Intro to Ohm's Law & Deeper Look at Voltage in Circuits

today we're going to introduce Ohm's law and take a deeper dive into the concept of voltage in electric circuits we'll use Ohm's law to calculate the current in a circuit and then build various circuits to verify it's true we'll then take a look at various different kinds of voltage sources including many types and sizes of batteries by building various circuits we'll answer the question why do we have so many different sizes of batteries with similar voltages and finally we'll wrap up by discussing the concept of AC versus DC current in electric circuits hello welcome back today we're going to have an introduction to Ohm's law and also a deeper look into voltage these two concepts are absolutely essential to do anything in circuits that's what we're going to conquer today I want to start out with a question this is a large battery some of you may or may not have ever had occasion to use it's six volts six volts that's the voltage for this battery all right this is a d size Cell It's A 1 and a half volt volt cell right this is a c size cell you can see the difference it's also one and a half volts you see the pattern here this is a double a cell one and a half volts these this is four of these what we call Triple A cells each of these one and a half volts and these little bitty Guys these little uh tiny little flat batteries three volts each so if I put two of these three volts batteries together I can get six volts which is the same voltage as this if I know that each one of these batteries is one and a half volts if I stack them in the right way I can add up to six volts the same voltage as this why do we have so many different size batteries that can they're really uh the same voltage if this is six volts and this is six volts what is the difference between these two batteries so in order to answer this today we're going to have to talk about the difference between Theory and reality in theory we have what we call Ohm's law it's the most fundamental equation in law that you have to master in order to understand electricity but we're going to apply it understand what a deeper look into voltage uh using Ohm's law and then we're going to use it to try to understand the difference in these voltage sources so this lesson is all about voltage sources trying to understand voltage a little bit deeper let's get started right now so let's Jump Right In by diving into Ohm's law we're going to talk about Ohm's law a lot but I need to introduce it here in order for us to make any progress at all Ohm's law is a very simple algebraic equation the three variables of Interest are voltage current and resistance which we've talked about in the past and Ohm's law states that the voltage across any passive circuit element I'm going to talk about what a passive element means in just a second the voltage across it is equal to the current passing through the electric current passing through that object multiplied by its resistance now this applies right now we're going to basically be talking about resistances we have to modify a little bit when we talk later about capacitors and inductors and we have to totally change the discussion completely when we get to non-linear components which are diodes and transistors we have to kind of modify things later but for now I want we to I want you to discuss Ohm's law with me in the context of only resistors we have to learn resistors first it's the easiest thing to understand now if the voltage across a resistor is equal to the current flowing through the resistor times its resistance this is an algebraic equation that you can solve uh for whatever variable you'd like another common way or a very useful thing a way to write it is that the current at I is equal to V over R just take this equation divide both sides by R and you'll be left with I is equal to V over R which is what we have here these two forms of Ohm's law are what you will typically see in books and they're exactly the same it's not that one is better than the other it's just like uh two sides of the same coin it represents the same exact relation all right now we mentioned in the introductory lesson that we have voltage current and resistance but we need to solidify it more what does voltage mean voltage is the push in an electric circuit this battery is providing a physical push to the electrons in the circuit the push is coming from a chemical reaction ultimately the push ultimately the push comes from what we call the electric field you know know from basic science you know two electrons repel each other like charges repel either two protons or two electrons they repel and Opposites Attract that electric force ultimately is where all electricity uh the force to push the electricity comes from it comes from the electric force in a battery it's coming from the chemical reaction that's wanting to push electrons out of the terminals and back around to the other side we'll talk a little more about batteries a whole lot in just a second but of course we have electricity that's generated by nuclear power and other means they're all generated various ways but ultimately the voltage that comes out is the push how much push do you have that's causing the electricity to flow so when we talk about voltage I want you to always replace it uh with the word push in your mind if I can make this correct push it's the push right the electric current itself is what is actually flowing it's what we call the flow we're going to talk about the definition of current very soon it's it's literally how many electrons per second are flowing past a point it's literally like the water flowing in a river whereas the voltage is maybe the height of a mountain when we talk about when we talk about voltage I want you to picture a mountain you're standing on the mountain top and you can throw rocks off the Mountaintop because you're at a high potential uh we call it potential energy above the ground in physics when you throw the rock it accelerates down the side of the mountain when it gets to the bottom of the mountain it has no more potential anymore so it eventually stops rolling right when you have a battery you're at the