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# Resistors in series

## Video transcript

let's make our circle a little bit more complicated now so let's say I have a battery again and let me do it in a different color just for a variety that's the positive terminal that's the negative terminal they have this perfect conductor let's say I have one resistor I have another resistor and I don't know just for fun let's throw in the third resistor and we know of course that the convention is that the current flows from positive to negative that that's the flow of the current and remember current is just the rate of change or is just the charge that flows per unit of time right or the speed of the charge flow but we know of course that in reality what is happening if there is any such thing as reality is that we have a bunch of electrons here that because of this voltage across across the battery terminals these electrons want to really badly get to the positive terminal and the higher the voltage the more that they really want to get to this positive terminal so what's going to happen in this circuit actually let me label everything so let's say let's call this R 1 let's call this R 2 let's call this R 3 now the first thing I want you to realize is that between elements that the voltage is always constant why is that well we assume that this is a perfect conductor let's say this this little segment right here right and so it's a perfect conductor well let's let's look at this end so you have all these electrons this is a perfect conductor so there's nothing stopping these electrons from just distributing themselves over over this wire so you can almost you know before you encounter a an element in the circuit before you encountered device whatever you want to call that you could view this ideal conducting wire just from a schematic point of view as an extension of the negative terminal and similarly you can view this wire right here this part of the wire as an extension of the positive terminal and the reason why I want to say that is because it actually turns out that it doesn't matter if you measure the voltage here so let's say if I take them if I take a measure of the voltage across those two terminals using what we call a voltmeter and I'll I'll later do a whole video on how volt meter's work but remember when we measure voltage we have to we have to measure it at two points and why is that because voltage is a potential difference it's not some kind of absolute number it's a difference between essentially how bad do electrons want to get from here to here so we measured the voltage between those two points it would be the exact same thing as if we measure the voltage between these two points theoretically as we know no wires really have no reason to resistivity all wires have a little bit but when we draw these schematics we assume that all of that the wires are perfect conductors and all the resistance takes place in the resistor so that's the first thing I want you to realize and it makes things vary so for example everywhere along this wire this part of the wire the voltage is constant everywhere or along this wire the voltage is constant so that's the first thing I wanted you to realize let me erase some of this because I don't want this to get too messy too messy let me erase this that's a big important realization when you later become an electrical engineer and have much harder problems to solve let me erase all of this let me erase all of that let me draw a redraw that because we can't have that gap there because if there was that gap current wouldn't flow and that's actually well I'll draw later and how you could draw a switch but a switch is essentially a gap it looks like a gap in the circuit that you can open or close right because if you open it no current will flow if you close a carnal flow okay so you know now know that the voltage between devices is constant the other thing I want to convince you is that the current through this entire circuit is constant and that applies to any circuit in series now what do I mean by series series just means that everything in the circuit is after one another right if we take the convention we say current flows in this direction will hit this resistor then the next resistor then the next resistor at no point does the circuit branch off and you know has to choose whether do I want to go down path a or path B so this circuit is completely in series and there's a couple ways I can convince you that the current but let's call this let's call the current here let's call this current here I 1 let's call this current here I - let's call this card here I three I could draw another one here I three in a couple of ways that can convince you that I 1 equals I 2 I 3 1 is I could just say if you experimentally tried it out using an ammeter which measures current you would see that they are identical but the other way to think about it and this would this time I'm going to actually talk about the electrons so let's talk about things going in this direction is okay so these electrons through this wire they can go as fast as they want to go or I don't know the speed of light are close to the speed of light since they have very very very low mass and then we'll go into relativity one day but once they get to this resistor they start bumping into things and they slow down this resistor is a bit of a bottleneck right so as fast as they're traveling here they have to slow down here and if they slow down here they have to slow down here because if they kept going super fast here and then they slowed down here then they would start building up here and that just doesn't make sense that because there we know that they're evenly spread out etc and similarly you know they might exit this resistor at a certain speed and then slow down even further as they bump into resistors here but if they're going down if they're going even slower at this point then there would be a bottleneck here so this so essentially they would have to go at that rate throughout the whole thing and another way to think about it is the resistance the resistance is kind of a probabilistic thing I don't know when you think on a macro level we say oh it has is resistant to just slows it down but the longer there's a resistor it increases the probability that some of the electrons are going to bump into something and create a little bit of heat and etc etc so when you put resistors in series what you're actually doing is increasing the probability that more electrons will bump into more things right say there's an electronic travel say somehow you know through freak luck it doesn't bump into anything as it goes here so it's going really fast but it bumps in something here right it only increases it probably something bumps into it so there's a bunch of ways you can think about and I encourage you you know let me know if there's other ways that help you but the current through this entire series circuit is constant now if we say that what else can we say well if the current here let's say the current through here is i1 if the current through here is i1 what is going to be the voltage if I measured it from here to here what is this voltage here alright I measured with a voltmeter well v1 is going to be equal to i1 times r1 I know I put in audits and whatnot and I I 1 times r1 right and similarly if I measure the voltage from here to here that voltage is going to be equal to i2 times r2 let's say that this is where I 3 is so the voltage if I were to measure it from here to here oh boy my phone is ringing it always gets me while I'm concentrating I'll answer it's my my-y phone she'll probably mind that I didn't answer it but anyway so if we look at the the voltage from here to here is going to be i3 i3 times r3 so what we see is is that the voltage across the entire circuit which I can write as V total is going to be equal to the potential drops the total potential drop across each of these devices so the way to think about it is is that well let's think about the electrons the electrons here they really want to get here but after they've bumped around a little bit and they get here the they've experienced some potential drop so the electrons here actually the electrons here are a little bit less eager to get here and then once they've gone through here maybe they're just tired of bumping around so much and once they're here they're a little bit less ly eager to get here so there's a voltage drop across each device right so the total voltage is equal to the voltage drop across each of the devices and let's go back to the convention and let's say that the current is going in that direction the total voltage drop is equal to v1 plus v2 plus v3 so the total voltage drop is equal to i1 r1 plus i2 our two plus i3 r3 and what's the total voltage drop well that's equal to the total current through the whole system I total write or the you know the we just call it I times the total resistance right is equal to I 1 R 1 plus I 2 R 2 plus I 3 R 3 well we know that all the eyes are the same hopefully you can take it as a as you know just conceptually it makes sense to you that the current through the entire circuit will be the same so all of these eyes are the same so we can just cancel them out right divide both sides by that I we assume it's nonzero so we i-i-i-i and then we have that the total resistance of the circuit is equal to R 1 plus R 2 plus R 3 so when you have resistors in series like this the total resistance of the their combined resistance is just equal to their sum and that was just a very long-winded way of explaining something very similar simple and I'll do an example let's say that this voltage is I don't know let's say it's let's say it's 20 volts let's say resistor 1 is is 2 ohms let's say resistor 2 is 3 ohms and let's say resistor 3 is I don't know 5 ohms so what is the total resistance through this circuit well the total resistance is 2 ohms plus 3 ohms plus 5 ohms so it's equal to 10 ohms so R is it total resistance is equal to 10 ohms so if I were to ask you what is the current going through this circuit well the total resistance is 10 ohms we know that we know Ohm's law voltage is equal to current times resistance the voltage is just equal to 20 20 is equal to the current times 10 ohms right we just added the resistances divide both sides by 10 you get the current is equal to 2 amps or 2 coulombs per second so what what seemed like a very long-winded explanation actually results in something that's very very very easy to apply when resistors in series we just add I'm up I will see you in the next video