Ampere definition

say you have a circuit with some current running and you're curious to know what's the value of that current how many amperes of current is flowing how would you figure that out experimentally you will say well all i have to do is just hook up an ammeter but here's my question what if the ammeter did not have any readings on it now how will you know how much amperage the current is oh you'll say hey that's not a great ammeter i'll buy another ammeter which has some reading here's a twist what if there are no ammeters in this world which have any reading on it there are no voltmeters no galvanometers no meters no electric meters that have any reading on it now how will you calculate the how many how will you calculate the strength of the current in other words i'm asking you how would you invent a reading for your ammeters how would you do that to do this we need to ask a deeper question we need to ask the question what does it even mean to say have a current of one ampere what is the definition of one ampere and in this video we'll see how one could define the ampere and experimentally how one could start inventing the readings for the ammeter now before we do this for current i thought let's do the same thought experiment for a more familiar unit let's try doing this for a kilogram so a similar question imagine you have a weighing scale but there are no readings on the scales so how would you measure the weight of anything and also just like before there are no weighing scales no digital weighing scales no kilogram stones nothing ever in the world nobody has anything so how would you how would you start inventing a scale over here well just like over here we have to go back and ask ourselves hey what is the meaning of a kilogram what does it mean to say that an object has a mass of one kilogram what is the meaning of that what is the definition of that well i don't want to look use the current definition which is a little complicated let's use some historic definition so that makes it easier to understand the concept so a very historic definition of a kilogram was one kilogram is the mass of one liter of water in other words you take one liter of water and whatever is the mass of that that by definition is one kilogram so you know so once i know the definition i can set my weight i can set my scale so what i can do now is i can pour that entire one liter onto this and after pouring the scale will show something and now i know that whatever the measurement is it has to be by definition one kilogram and so now that i know that this is one kilogram i can start making my scale and then i can use this now to build more more scales i can use this to build my digital scales and i can use all of that so once you know the definition you can start building your scales now of course this definition you know is not very accurate because this means that you need to have accurately make one liter bottle you need to make sure that you completely affiliated with water and the temperature of the water all of that matters but don't worry too much about the accuracy you get the concept right of why definition is important to start building a scale now we can go back to our original question our original question was how do we invent a scale to measure current and so for that we need to define now what one ampere is now my first thoughts are hey we know the definition of an ampere it's one coulomb per second this means in one second if one coulomb of charge passes through a cross section of the wire then i know by definition the current is one ampere can't i use that yeah you can use that but the problem is do we know how do we how to measure a coulomb the answer is no we don't have any meters that measure how much coulombs of charges are passing by so although that's a good definition it's not a very useful one to build a scale so we need something more experimental and that's where mr ampere comes in remember in a previous video we discussed the ampere's force law which basically said that if you have two wires long wires carrying current i1 and i2 separated by some distance d and we saw that these wires will start attracting each other and that force per unit length force per length with which they're attracting each other is equal to mu naught 1 i 2 divided by 2 pi d and if you're wondering where did this come from we've talked about this in great detail in our previous videos of force between two long straight wires feel free to go back and check that out but you may be wondering hey what does this have to do anything with the definition everything everything my friend so here's how mr ampere is thinking imagine the currents in the wire was one ampere okay we don't know how to measure it but let's say the current turned out to be an ampere okay if this was one ampere this was one ampere and let's say the distance between the two wires is kept at one meter this is something i can do okay what would be the what would be the value of this well it's going to be this will be 1 this will be 1 so we'll just get mu naught by 2 pi and we know the value of mu naught mu naught value is 4 pi times 10 to the power -7 these 2 is 1 divided by 2 pi and d is also 1 so this cancels and so now i get force per length to equal 2 times 10 to the power -7 newtons per meter and now ampere says aha i can now define an ampere okay so i asked mr ampere how he says look take two long straight conducting wires and keep them one meter apart in vacuum and i ask why vacuum well it turns out because the value of mu naught is four pi times ten to the power minus seven only when that's in vacuum so keep them one meter in acu vacuum and start passing some current through it hook up a ammeter somewhere it's not a complete circuit i'm sure you can build a circuit to make sure make sure that the current through both the wires is exactly the same same current flowing through both the wires hook up an ammeter and measure the force between the two wires find a way you experimentally measure the force now as you start increasing the current the ammeter needle will start moving and the force between the attractive force between them will start increasing measure that measure that and when that force per length per meter force per meter is exactly 2 times 10 to the power minus 7 newtons per meter when that happens i know that the current is one ampere and so now i can put my measurements um and i have built myself a scale so what's the definition of an amp here an ampere is that current which when flows through two long straight wires kept one meter apart in vacuum attract each other with a force per unit length of two times ten to the power minus seven newtons per meter and this my difference is how we define an amp here and build a scale for measuring current now one final question i had was how do you experimentally measure the force between two wires and i googled and i found that there is this device that we use you know in in recent modern times we use this device called as kimball balance and that looks super super complex i don't even know where to begin to start thinking about how it works but the concept behind this is something that can be understood i think so the whole idea behind this what ampere might have used during his time is you have two wires kept one meter apart one meter in length because we're calculating force per meter so one meter in length kept one meter apart and one wire is fixed and the other wire is actually free to move a little bit um it's it's attached to a lever so what happens when you start you know putting current through it start passing current through it is they'll start attracting each other and because of that attraction the this this wire which is allowed to move starts bending down and now what you do is you start adding weights on the other end of that lever and you make sure that it comes back to the original position and so once you add weights if it has come back to the original position this means that the weight that you added if the arm lengths are equal the weight that you added here should be exactly equal to the force that's acting over here and so by calculating the weights that you have added you can then calculate the force and this is something that ampere used we call it as an ampere balance to figure out the force between the two wires force per unit length between the two wires