Potentiometer principle (logic) & working

i give you a circuit with a couple of bulbs connected to a battery and i ask you to measure the potential difference across say this bulb how will you do it you might look at me in a funny way and say that's so obvious mahesh i'm just going to hook up a voltmeter across it okay that's probably what i would do as well but here's a problem with the voltmeter the moment you attach it across it's going to start drawing some current and when you do that the current in the circuit is going to change we have disturbed the circuit and so the voltage has also changed a little bit and therefore the voltage that you're measuring right now is not exactly the voltage that was before you attach the voltmeter and so our reading is not very accurate now of course in most of the circuits this current drawn is extremely small and so we can neglect it however if you want an extremely accurate measurement of the potential difference then we cannot neglect it and so this brings us to the main question of the video how do you measure voltage between any two points without drawing any current from the circuit and you may have probably guessed from the title of the video we're going to do that using a potentiometer now when i was introduced to potentiometers i always got confused because there were so many circuits primary secondary and so many things were happening and so what i want to do over here is start logically not with the circuit so let's start with the logic understand the principle behind the potentiometer and then we'll get to the circuits and all the details all right so coming back to our voltmeter if you wanted to make sure there is no current drawn over here then the only way to do that is to have incredibly high infinite resistance infinite resistance and that's practically not possible and so we need to move away from voltmeter here's how i like to think about the principle of potentiometer i'm going to first connect a battery across the bulb through a through a galvanometer at first this sounds ridiculous you may be wondering why are we attaching a battery isn't that going to disturb the circuit as well and that's not even a measuring device and what how are you going to measure voltage using a galvanometer so many questions right and you're right it sounds ridiculous but it makes sense in a second so notice that this is not an any normal battery is a battery whose voltage can be changed so imagine there is a knob over here with which i can increase the voltage from say 0 to 5 volts so the voltage of this battery can change so what you may be thinking right well let's dig into this now so let's think about the potential difference here we have some potential difference and this is the positive potential higher voltage because it's connected to the positive of the battery and here we have some lower voltage let's call that lower voltage as zero volt you know just to keep things simple and so all i have to do if now to figure out is what is this value if this value is a plus two then i know the potential difference is two volt and i'm done okay now coming back back to our battery right now this since is directly connected to the negative terminal of my battery and we can neglect the resistance of this wire we can say this is also at zero volt and let's say my battery voltage currently is also close to zero that means this is also pretty much zero right now we don't have any potential difference over here so in this situation there is some voltage here and there is zero voltage over here and so we would expect some current to flow over here right and so in this situation the galvanometer will show me some deflection so if i look at the galvanometer there it is it is showing some deflection and of course right now the circuit is disturbed and this is not the position i'm intending for however let's say i turn this knob a little bit and now push this to one volt so i push this to one volt what do you think is going to happen now since i've increased this voltage the potential difference between these two points has reduced right does that make sense it has reduced and as a result the current flowing through the galvanometer also reduces and i can see that in the deflection of my galvanometer and so you see where i'm going with this as i turn up this voltage the galvanometer deflection becomes smaller and at one point it becomes zero so right now my voltage is at three volt as you can see in the bar over here and the galvanometer deflection is zero which means how much voltage should be over here oh the voltage over here must also be three volts because if it was any other number there would have been a potential difference across the galvanometer and current would be flowing so the very fact that there is no deflection means the voltage over here must also be 3 volts and notice since there is no current flowing through the battery the galvanometer right now i am not disturbing the circuit i have measured the voltage across these two points without drawing any current ta-da that my dear friend is the principle of a potentiometer you put a voltage source across with a galvanometer and you keep increasing that voltage source eventually when the galvanometer deflection becomes zero we know the voltage over here must be exactly equal to the voltage that we are measuring and that's how you calculate the potential difference okay you now understand the core of the potentiometer the principle of the potentiometer all we need to understand now is how to convert this into something more practical you see batteries with the whose voltage can be changed these are hard to come by so the next question we want to have to make it more practical is how do you achieve this by using a regular battery whose voltage you can't change how do you how do you calculate the voltage now now what we will do is instead of directly connecting it to our circuit we will connect this battery to a wire why are we doing this to be able to vary the voltage just like before but now with the wire here's how it works see if i were to connect these two points then the voltage that i'm providing now is 9 volts and i can't change that right but what if i were to connect between this point and the midpoint of the wire then how much voltage would that be i'll be providing over there oh that would be just half of nine volt because i can now say that this part of the wire and this part of the wire are identical and they have the same resistance and so the voltage should get divided equally and therefore between the midpoint i would get only 4.5 volt what if i were to connect this and over here i would get even smaller voltage oh so you notice if i connect this over here