Conversion of galvanometer into voltmeter

your friend has a galvanometer which measures tiny amounts of current in this example up to 10 microamperes and she wants to use it in an experiment to measure voltages up to 10 volts now she doesn't want to buy a voltmeter so she comes to you and asks you hey can you make this galvanometer somehow measure up to 10 volts and being a physics enthusiast you say sure i can do that i can you know change things inside but it'll cost you a little bit it might cost you about 300 rupees and she will say yeah cool i will give you that no worries and so the question we want to try and answer in this video is how do you take a galvanometer and convert it into a voltmeter to measure up to some specific amount of voltage now before we begin the first question you might be having in your mind is hey this is a current measuring device how can we measure voltages across it how does that work well i have one word for you ohm's law well actually that's two words but what i'm trying to say is if you know the current across you know current flowing through any device then from ohm's law we know the voltage across that equals i times r which means if i knew what the resistance of this galvanometer is then knowing the current i know what the voltage across it is so for example let's say the resistance of this galvanometer was just for the sake of example let's say it was 100 ohms and if we didn't know we could calculate it so that's not a big problem we can measure it for it that's not a big problem so if we knew the resistance was say 100 ohms and let's say when we're using this galvanometer let's say the galvanometer deflection shows 10 microamperes let's say this is the situation right now then i know the voltage across the galvanometer let me just call it as vg or something v g okay that voltage across the galvanometer maximum voltage you can think of it over here that would be the current to the galvanometer which is 10 microamperes times the resistance of the galvanometer which is 100 ohms and that would be in this example at least a thousand micro volt or one millivolt so you see i can think of this as a very very tiny voltmeter and i can just change the sticker and i can say look this is a millivolt meter all right so even though we don't think of it that way galvanometers can also be thought of as tiny voltage measuring devices as well excellent so that means i already have a tiny voltmeter which can measure up to 1 millivolts i just have to change the sticker all right so the nut question is how do i make this tiny voltmeter measure up to 10 volts that's the question we want to try and answer this can measure only up to a millivolt if i put more than that there'll be more current flowing through and this will break so how do i make this measure up to 10 words how do i do that another way to put this question is how do i ensure that when i put 10 volts across this galvanometer that's when the deflection shows 10 because if i could achieve that then i could just change the sticker put it to v volts and i'm done then when i put say 5 volts across this this is a linear devices galvanometers are linear devices so when i put 5 volts across this automatically the deflection will be half of this and it will show 5. okay and of course if we were extending it to say 100 volts i could use the same logic i could just put 100 here and 50 here and so my big question is when i put 10 volts across it i want the reflection to show maximum 10. how do i do that well we already know that in order for this galvanometer show deflection of 10 i need 1 millivolt across it not 10 but i need 1 millivolt across it which means our question becomes how do i ensure that when i put 10 volts across this device somehow the galvanometer only really gets one millivolt do you get the question i repeat when i put 10 volts across it i want to make sure the galvanometer only gets one millivolt in other words the rest of this voltage should get dropped somewhere else oh you see where i'm going with this if you want the rest of the voltage to get dropped somewhere else we need to attach something in series with it so here's how i'm thinking if i could attach something in series with it and ensure that when i put 10 volts across it only one millivolt comes across the galvanometer and the rest of the voltage comes across say whatever i'm attaching over here rest of the voltage which is 10 volt minus 1 millivolt should come across this device then i'm done because then what i could do is i could just put a box around it so that my friend doesn't see what i did okay and i can give this box to her and as far as she's concerned this is a voltmeter when you put 10 volts across this entire device it'll show 10. but you and i know that in reality when you do that 1 millivolt comes across this and that's why it's showing 10. so we need to add something in series to convert it into a voltmeter but now comes that question what should i add something what should i add over here and how should i think about it like you know what should i measure about that material that i'm adding so it's an open question i want you to think a little bit about it what do you think would you how would you go ahead with this what should i add and what measurement should i be worried about over here all right here's how i'm thinking since i want the voltage the 10 volts to split up so some voltage comes here and the rest of the voltage gets dropped over here and since these are in series current is the same so the voltage that they get really depends only on the resistance so i really