what it is I did this for currents that is I told you that a current 1 ampere flowing from a to b is exactly the same as a current of minus 1 ampere flowing that way and similarly if you have 2 points let's say x and y and having a 1 volt difference in this direction is exactly the same as x and y and I will measure with respect to x the voltage in this direction being minus 1 volt so this is just so that you are comfortable with the sign convention so again for instance I could have some 2 points and I will write v1 this way this does not necessarily mean that this is at a higher potential than that it says that it is higher by v1 and v1 itself could be positive or negative ok so I think in today's lecture we have discussed a number of things basically definitions of voltage and currents and the laws governing them ok and we will continue from here in the next lecture there are a couple of more questions some of them are related to frequency of the voltage and so on I will not discuss those things here as they are not really relevant ok because even if let's say v1, v2, v3, v4 or time varying because voltage law says that at every instant of time the sum of those things has to be 0 ok similarly for the currents now the sum of currents i1, i2, i3, i4 is 0 for this particular example here ok now this is true even if those currents are time varying they could in general be time varying and every instant of time the sum has to be 0 ok so that is the meaning of current law now there is one very interesting question which is what are the circuits that do not know whether it is voltage law or current law ok are there common examples now it turns out that there are there is also so there is one very common example which is basically if the dimensions of your circuit are very large now by very large what do I mean very large compared to the wavelength of the signal then these things do not hold good ok we can perhaps elaborate on this later what I mean by that is let us say I have a really long wire ok and again I will think of positive charges flowing this way now always we think of charges flowing instantaneously but we know that it moves at the speed of light ok at least it is limited to the speed of light it can only move slower than that now let us say that you drive a current and you reverse the direction before the current can get from here to there ok because there is always some length to the wire and then it takes some time to get from here to there and before that if you reverse the direction of the current so let us say you are driving a current from one side you have to worry about how to do it before it gets from here to there the charge gets from here to there you reverse it then you look at different parts of the wire they will be carrying different currents ok and a very common example of this is the antenna I think all of you are familiar with antennas which are just single wire it could be sticking out of your radio or your car it is just sticking out and you will drive a current into it it looks like it is just hanging in the air so clearly Kirchhoff's current law is not valid here what really happens is that the length of the antenna is comparable to the wavelength that is before the current reaches from one end of the antenna to the other the direction of the current driving it changes and then so you have a consistent situation without Kirchhoff's current law being violated ok we will only be talking about those situations where the dimension of those circuits are much smaller than the electrical wavelength of the signals that are driving it so in our cases Kirchhoff's current law will be valid and similarly for Kirchhoff's voltage law so in general these things can be violated if you have a very large circuit and large relation to the electrical wavelength or in general if you increase the frequencies of the signals ok any questions ok so there are so there are some general questions which we will deal with later so in the next lecture what we will do is take some electrical circuit elements which are commonly used discuss their relationship between voltages and currents what we did today was to see general properties of voltages and currents and their definitions ok so in the next lecture we will look at some elements and then make some simple circuits out of them thank you everyone's posted it will have a definition forum where we can ask questions that will be moderated ok and there is an announcement also the online courses website with the recorded lectures and it will have a forum for you to post questions where I can post answers or perhaps others can also do that and so on ok and it will also have the syllabus and assignments and all of those things ok so please consult the online forum so and this class this lecture there were some glitches I think from the next lecture onwards things will be a lot smoother thank you