 I give you a banana and ask you, what's its electrical resistance? What do you do? You look at me in a funny way, but then you will remember, ah, ohm's law. You will say, I'll just hook this up to a battery, calculate the voltage across it, the current flowing through it, and use ohm's law, right? That's how you can calculate the resistance, isn't it? True, but there's a small problem when it comes to accuracy. You see, in practice, if you want to calculate the values of the voltage and the current, you need to introduce some additional devices in your circuit. And when you do that, their resistances also get introduced in the circuit. And so the values of the voltage and the current slightly changes. And so the resistance will not be exact, it won't be very accurate. So the question is, how do we measure this resistance more accurately? We do this by using something called a meter bridge, which works on the principle of Wheatstone's network. So in this video, you will see how we can take this meter bridge and calculate the resistance of that banana with more accuracy. But before we get to the meter bridge, let's back up a little bit. What exactly was a Wheatstone's network? Well, a Wheatstone's network is a circuit which looks like this, which there are four arms with four resistors, and you have a resistor in between. And the whole idea is, if the resistances have the same ratio, like in this example, one is to two, one is to two, then the voltage here and here will be exactly the same. And as a result, we'll find no current flowing through this resistor. So the current over here would become zero. Provided, these are having the same ratio. And it doesn't matter what this resistance value is, or what the value of the battery voltage is, or even the value of the resistors, all that matters is the ratio over here should be exactly equal. Now if you're wondering why that is the case, then we've talked about this in a previous video called Wheatstone's network. We looked at it logically. And we also looked at how we can extend this whole concept and all the fun stuff over there. So if you need more clarity or a refresher, feel free to go back and watch that video. But our goal is to see how this balanced Wheatstone network is useful in calculating the resistance of that banana more accurately, right? So the way to do this is, we can use one of these slots and put our banana in one of these slots. So let's say we put our banana somewhere over here. So we put the banana over there. Another principle is, if you can find, if you know the values of these three resistances, let's say, and imagine you could change the values of these resistances. Okay? Let's say they're, you know, we call them as variable resistors. Basically you can change their values. If you could do that, then in principle, you could keep changing the values of these resistances until, until, this is an experiment, until you find the current over here to be zero. Does that make sense? You keep doing that until the current over here goes to zero. Now when that happens, you know for sure that this network is balanced and therefore the ratio of these two resistances must be exactly equal to this ratio. And then I can just equate and calculate because I know the values of these three and that's the principle behind the meter bridge. And of course you might ask, how do I know whether the current is going to be zero over here or not? Practically. How do I know? Galvanometer over there. If the galvanometer deflection shows zero, then I know the current is zero. Now you might ask, hey, here also the resistance of galvanometer wanted, wanted to screw up with our calculation just like before. No, before the resistance is mattered because we are calculating values of voltage and current. Those values will change when we introduce, you know, the galvanometer or ammeter or voltmeter. But over here, notice in this balancing condition, there is no current flowing through the galvanometer. Right? So the galvanometer is not even a part of our circuit. And so its resistance won't matter at all. Get that? And even the voltage of the battery won't matter or the resistance of the battery also won't matter. All that matters is the resistance values of these three. If you calculate them, if you know their values accurately, you can accurately calculate the value of the resistance of the banana. And that's why this method is more powerful than the previous one. Hopefully this makes sense. And now you might get more excited and say, ah, I'm going to try this at home. But then you start thinking of another problem. Hey, practically, isn't it very tedious to keep changing the values of this resistance and, you know, keep looking at the deflection of the galvanometer? How do we do this practically? And that brings us to the construction of meter bridge. Let me take this network and keep it over here. And so the meter bridge consists of two L-shaped arms and one straight metallic. These are all metals. And these are screws to attach wires over there. And in one of the slots over here, we can attach our banana, whose resistance we need to calculate. And in this slot, we usually attach a resistance whose value is known. This is a fixed resistance. We're not going to change that resistance values at all. And immediately when you compare this with our Wheatstone network, you can kind of see this is our banana. And this resistance now is becoming the resistance of the fixed resistance that we have kept. And now the thing to concentrate on is the bottom part. We are not going to add any more resistors over here. Instead, we're going to take a wire, which is exactly one meter long. It has a uniform area, and you'll see why that has to be required. And we're going to have a ruler over here, just to show