 Let's solve some problems with cells connected to a simple circuit. So the first one, we have a cell with EMF 10 volt. It has an internal resistance of two ohms, and it's connected to a resistor of three ohms. Our goal is to calculate this thing called terminal voltage, something we've seen before, and what the current in the circuit is going to be. So there's going to be some current, since this is the positive terminal, the current will be this way. I need to find out what that current is. So how do we do this? Well, I'm going to start by something that we've already seen before. We've seen how to calculate terminal voltage before. We saw that the terminal voltage, I'm going to write that equation first, so the terminal voltage equals the EMF of the cell E minus I times R. And we don't have to remember this equation. We can do this logically, something we spoke about in a previous video. But just to quickly recall, what is this equation saying? The terminal voltage is the voltage across the ends of the battery, terminals of the battery. And that represents the energy gained by a coulomb of charge when it moves from one end of the battery to another. What is that equal to? That equals the EMF, which represents the energy transferred by the battery to that charge minus the heat lost due to the internal resistor. So as the charge moves across the battery, it gains some energy, that is the EMF, and it loses some energy due to the internal resistor. And that's why when you subtract them, you get the net energy gained. And if this concept is not familiar to you or you need more refresher on this, then feel free to pause the video, go back and watch the video on cells, EMF, terminal voltage, and then come back over here. Okay. But if you're clear on this, let's continue. So let's see if we have everything we need. We have the EMF. I want to calculate terminal voltage. I need to find out what this VT is. We have the EMF. That's 10. We have R that is two. That's the internal resistor, but we don't have the current. Hmm. I don't have the current. So I need to first find out the current and the question now is how do I calculate current over here? All right. Can I do this? Here's my question. And I want you to tell me where can I do this? Can I say, Hey, the battery voltage is 10 volt. So can I just say this, this voltage is 10 volt. And then I say, Hey, Ohm's law. So I is going to be equal to V over R. V is given R is given. So can I just say I is equal to 10 divided by three, something like 3.33 amperes. Can I do this? Pause the video and think about it. If you've understood this concept, you'll be able to answer whether I can do this or not. And why? So pause and think about it. All right. So you can't do this. The reason why you can't do this is because the voltage across the resistor will not be 10. The voltage across the resistor is the terminal voltage. It's going to be 10 minus something. Right. And we don't know what that is. We have to figure that out. Are we clear? So all I'm saying is, although it looks like the EMF, although it feels like the voltage across these two points is 10 volt, it's not because there is internal resistance and some voltage is lost over there. Some energy is lost over there. So that's why to make sure that we don't get confused like this, we don't confuse EMF and internal terminal voltage, what we like to do is while drawing this, we like to draw the internal resistance over here. So let me show you what I mean. So let me get rid of this. And what we like to do is we like to draw that internal resistance here. So this is our internal resistor. We like to imagine this whole thing now is our battery. This is our battery. So you can imagine like a normal battery. It's the positive side. The positive side has that button. So this is our battery. And now things become very clear. So you can imagine your battery is made up of a perfect cell of 10 volt, which has no internal resistor. And then you can imagine there is a resistor connected in series with it of two ohms. And now this voltage you can say is 10 volt, but you can clearly now see the voltage across these two points will not be 10 volt. It will be less than 10 volt. It will be 10 minus whatever I get I times R. Is this clear? And so whenever we have cells, just to make things easier and so we don't get confused, all we have to do is attach an internal resistor in series with it and then imagine the whole thing as a battery and then solve the problem. All right. So with this, let's see if we can calculate what the current is. How would we do that? Well, now what I can do is now I can say, look, I have a cell of 10 volt over here. And I know the voltage between these two point is 10 volt, right? Because I've removed the internal resistor and put it out over here. So the voltage between these two point is 10 volt. And I can say now that the resistance between these two points going from here to here, I can go from here to here. The resistance between these two points, if I go from here to here is three plus two, they're in series. So I know the voltage between these two points. I know the resistance between these two points. I can now use Ohm's law. So why don't you pause the video one more time and see if you can now solve the value of solve for current. All right. Let's do this. So Ohm's law says V equals IR. So I is going to be V or R. So I is going to be here. V is the voltage between these two points. That is the EMF. See, between these two points, the voltage is just the 10. Between these two points, the voltage is this, which I don't know. So between these two points, the voltage is just 10. That's the EMF, 10 volt, divided by the resistance between these two points, the total resistance. And that is three plus two Ohm. That's five Ohms. And so the current is going to be I equals two Amperes. And there we have it. We have the current as two Amps. And now that I have the current, I can plug it in over here and calculate the terminal voltage. Again, if you want, you can pause and try so that you do it. All right. So over here, VT is going to be EMF, which is 10 volt minus current. I, which is two Amperes times times two, which is internal resistance. So that's going to be 10 minus four. And that's going to be six volts, six volts. So what we're saying