top of the mountain and it's pushing the electrons but when they get it back around to the other side when they go out of one turn terminal and get back around going to the other side then they have lost all of their potential energy and then they go back into the battery to be accelerated and pushed out the other side again so it's very much like a mountain the higher you are above the ground the more potential you have to do work the higher the voltage in a battery so voltage is push at the top of the mountain what is Flowing is the actual electric current and if there are any obstacles in the way or resistors in this case we call it the resistor the resistance R okay now I want you to remember we're going to go over units again voltage uh with the voltage is in volts of course the current is uh you can use capital or lowercase i and the resistance we usually call R so V equals IR that's these three variables right here now the base units of voltage are volts but of course we might instead talk of millivolts that one that's one one thousandth of a volt we might talk about kilovolts which is thousands of volts but it's just a modification of the basic unit of a volt same thing for uh current we might have uh the base unit of current is uh called the Ampere which we abbreviate a but we might instead talk about milliamps which is thousandths of an amp right we might talk about microamps which is millions of an out of an amp and we might talk about kilo amps which is like thousands of an amp right in terms of resistance we might talk about ohms we use the symbol Omega for ohms but we might modify it we might talk about milliohms we might talk about micro ohms and Nano ohms and so on but it's more common to talk about kilo ohms or even Mega ohms okay now this is all stuff we've talked about in the past but it Bears repeating because you have to understand the definitions when we talk about the circuit if somebody tells you hey that circuit has a million volts of electricity flowing through you you know that this person does not know what they're talking about because voltage does not flow what do we say flows the current flows the current the current is the only thing that flows it's literally the electric flow of charges in a closed path the current flows but the push required to start the flower to continue the flow is the voltage and if there are any resistors in the way it tends to reduce the amount of current that's why it's called the resistance all right in the interplay between these three variables we call ohms law now we want to learn about all of these things in Practical detail we want to build some circuits so let's take a theoretical circuit the absolute sample is circuit that I could possibly think of right we're going to have a voltage source there's many symbols for a voltage source I'm going to write it like this plus minus and we're going to uh say that this voltage source is connected directly in the path with a resistor this is a symbol for a resistor and in this case I'm going to say that this voltage has a voltage of one volt and the resistance has a resistance of 10 ohms now I want to ask you if I take a one volt source and I connect it directly in the path with a single element which is a 10 Ohm resistor how much electric current will flow we know that there will be current flowing here going around back to the other side remember we know the electrons are coming out of the negative side we know that but we talked about in the last lesson that algebraically since electrons are negative and they are coming out this side mathematically it's the same thing as talking about the opposite current we call the whole current coming out of the positive side and going this way now I don't care personally what you do but when you take electrical engineering classes we always talk about the positive current flow it makes the equation simpler because there are no negative signs but if you want to think about electron flow that's fine I'm just telling you that they're mathematically the same thing it's like you know positive 3 is the same as negative negative three put two negatives together you still get a positive three it's you can write it different ways but it's the same thing all right so this is our circuit how do we determine the current flow we go up to Ohm's law I can use either form you want but we're trying to find the current so we can say that I is equal to V over r but we know that the voltage across this resistance is one volt and we know that this resistance is 10 ohms now we're working in the base units we know that the base units are voltage uh in volts and then amps is the base unit and ohms is the base unit of resistance so if I know I've put a a unit of volts in here and I know I've put a base unit of ohms here then I know that the current I calculate is going to be in the base unit of amps all right so what's 1 over 10 it's 1 10 or 0.1 amps so what we expect is we expect if we connect a one volt Source directly across a 10 Ohm resistor that there should be a current flow of 0.1 amps which is one tenth of an amp so here is where we have to go from Theory to reality in reality you're not going to be able to get exactly what you write down on the board because your voltage source is not going to be exactly at one volt your resistance is not going to be exactly at 10 ohms and the measurement apparatus whatever measurement apparatus you're going to use an ohmmeter or voltmeter or whatever is not going to be infinitely accurate but you should still be able to convince yourself that you're getting something close enough to this that we're representing reality so what we're going to do we're not going to use batteries yet we're going to use my voltage source right here and we're going to connect it across this resistor now this resistor is a physically large resistor in the last lesson I worked with resistors that were very very small well we're going to have a whole lesson on resistors and resistance very soon but just know that the reason I'm using this very large resistor physically notice it says 10 ohms printed on here and it says 10 watts the W is y we haven't talked about power yet but this resistor is