 A common 9V battery provides a pretty high internal resistance to the flow of charges because of which the maximum current that you can ever draw from that is very tiny. And so this is safe and you know we can let kids play with that. On the other hand, if you take a hard battery which is just 12V, not that much difference compared to this battery, it has an extremely tiny internal resistance. Now because of that, the amount of maximum current you can draw from the battery is lethal. So forget kids, even adults are not supposed to play with this. So clearly internal resistance plays a major role in the working of a battery. And so the goal of this video is to figure out how do we measure this internal resistance of a battery. And from the title of the video you may have already guessed, we're going to use a potentiometer. But we will not start with the potentiometer circuit because you know that's always been confusing me. Instead, we'll first logically understand how to measure the internal resistance and then we will build the circuit together. So let's say my friend throws a random unknown battery at me and asks me to calculate its internal resistance. How do I do that? I don't know it's EMF let's say, I don't know anything. And I'm not going to read over here, it's given but I'm not going to read because I'm not going to cheat. So the question is how do I calculate, how do I measure, what experiment will I do to calculate the internal resistance? So the first step would be what I would do is I would first model this battery. I would say, let's imagine that this particular battery internally is made up of an ideal cell which has no internal resistance of its own, an ideal cell of EMFE. And along with that, all the internal resistance is connected in series with that cell. That's how we can imagine it. And that's what we always do in a circuit, right? We concentrate all the resistance at one point and we're concentrating all the EMF of that battery at one point. All right, now how do I calculate R from here? Well, the first thing would be to build an equation for that. So to build an equation, let's first attach it to, you know, let's make a circuit out of it and let's see if you can use Ohm's law to build an equation. So imagine I attach it to some resistance over here, I will show it as a bulb. So let's say I attach it to some resistance or some bulb which has a resistance R. Now comes the question, hmm, can I build an equation with small R in it? And the answer is yes. All I have to do is figure out what's the voltage across the battery and that equation will have small R in it, all right? So can you try and give this a shot? Can you figure out, you know, just by using Ohm's law, what is the voltage across these two points of the battery right now? And I'll give you a clue. The voltage across the battery is the same as the voltage across the resistor. All right, with that, I want you to try and give it a shot. And remember, the answer should be in terms of E, capital R and small R, all right? So you prime pause the video and see if you can, you know, give this a shot. All right, let's see. So the voltage across the battery, I'm just going to write as V bat. It's not a bat, it's a battery, you get it right? So the voltage across the battery is going to be the voltage across the bulb. And what's the voltage across the bulb from Ohm's law? It's going to be the current I through the bulb times the resistance of that bulb. All right, now I don't want to, I don't want I in this. I want to somehow bring E and R into this. So how do I get rid of that I will again use Ohm's law in this circuit to figure out what the current is. Now this time I will use Ohm's law between these two points because I know what's the voltage across these two points. That's E. I also know what's the resistance across these two points. That's R plus R. So if I use Ohm's law, I equals E divided by the total resistance R plus R. So what I can do is I can get rid of this I and I can say that's equal to the EMF E divided by R plus R. And I've built my equation. My first step is done. Now let's see what I need to measure. I need to measure small R. So let's see what are the other things I know. I know the value of capital R. Now you don't have to use a bulb, right? I used a bulb, but you can use a standard resistance. So if you use a standard resistance in a lab, capital R value is something that you know. So that's not a problem. Okay, next, how do I calculate the voltage across the battery? Well, we have potentiometer with us. It's an excellent measuring device. So all I have to do is hook this up to a bulb and measure the voltage across the battery using that potentiometer. And I can do that. So to calculate this, measure the voltage across the battery with the bulb. I can directly measure it with potentiometer. So measure with the bulb. So this I can measure in my experiment with the potentiometer. Okay, now the interesting question is what about EMF? How do I measure that? Because the EMF, at least in this drawing, ideal drawing, it's the voltage between this point and this point. That you can't directly measure. So what do you do? Again, I want you to pause the video and think a little bit about this. How would you measure E? Because if we do that, we are done. Okay, have you given it a shot? The secret is you get rid of that bulb and recalculate the voltage across the battery. Let's see. If you calculate this point, we'd have the same voltage as this point. There is no resistance in between. But now the voltage at this point will be the same as the voltage at this point because I'm not drawing any current from this battery right now. And so there is no potential difference over here. In other words, now if I calculate the voltage across the cell without drawing any current from it, now that voltage is going to be the EMF. So all we have to do is measure the voltage across the battery but without, measure it without attaching it to a bulb. And just to quickly remind you, this is the battery equation, which basically says when you connect to anything across a battery, the voltage that you measure drops. It becomes smaller than the EMF because there's a small drop that comes across the internal resistance. Anyways, now we can bring in our potentiometer. And just to quickly recap, a potentiometer is basically