but from here if i were to slide across this wire i would be the amount of voltage i provide will keep increasing just like what i did over here and then i using then i can use a galvanometer find the balancing point and figure out how much at what voltage i would get zero so just like before we're going to connect with a galvanometer but over here i'm going to use a slider and say right now the voltage that i'm providing is pretty small compared to the actual voltage let's say and therefore there is some galvanometer deflection and so there's a current running but as i move the slider to the right the voltage that i'm providing increases and just like before the galvanometer deflection starts decreasing decreasing my voltage is coming closer to the measured voltage the voltage i'm measuring it's coming closer it's coming closer and right now ah here we go right now the galvanometer deflection is zero meaning the voltage over here is exactly equal to the voltage over here so all i have to figure out now is what is the voltage across this part of the wire and there you have it this is your potentiometer circuit we usually call this as the primary circuit this is the circuit secondary circuit but you get the idea right it's very similar to what we did over here but of course here directly the voltage calculation was available to us over here how do we calculate the voltage that's the question that we're going to ask now how do i know how much the voltage across this part is this is nothing to do with the potentiometer now we just have to do some basic you know electricity calculation so here's how we'll glue it i know that this particular length of the wire let's say this length of the wire was let's say this wire was i don't know maybe three meters long okay and let's say that we found the galvanometer deflection to be zero at two meters so we'll call this as the balancing length or the null point because current is null and this is at 2 meters let's say the question is what is the voltage across these two points let's call it as point a and point b i want you to give a shot and take a shot at this because there's nothing to do with voltmeter think about this the entire three meter wire has nine volts across it so the question is how much voltage is across the two meter wire can you can you give this a shot pause the video and try all right here's how i would do it i know that three meters of wire has nine volts so per meter how much voltage do i get so that number the voltage per meter is often referred as often denoted by phi and that number for us is going to be 9 divided by 3 so 9 volt divided by 3 and that's going to be 3 volt per meter so i know every meter of this wire has 3 volts and also it's important to understand it's a linear thing because see every meter of wire is identical right the whole wire is uniform and that's important the wire is the you know the area of cross section is uniform over there and because of that the voltage across each meter must be exactly the same and so it's a linear relationship and so now i know that every meter has three volts of potential drop across it so how much does two meters have i just multiply that so the voltage between a and b that's what i'm interested in the voltage that i'm measuring this is also a and b now because there is no current flowing both are at the same voltage remember and so vab should be equal to 3 into 2 so that is 6 volt and so in general whatever voltage we are measuring is going to be the voltage per meter which is phi times the balancing length and there you have it this is how you calculate the voltage through a potentiometer and i don't want you to remember this formula or anything this comes if you understand you know the logic behind this then this formula can be understood from first principles and of course now in actual practical circuits things get a little bit more complicated because there are additional resistors involved in our primary circuit we don't want to directly connect the battery to the wire and so how does that change things the only thing it changes is the voltage across this wire the primary wire right now it's nine but if you put a resistor over there that voltage will change and you can calculate that using maybe kirchhoff's laws or ohms law but once you do that the main thing we need to calculate is how much potential difference you have per meter all right and there's a technical term we usually call this the potential gradient gradient means how much things are changing per meter and so if you know this number for any potentiometer you can just multiply it by the balancing length and you get the voltage measured final couple of things i want to mention before we wrap up is one is how do you make this potentiometer even more accurate one way to do that is to make it more sensitive as i move the slider across let's say i want to make that galvanometer deflection happen very slowly so that when it comes to exactly zero i stop it right in order to do that we need to make it more sensitive and one of the ways of doing that is by increasing the length of the wire imagine this wire was not 3 meters but say 10 meters long the voltage across this is still 9 volts meaning the potential gradient would have now reduced right this big number becomes 10 meters so potential grade will be smaller and so as i move my slider across my you know the galvanometer deflection would slowly change and i would be able to precisely find the balancing point and it's for that reason the potentiometers that you find in your labs will have so many windings of the wires the whole idea is to increase the length of the wire as much as possible finally one last interesting question would be when you're conducting this experiment let's say you don't find the balancing length at all it doesn't matter where you go your galvanometer doesn't show zero at all until the end what could that mean you think about that there are two possible scenarios in which that can happen all right one scenario is if the voltage that you're measuring is larger than the entire voltage across the wire i mean think about it if this voltage was let's say 10 volts then it doesn't matter where i go i will never be able to balance it out right and so it's important that the voltage that you're measuring has to be smaller than the voltage of the wire or you can just say to be safe has to be smaller than your battery voltage in your primary circuit okay but there's another possibility even if the voltage is smaller let's say you took care of that there is another possibility in which the galvanometer deflection could never ever become zero and i want you to think about under what circumstances that could happen stay curious