physically large so that it can absorb a lot of heat without burning itself up I wanted to use a large one because I don't want to burn up my resistors teaching you these Concepts but the larger the resistance the larger physically the resistor is in general the more power that it can take the more heat it can dissipate without burning itself out all right so what we're going to do is connect one side these are coming straight out of my power supply over here which I can control very carefully in a minute we'll be using batteries but right now I want to use my my digital Source here and so what we all we have is literally a single circuit element the single resistor coming straight connected to our voltage source now I want to dial this thing up so that it goes up to one volt so I will increase the current the voltage from my source here whoops I'm turning the raw knob I will increase my voltage source and try to get it I'm going to use the fine knob to get it as close as I can to one volt right now it's 1.01 volt there's 1.00 volts so we said when there was one Volt across a 10 Ohm resistor we should get 0.1 amps and notice that we have 0.104 amps so this is what I'm saying it's not exactly 0.1 amps but that's just because there's a little play in the knob here there's a little bit of inaccuracy in the display there's a little bit of resistance in the in the wires connecting everything together and also this resistor is not exactly a 10 ohm resistor but notice that we get exactly what we predict 0.1 amps let's just for Giggles disconnect it from here I'll turn my voltage down and I'm going to turn my meter on over here this is a you can measure voltage you can measure current and so on with this and just for Giggles let's go ahead and measure the resistance of this resistor here so all I'll do is I'll connect to each side here and we'll measure and see what it says we'll give a nice good contact pressure and see what it comes up with and we see right here 10.2 ohms so it's not exactly 10 ohms that's one thing I told you the resistor has a certain tolerance to it they can't make them infinitely accurate okay and also when I touch the resistor with these probe tips that introduces a little contact resistance as well so in the real world with circuits you calculate based on your desired values but you know in real life the real values will be a little bit different than what you calculate just because in the real world it's not perfect all right so let's go back and let's reconnect I got my voltage all the way down so I'll reconnect my circuit here so we verified that when we put one Volt across this we uh we uh got the 0.1 amps out so that's correct Ohm's law is validated right now what we're going to do is play with this a little bit more right so we're going to go up to two volts so what if I put two volts across this so I change the one volt to two volts I can erase this if you want put a 2 there but if I put this and replaced it with two volts it would be I is equal to V over R but the voltage would now be two volts and the resistance would still be 10 ohms so I'm working in the base units of voltage and amps and so what I'm going to get is the current in this case 2 over 10 is going to get me 0.2 amps now let's go over here and see if that's what we get we haven't changed anything we're going to now increase this thing to instead of 0.1 volt we're going to go up to two volts and I've overshot so I'm going to go down it's kind of hard to get it exact so I'm going to try to go very very slow and it looks like I've overshot again so I'm going to go down and I'm going to use the fine knob to go up to two volts what do I get 0.204 volts again I mean amps uh again not exact but it's close enough that we know that what we're predicting with Ohm's law is matching reality this is a nice device because this voltage source also tells me how much current is Flowing I could use this meter to of course hook into the circuit and measure the same thing but it's just too easy to use the source that I have all right so let me turn it off I don't want to dissipate any any power for for no reason let's predict what's going to happen uh let's do a couple more let's say it's three volts I is equal to V over R let's say I change this thing to 3 volts so 3 volts and 10 ohms so 3 over 10 is 0.3 0.3 uh amps and we're going to check that we know that this one's correct and I'm going to go and calculate the last one again I'm working my way up to six volts because uh remember I have this 6 volt battery I'm going to start playing around with the 6 volt battery soon so I want to show you what happens when we get up to six volts so when I use the battery we'll see the difference right if there is a difference so let's change it from 3 volts to 6 volts and 10 ohms and so would you get 6 over 10 0.6 amps so we have two of them to check 3 volts and 6 volts and let's just see what we get so we'll go up to 3 volts and I'll overshot so I'll go down very very close and I'll go three so at 3 volts I get 0.302 amps so according to Ohm's law that's what I predicted that that's correct and then I'm going to go up to 6 volts there's 5 volts and there's 6.06 so I'm going to go down a little bit right here with the fine knob I'm going to go down to 6 volts whether I get 0.583 all right which is very very close if you round it up to this now you have to ask yourself oh why is it different what's wrong with that what am I doing wrong well there are uh res there are this wire is not a perfect resistor right so this is the the the difference between Theory and reality it's not a perfect conductor this wire even though it's made of copper actually has a very small resistance also notice I'm connecting these things with these alligator clips so the contact there's a little contact resistance where they connect and also you can't see it off the camera but I have another connection point from the power supply to these wires there's another contact point the higher and higher I go with the voltage these little imperfections are going to be magnified a little more so at three volts it was pretty close to act it was very close to Accurate 0.3 amps when I get to 4 volts let's go down to four