a battery connected to a slide wire, maybe with some resistors in between. And the whole idea is, if you want to calculate voltage between any two points, then you attach it with respect to a galvanometer. And the whole idea is the voltage when, and as you slide this, and as you slide this particular slider, when the galvanometer deflection shows zero, say at around this point, the voltage across these two points must be exactly equal to the voltage of this part of the wire. So to measure this, all I have to do is calculate the voltage of this part of the wire. And how do you calculate the voltage of this part of the wire? Well, you calculate what that length is. And if we know what the voltage per meter of this wire is, which we call the potential gradient, then we just multiply it by L. So the voltage required would be the potential gradient, which is the voltage per meter of this wire, into the length of the balancing length. And if you're not familiar with this concept or you need a refresher, feel free to go back and watch our video on potential meters. We have explained this intuitively, logically, where all of this comes from. All right, we have recalled our potential meter. We have our theory. I want you to think about how you connect these two and what experiment will you do? What procedure will you carry out to figure out the internal resistance? Remember, it's okay to be wrong, but wondering and exploring is super important. So please, please give this a try. Think about what circuit will you build now? All right, if you're given this a shot, let's see. Let me first bring back the bulb. Okay, so how do we attach our potential meter? So here's our potential meter slide wire. Since I want to calculate in both these cases, I want to calculate the voltage across the battery. I'm going to connect my galvanometer and the other circuit also, other wire also across these two points. So here's how I'm going to make the connection. Okay, remember, I want to do two measurements. First measurement, what I will do is without the bulb. To calculate the EMF, I need to find the potential difference here without the bulb. And the way to do that, I mean, this is a practical circuit. I don't want to detach again. So what I'll do is I'll just introduce a switch in between, okay? Think of it as a key. If I remove the key, the bulb got detached. If I add the key, the bulb got attached. So I first detach the bulb and calculate what the potential difference across the battery is. And how do I do that? Well, I go back to my galvanometer. I notice there is a deflection right now which says that the voltage here is not exactly the voltage of the battery. So let's start sliding. As I slide to the right, notice the deflection reduces, reduces, reduces, reduces, reduces, reduces. And here we go, zero. Because the deflection is zero, I know the voltage here must be exactly equal to the voltage of the battery, which is the EMF. So now the question is, what is the voltage here? To do that, I'm gonna calculate the length of that wire. So let's say that length is L1. And just like what we saw before. Now, length is L1. That means the voltage over there, the voltage across the battery, that's going to be phi, which is the voltage per meter, times L1. And you may be wondering, do I know the value of phi? Well, usually when a potential meter is given to you, the value of phi is usually given, but over here you will see that's not even required as you will understand. Okay, now the next step is I want to calculate what the voltage of the battery is with the bulb. So I'm going to plug in the key now to connect the bulb over here. And my question to you is, when I plug in the key, do you think the galvanometer deflection will still be zero? Will it still be balanced or not? Take a moment to think about this. Let's see. It's not. The reason it's not is because as we discussed earlier, now the voltage across the battery has reduced. So we are not at the balancing length. So I have to slide again. Should I slide to the right or should I slide to the left? Let's see. If I slide to the right, ooh, the reflection increases. Of course, because the voltage has reduced here, right? If I slide to the right, I'm increasing the voltage difference even more. So I need to slide to the left. The voltage has reduced. I need to reduce the voltage here as well. So I'm going to slide to the left. Slide, slide, slide. And here we go. So now I'm getting the new balancing length. This balancing length refers to the voltage across the battery with the bulb. And so if I call this length as L2, and this voltage, which is the voltage across the battery with the bulb, is going to be phi times L2. And guess what? We are done. Because notice in this equation, phi cancels out and you can do the algebra, right? Again, feel free to pause the video and do the algebra and see what R equals to in terms of L1 and L2. And if you do that, I'm pretty sure you can. You'll end up with this equation. But again, I want to stress you don't have to remember the equations. How many equations will you remember? You know how to do the algebra, right? So you don't have to remember the equations. Stop remembering equations. Concept is all that matters. So to quickly summarize, the first thing we did to measure the internal resistance is build the battery equation, which can be done using Ohm's law. And the insight over here is that the voltage across the battery reduces when you attach anything across it. And when you don't have anything across, the voltage of the battery is the EMF. Once we got that knowledge, then we went ahead and used the potentiometer. First, we used the potentiometer to calculate the voltage of the battery without the bulb. That gives us the EMF. Then we went ahead and hooked up the bulb and recalculated the voltage across the battery. Since that voltage has reduced a little bit, we got a little smaller value of the balancing length. And once we got that, we plug in, we simplify, and that's how you measure the value of R. And of course, in your lab, you'll also have a switch over here. You don't want to keep this primary circuit on all the time. And you might have another internal resistance over here which I've ignored. And of course, you would be doing this experiment two or three times and calculating the average value that you'd get.