is that the voltage across these two points, that's the terminal voltage, that we are saying is six volts. And again, think about it. Why is that six volts? Why is it not 10? Because out of 10, four is lost as heat when the current goes through this resistor. And that's why it's 10 minus four is equal to six. Now, another way, just to show you there are multiple ways of calculating this. Now, another way I could have calculated the terminal voltage is I could have said, hey, the voltage across the ends of the battery is the same as the voltage across this resistor, external resistor, right? Because this point is same as this point. This point is same as this point. So I could have said, hey, the voltage across this resistor is the terminal voltage. And I can apply Ohm's law here. Is that making sense? So think about it. What would be the voltage across this resistor? If I used Ohm's law, I would get that voltage across this resistor is going to be just IR. I just found out I, that's two, multiplied by R, which is three. And that is what I get. I get six volts. I get the same answer as I did over here. You have to because voltage here is the same as voltage here. Does that make sense? I know at first this might be all confusing, but you know, as you practice and you can practice more with our exercises, this will make a lot of sense. So just for practice, let's do one more problem. Here we are given a battery again with EMF five volt and some internal resistance one Ohm, but this time current is given to us and we're asked to calculate again what the terminal voltage is and what this resistance is. So again, can you pause the video and see if you can try this yourself first? Again, there are multiple ways to approach this. So feel free to try your own approach. All right. The first thing I like to do is just to make things easier for me. I'm going to add this internal resistance over here. Add this internal resistance. So this is our one and imagine this is our battery. This is my battery. All right. And so I need to first calculate the terminal voltage. I'm going to say, well, I know now how to calculate terminal voltage. Terminal voltage VT equals the EMF minus IR. So EMF minus I times R and I know all of them. The current is given to me. I know EMF. I know internal resistance. Oh, I can directly calculate. So EMF is Phi minus I is two and R is one. So two times one is two. And so the terminal voltage becomes immediately three volt. And so what does that mean? That means the voltage across these two points of our cell is three volt. Why is it three? Why is it less than five? Because it's charged gains five volt, but then it loses two volts to heat. And as a result, you get only three volts. So I got my terminal voltage. Now comes the question, how do I calculate the external resistance? And again, I want you to pause the video if you haven't tried this. Pause the video and see if you can try this now. We know the voltage across the battery, which is the same as the voltage across the external resistor. So feel free to try this now. All right. Let's do this. So I know that this voltage is three. So this voltage must also be three volt, right? I know that. And I know the current is also two, two amperes. I can use Ohm's law. So almost lost as V equals IR. So let me just write Ohm's law. V equals IR. So R is equal to V divided by I. I know what V is. That's three volts. I know what I is. That's two amps. And so my resistance has to be 1.5 Ohms. So that is my internal. Oh, sorry. That's my external resistor. All right. If you have come to this far, I have a bonus question for you before we wind up. The question for you is in what is the maximum current I can ever draw from this cell? Imagine you could change this resistor to whatever value you want. My question to you is what's the maximum current I can ever draw from this cell? Can you pause the video and think a little bit about this? Again, this is like just to get practice of this whole logic. All right. Let's see. If I want to get maximum current, the way I'm thinking is I need to try and draw as much current as possible. So I need more current. The question I asked myself is to get more current, what should I do with the resistor? Well, I should decrease the resistance. Now I don't have a choice with this. It's fixed. This is inside the battery, but this I can decrease it. I can make this resistance smaller and smaller. And if I make the resistance smaller, I'll draw more and more current. What is the smallest value I can make? Well, theoretically, I can make it zero. Right? So let's see what happens if I make this resistance zero. So let me draw another circuit for that. Or, you know, let me just do that over here. If this, let me draw another circuit. So if this was zero, so it's sort of like a short circuit. I'm not attaching any resistor over here. I'm short circuiting it. And here's my battery and here's my internal resistor. What will be the current in this situation? That should be the maximum current, whatever current I get in this situation, because I have the minimum resistance. So can you pause now again and see if you haven't tried before? If you didn't get it before, can you try now? What would be the current in this situation? Well, let's see. Again, to calculate the current, what I'm going to do now is I'm going to say, look, I'm going to consider between these two points, because I don't have an external resistor. I'm going to consider between these two points. What is the voltage between these two points? It's five volt. What is the resistance between these two points? It's one ohm, right? From here to here, there's only one ohm. And therefore, now the current, which is the maximum current, it's going to be the voltage five divided by the internal resistance one. That's going to be five amps. So from this cell, the maximum you can ever derive current is five amps. You cannot get more than five amps. And to do that, you have to short-circuit the battery. And that's bad, practically that's bad, because all of that energy is dissipated over here. Because there is no external resistance, all that energy is dumped into the battery. And so basically, the battery gets heated up. So this is a bad idea to do that. But this is how you calculate the maximum current. Thank you.