If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:9:01

Video transcript

in this video we'll attach a resistor to our ac generator and see what's the relationship between the current in the circuit and the voltage of the generator now just to quickly recap we've or we've seen the voltage equation before the generator equation can be written as voltage at any point in time we call this the instantaneous voltage and s stands for source i'm writing this as a source voltage can be written as equal to some value v naught times sine omega t v naught represents the maximum value of the voltage because the voltage is continuously fluctuating and this function tells you how the voltage is fluctuating and again just to quickly briefly recap whatever we have seen we've drawn a graph before it's a sine graph because you have a sine function over here and what is the graph saying the graph is saying that the voltage fluctuates between some positive maximum and some negative maximum and these values are our plus v naught and minus v naught and i always had a hard time understanding what this graph even meant i thought it was a wave like water but it's not a wave it's an oscillation and to you know to really visualize that you have to think about think about it this way this is the time axis right so this represents current present and this represents the future and so if you have to imagine what's happening over here you can imagine moving the time axis forward so you move the time axis forward and see what happens to the value see voltage is increasing increasing increasing reaching the maximum value and then decreases decreases decreases let me show you in a better way i will dim everything except for this and now let's see what happens all right as i move forward you can clearly see how the voltage is increasing you see that voltage increases increases reaches positive maximum decreases decreases negative maximum and so on and so forth now i want to make sure that you visualize visualize it perfectly and so what i'll do is i'll show you an animation instead of moving the time access forward i can just move the graph backward right and and see what happens over here it's the same thing right so let me show you an animation of doing that so here we go let's look at that i'm going to dim everything and you can see voltage going up and down can you see that and we can draw an arrow mark now that represents this oscillation and that the length of this arrow mark represents vs the instantaneous value and so right now it's some negative value goes to negative positive maximum 0 negative maximum positive v naught 0 negative v naught this is how you imagine how it's oscillating and how quickly it oscillates so let me get rid of this now and so the number of oscillations per second depend upon this number omega omega gives you the radians per second and at first i used to always wonder what do you mean by radians where is the angle over here it's oscillations right well the way to think about it is you can imagine one full oscillation corresponds to two pi variants we imagine it to be like a full circle we'll talk more about that in the future and so it's quite it's called a phase angle because not real angle okay but anyways let's not worry too much about that um so one full oscillation equals two pi radians so if we had say 10 oscillations per second as an example then that would equal 2 pi times 10 radians per second okay these are all the recap that i'm doing we just seen before so in general if we have f oscillations per second we can say omega would be 2 pi f radians per second and so notice if you know omega value you can calculate f you can divide omega by 2 pi and calculate f and so what we want to do now is now that we know about everything about voltage we want to figure out the same thing for current what's going to look the current look like what's going to be the graph of that current how the oscillations would look like and we want to compare those oscillations with the voltage oscillations so how do we figure out the current well let's assume the current is flowing i don't know maybe this way and let's say the current is i now all we need to do is figure out an expression for current an equation for current so where do we begin well since we only have a resistor in our circuit we can go for ohm's law we can say whatever is the voltage across the source same should be the voltage across the resistor because you have only one element and then we can use ohm's law so it'll be a great idea to pause the video and see if you can figure out the equation for current yourself all right so we can directly say from ohm's law the current equals voltage divided by r so voltage across the resistor divide by the resistance and we need to be very careful at least right now there's only one component but in future we might have more components so it's voltage across the resistor divided by r it's not just any voltage but in our example voltage across the resistor happens to be the source voltage so that divided by r and this happens because there's only one component and we know our source voltage is just v naught sine omega t sine omega t so our current is just going to be this divided by r and tata we have found our current directly from ohm's law and what is the equation saying the equation says that the current is also oscillating we also have the same sine function over here which is not a surprise not really all that much of a surprise it also tells us let's look at the relationship between the two it also tells us that it's oscillating in sync with voltage what does that mean this means when the voltage let's say when the omega t is zero then our vs will also go to zero because sine zero is zero at the same time current will also go to zero similarly when omega t is 90 degrees or vs goes to maximum this will also be maximum current will also go to maximum so you can see because they have the same function they'll be oscillating in sync with each other does that make sense and again that makes sense to me because ohm's law it says when the voltage is maximum current should also be maximum when the voltage goes to zero current should also be zero so that kind of makes sense it's nice and what does this number represent we not divide by r that represents our maximum current and we can call that i naught now and again it's not a very much you know it's not a big surprise that the maximum current is just the maximum voltage and divided by r so now would be a great idea for you to pause the video and see what the graph for current is going to be so can you visualize or try drawing a graph on on top of this itself current graph pause the video and see if you can draw it yourself okay let's do this this is what it would look like and so now this peak value represents the positive i naught and this would represent negative i naught so this would be our positive y naught this would be our negative y naught and notice how the graph is the graph is not shifted like this the graph is exactly this way because they're in sync they go to zero together maximum together zero together minimum together and so on and again if you want to visualize this we can dim everything and we can move our time axis forward so just concentrate over here okay if you move the time axis forward see how they oscillate they both go up together they both go to zero together both go to the negative maximum together and so on and so forth that's how you visualize they're oscillating in sync with each other and again i have an animation for you we can move the graphs to the left and we can decrease it you can use the same thing and again we can draw an arrow mark because it makes it easier to visualize with an arrow mark and you see they're both oscillating together this represent the length of this represents vs and the length of this arrow mark now represents the current i okay and so it goes to maximum 0 minimum and so on and so forth i have one question for you and i want you to think about it i have drawn the current length to be bigger than the voltage length over here same here currently current maximum to be bigger than voltage maximum why why is that can you pause the video and think a little bit about that well the answer is no reason it's wrong to say that i naught is bigger than v naught or v naught is bigger than i naught because they are two different units it's like comparing uh three seconds and five meters you can't compare them you can draw however big three seconds you want as an arrow mark and you can draw however bigger five meters you want as an arrow mark you can't compare them so these are two different graphs with their own scales and we've just drawn them on the same graph so that we can compare and even numerically sometimes i should think but wait a second i naught should be less than v naught right because it's v not divided by r even numerically but think about it r can be a fraction so there's no necessity that i naught has to be smaller but of course you can't even that statement doesn't even make sense i know it is smaller than v naught anyways this sets the stage for all the future circuits more interesting circuits where we'll have inductors and capacitors and we'll look at all of that in the future videos