you that this is one meter long, and the ruler will also be required later on. And of course, we'll connect this to our battery. And of course, there will be a key over there to switch on and switch off the circuit. And in between this, we will have our galvanometer. And the thing to notice about the galvanometer connection is this side of the galvanometer is not attached to the wire. It's an electrical contact. So there will be some kind of a slider over here with a metallic contact over here. But you can move that. So you can move that slider like this on that particular wire. Now before I continue, can you pause the video and think a little bit about why we need a slider over here and how this part resembles our Wheatstone network? Just pause and wonder a little bit about it. Before we continue. OK, hopefully you're given this a thought. So if you look at the bottom part carefully and compared with the Wheatstone's network, you will see now that this part of the wire represents this resistance, this resistor. And this part of the wire represents this resistor. And so as we move the slider, say, towards the right, you immediately see that this wire starts becoming bigger. So let me just switch that. Yeah. As I move this towards the right, this resistance increases because more wire. And this resistance starts decreasing. So notice automatically the ratio of these two resistances keep changing. Does that make sense? And that's how I practically change the ratio of the resistance. And I keep doing that until the galvanometer deflection shows zero. Let me show. Let me go ahead and do that. Let's say here is our galvanometer. Notice right now it's not pointing to zero. There is some current, which means right now we are not in the balanced condition. So I'm going to move this slider towards the right. Oh, you can see the galvanometer is coming close to zero. The reflection is going close to zero. Oops, it overshot. All right, here it is. Now our Wheatstone network is balanced, meaning the ratio of these two resistances must be exactly equal to the ratio of these two parts, you know, the resistances of these two parts of the wire. And so we can now go ahead and calculate it. Before I do that, one thing I would like to know is what's the length of this wire. Right. And that's why that's why I have the ruler over there. So with the ruler, I can calculate it. Let's not put a number over here. Let's just call this as L. And so now I can go ahead and say the ratio of these two resistances which is X divided by R. Let me just write that a little bit to the top. X divided by R. That should equal to, because it's balancing condition, we reached the balancing and that should be equal to the ratio of these two parts of the wire. So this part of the wire, I will say the resistance is RL. I don't know what that is. I'm just going to call this RL. And this part of the wire, well, if this is L and I know the whole thing is one meter, then I know this has to be one minus L. If I keep it in meter, if it's in centimeter, it'll be 100 minus L. Let's keep things in meter. So I can now say that this would be divided by resistance of this much length of the wire, resistance of one minus L. Now, again, we might run into a problem. I know the value of R. This is known. But how do I calculate the resistance of this wire? That's not given to me. Again, I want you to pause and try this on your own. Think about it. How would you calculate this ratio? How would you calculate the resistance? I'll give you a clue. Think about some connection that you may have learned between the resistance and the length of a material. So did you remember the relation? The relation was R equals rho into L divided by A, right? So I can use that for this part of the wire. I can also use that for the bottom part of the wire. For the bottom part of the wire, the rho stays the same because it's the same material. Rho is resistivity only depends on the material and the temperature, which is the same. And so it's the same rho. The length of this part of the wire I know is one minus L. This is one minus L. And the area of cross-section of this part of the wire is also the same as this one. So it's gonna be the same value as the one on the top A. And that's why it's super important that this needs to have uniform thickness. And so now I can cancel this and notice all that matters is the lengths. And that is what I'm calculating practically. And I'm done. So from this, I can now rearrange and I can say X, the resistance of the banana equals R times L. We call this the balancing length. We also sometimes call it the null point because this is the point where there is no current flowing through. So null point divided by, divided by, what was that? R into L divided by one minus L. And you can do this and you will get your answer. And in short, that's how you can use a meter bridge to find the resistance of an unknown material. So long story short, meter bridge works on the principle of balanced Wheatstone's network. And when the galvanometer shows zero deflection, we know that the ratio of these two resistances must exactly equal the ratio of these two lengths. And why is this superior to the previous method of just using Ohm's law? Well, there, since we are using voltage and current to do the calculation, the resistance of your ammeter and voltmeter screws up or decreases the accuracy. But over here, notice in the balancing condition, there is no current flowing through the galvanometer at all. So the resistance of the galvanometer won't matter. We're not using voltage or current calculation. All that we're using is the length of the wire and this known resistance. So as long as we do that calculation accurately, we will be able to get a much accurate value of the resistance of that banana.