Meter bridge principle (and working)

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'll 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 and 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 wheatstones network well a wheatstones 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 do one is to do 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 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 a 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 0. does that make sense you keep doing that until the current over here goes to 0. 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 well you put a galvanometer over there if the galvanometer deflection shows zero then i know the current is 0. now you might ask hey here also the resistance of galvanometer won't it won't it 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 introduced 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 gonna 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 so 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 metal metals and these are screws to attach wires over there and in one of the slot over here we can attach our banana whose resistance we need to calculate and on 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 are 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 gonna even have a ruler over here you know just to show you that this is one meter long and the ruler will also be required later on and and of course we'll have you know we'll connect this to our battery and of course there will be a key over there to switch on a 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 a it's an electrical contact so there'll be some kind of a slider over here with the 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 okay hopefully you've 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 as the 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 this this uh 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 so 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 gonna 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 uh all right here it is now our reach to 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've reached the balancing end 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 1 meter then i know this has to be 1 minus l if i keep it in meter if it's in centimeter it will 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 1 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 hmm 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 this bottom part of the wire for the bottom part of the wire the row stays the same because it's the same material row is resistivity only depends on the material and the temperature which is the same and so it's the same row the length of this part of the wire i know is 1 minus l this is 1 minus l and the area of cross section of this part of the wire is also the same as this one so it's going to 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 links 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 is that um r into l divided by 1 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'll be able to get a much accurate value of the resistance of that banana