volts we expect 0.4 let me go up just a little bit we expect 0.4 amps notice it's very close but not quite then when I get to 5 volts it's a little bit different right you can see the difference there and when I get it six volts it starts to be Amplified enough where it's different here okay 0.584 amps so but we still know that as we increase the voltage the electric current in the circuit seems to go up by uh not by an equal amount but by a proportional amount the reason I'm doing this is to show you that when we have linear components in the circuit and what I mean by linear components basically is in this case resistors we'll talk about capacitors and inductors later but we have non-linear components we're going to talk about later diodes and transistors that amplify things those are non-linear components the current and the voltage relationship in a transistor is not linear like this in this case when I started over here when I started at one volt I got 0.1 amps 2 volts 0.2 amps 3 volts 0.3 amps 6 volts 0.6 amps even though it wasn't exactly you know matching because of reality we know that that matches the theory right every time we increase the voltage by the same amount the current increased by the same constant amount we increased by one volt one volt one volt one volt and then we go from here that's 0.1 amp then another 0.1 amp then another from here to here 0.3 amps actually went three volts and we increased 0.3 amps so they they increase with lock step from one another the current and the voltage through a linear uh element like this increases linearly as you increase the voltage the current goes up by a proportionally uh by proportional amount right and the reason it's like that is because if you go back and look at Ohm's law I is equal to V over R this relationship is a linear relationship what do I mean by a linear relationship remember back to algebra class right in high School you spent a lot of time everyone spends a lot of time graphing lines we say this is an equation of a line what does the equation of a line look like right y equals m times X plus b and you learn in an algebra class that this is the thing called the y-intercept and this is the thing called the slope and this slope tells you how steep the graph is but basically if you can put any equation into this form you know it's going to form a straight line we call that a linear relationship but what is Ohm's Law I equals V over R if I say that I is equal to V over R you say well wait a minute that doesn't look like that but then you say okay notice that the resistor was constant that never changed all I changed was changed with a voltage and I measured the current so I can write this as instead of like this I can write this as 1 over R multiple multiplied by V think about how we multiply fractions if I make this V over 1 then you have V multiply get a v on the top and an r in the bottom so I don't need to write it like that I can just leave it like this but then what happens if I say okay I'll just change the y-intercept to be zero then this equation the equation for the current through a resistor is a line and it's a line because we can then say that the slope of this line is just one over the resistance if you think of it that way that this is just a constant right because the resistor was 10 ohms so this is just a constant number one over ten right and this is the slope of the line then it's I equals m x plus b where the y-intercept is zero and the reason it's zero is because when you drive it with zero voltage you get zero current so of course the line has to go through the origin because if you don't put any voltage in you don't get anything out that just means the line goes through the origin so I don't want to graph it and draw but you get the idea I just wanted to show you that it behaves linearly because Ohm's law is the equation of a line that's all I wanted to get across to you so that you understand it and just as a preview when we get to transistors and diodes later the current voltage relationship will not be aligned it will be a non-linear type of deal because of the way those devices are constructed and because of that you can you can amplify things that's one of the main uses for transistors we'll get to that much much later all right now we need to transition ourselves to talking about the batteries why do we have all these different size batteries if they're all about the similar voltage range all right now I told you to take my word for it earlier now I want to actually show you this is a six volt battery it's printed right on the side here and if I uh connect my voltmeter across the two Terminals and measure the voltage I get a negative because I've got them flipped around if you look over there it's 6.427 volts right now this is a six volt battery this is another theory versus reality thing it's printed on here that this is a six volt battery but when it's fully charged like this it's a little bit more than six volts as it is depleted that voltage is going to come down and down and down but usually these things are a little bit more than their stated voltage when they're fresh out of the box like this so this is what we would call a six volt battery even though it's a little bit more than that now let's go down stream a little bit we'll put the six volt battery off to the side and I want to talk to you about these things these are called D size batteries or D cell batteries I'm going to take one of them out right if you read the fine print on this thing it says that it's one and a half volts let's see so what I will do is I will connect my meter across the top like this and again notice it's not 1.5 volts that's what's printed it's a little bit more than that because it's fully charged now if you take two of these things and you connect them you gotta again think about voltage as a mountain this literally represents like the top of a mountain right and uh you're at the height the high part of the mountain when you're when you're talking about the top terminal compared to the bottom if you stick two of them together it's like stacking two mountains on top of each other so what do you think the voltage should be if I've got them stacked