only care about the resistance of that material so i might also just add some resistance over here so now our question changes and our question now becomes the final question that we have about design is what resistance we should add in series with this such that when i apply 10 volts across it 10 minus 1 millivolt comes across this resistor and you need to add a very specific resistance because think about it if you add a very low resistance then a very low voltage gets dropped across this and rest of the voltage will drop across this and this galvanometer will blow up you don't want that you also don't want very high resistance if you put a billion ohms let's say then all the voltage will get dropped across this nothing will get dropped and your galvanometer will not read anything so that's also bad so we need to add a very specific resistance so that the voltage gets divided divided precisely like this and so now this is a more fundamental electricity question how do i calculate what resistance should i put over here again i'll give you a clue ohm's law can you think about the situation from ohm's law perspective and figure out how to calculate the value of r go ahead give it a try pause the video and give this a shot all right so here's i'm thinking i already know the voltage across this resistor is supposed to be this much and i also know the current that's supposed to be when the voltage is this much the current has to be 10 microamperes right that's the current that's flowing through the galvanometer it's showing 10 it's really 10 microamperes right and so i know both voltage and current i can find the resistance so the required resistance is voltage that is 10 volt minus 1 milli volt divided by the current which is this much 10 microamperes that's the current and if i substitute i get my answer and that would be the resistance to be attached over here and if i do a quick calculation i can neglect this one millivolt in the numerator because it's very small compared to the 10 volts and if you divide this by this then the 10 cancels you get 1 divided by a micro and that's about 10 to the power 6 right that's about a million so you'll have to add a million ohms of resistance in series with this and this immediately tells you that voltmeters tend to have very high resistances as you can see because we want a lot of voltage to get dropped across that series resistance but anyways conceptually we now understand that a high resistance has to be added in series with the galvanometer and once we do that then we can just package it like this so that your friend doesn't see what we did and we can tell your friend that hey if we did a lot of work you know took a lot of time and effort and then we'll get paid our 300 rupees and we would have made a profit because resistors only cost what 10 or 20 rupees wonderful isn't it because as far as she is concerned this is a voltmeter if you had to put i don't know maybe say two volts across this or let's say one volt across this 10 times smaller then automatically this would be 10 times smaller this would be 10 times smaller the current would be 10 times smaller because it doesn't change the current would be 10 times smaller the deflection would be 10 times smaller and it would show one volt so you see this is as far as she's concerned a voltmeter that can measure up to 10 volts finally if you are wondering what should be in general what is the general expression for the resistance that needs to be added to convert a galvanometer into a voltmeter we can just look at this and figure out see 10 volt was the voltage up to which we were extending so this is the voltage to which you need to extend your galvanometer's range to minus one millivolt was the voltage that your galvanometer maximum voltage that your galvanometer could measure for full scale deflection that is the maximum current that your galvanometer can you know measure ig we'll call it g four galvanometer times the resistance of the galvanometer so this is the maximum voltage your galvanometer can handle divided by the current maximum current that your galvanometer can handle so this you can think of it as a general expression of the resistance that needs to be added in series but i highly highly encourage you not to remember this formula in fact i wouldn't get rid of this formula the reason for that is there are a lot of formulae in physics and you know you can't remember all of them very easy to you know get confused and go wrong so whenever numericals are asked yes formula would be easy faster to do it but this is a more conceptual way to do it i don't remember the formula seriously i will always try to do it this way and also if the questions are very twisted if you get a different question say they will give you an ammeter and ask you to convert into a voltmeter right it suddenly looks like a different question now but the concept stays the same and so if you understand the concept you can solve any numerical all right so to quickly summarize how did we how did we do this we first thought of our galvanometer as a tiny voltmeter we figured out what is the maximum voltage it could measure 1 millivolt and then we said okay now we need to extend its voltage to 10 volts then we said look that means when 10 volts comes across this only one millivolt should come across this our galvanometer and so the rest of the voltage should come across some resistor and so that's why we added a resistor in series and then we figured out what that resistance should be using ohm's law so to convert a galvanometer into a voltmeter add an appropriate resistance in series