like this well it should be adding the two together because it's literally like stacking two mountains one on top of another and if I look over there the 1.6 plus the 1.6 is 3.2 so that's exactly what we get so when you see these little uh devices like this these little battery holders like this all that's going on is it's alternating the direction but all that's happening is you're putting them end to end to end to end like this so if I put the flat part on the spring right here and then the flat part on the spring right here like this and then these are oriented the same way all I've done is instead of stretch them stretching them out in a line I've folded them up but they're still end to end like this so if I take a look at this then I know it's about one and a half times four so it should be about six volts let's see what the actual voltage is so I'm going to hold this side of the wire right here and then the red side I'm going to hold with this one right here and we'll read the meter over there 6.5 volts is what I get here for reference remember that this one was about the same 6.4 so the question I have for you and that what we're going to answer is if this is about 6 volts and this is about six volts why do we have these different size batteries right let's go through the different sizes I have I'm going to give you the punch line and tell you why we have them and then we're going to do a little experiment to show you why what I'm telling you is correct all right so let's put these away these are the D cell batteries now these are the C cell batteries if you read the package on these very carefully these this package will also say that each of these batteries is about one and a half volts so once they're into in like this same kind of deal I'm going to hold it like this again you're going to get just a little bit over six volts notice they're all coming out to about 6.4 volts once you stack them together these are called double a batteries if you read the package each one is one and a half volts what do you think we're going to get if we uh stack them together end to end like this and measure the voltage that one's a little bit higher 6.5 volts but still in the same range all right this one over here is even smaller it's called a triple a battery and the AAA battery if we do it correctly should basically measure the exact same thing so we're going to this wire is flopping around over here we got them end to end over there a little bit lower 6.3 volts but you get the idea same range and then finally these little batteries let me get them out here and put them out in front here these little batteries are used in very small devices right calculators and things like this each one of these is not one and a half volts each one is three volts so what I'll do is I'll just put one side on on one and the other side here and we'll see it's just a little bit over three volts so if we stack two of them end to end just like this we're stacking the mountains together and what do we get just a little bit over six volts so these two batteries stacked together is six volts this gigantic battery here is also six volts why in the heck do we have all of these different sizes when the voltage is the same what I'm going to do is tell you the punch line all right but then I have to prove to you that the punch line is correct and we're going to prove it by building stuff so let me tell you the punch line we learned that we have Ohm's law that that tells you how much current you will get when you put the voltage in and you get the resistance so you think that if you put 6 volts into here divided by whatever the resistance is let's say it's a 10 Ohm resistor we already did that calculation 6 divided by 10 we should get 0.6 of an amp that's what we should get but we also know that these two little batteries when you add them together is also six volts so six divided by if we do a 10 ohm resistor we should get again 0.6 amps supplied by this we can pick any of these others that we have used this is about six volts six divided by again 10 ohms we should get the same thing 0.6 amps no matter what batteries we use because the voltage is six volts I've arranged them so that all six volts if I hook them up across this 10 Ohm resistor we expect to get exactly what we already got before but we're not going to get exactly what we got before what we're going to find out is that the physically large battery can generally keep up and Supply the correct amount of current as predicted by Ohm's law but the small batteries are going to try but they're not going to be able to physically Source the amount of electricity that Ohm's law is calculating that you should get so again this is the difference between Theory and reality Ohm's law will tell you what you should get but in reality inside this battery is a chemical reaction and I don't feel like drawing a picture because I think it'll it'll distract us from the main point but in a chemistry class we would draw the picture of what's inside of here and I'll describe it you have a two conductors which are separated by an insulator so they're not touching and they're rolled up like a gigantic jelly roll inside of this thing and there are chemicals inside of here that when you select the correct chemicals and the correct Metals for the ribbons that are inside of here they they uh they basically lose and gain a lot electrons from the chemical reaction and the electrons want to come out once one terminal of the battery go through and then back into the other terminal when the electrons get into the other terminal they go back through the battery and it's like going over and over again but eventually the reactants that are in here get depleted and the chemical reaction cannot be sustained and so the battery dies that's what we say that the battery is now dead right but even though this is six volts and even though these two things are over here this here is also six volts there's a huge difference between them the main difference is that inside of here there's a large surface area of contact area for the chemical reaction to take place inside of here it's constructed in the same way or in a similar way but there's a very a much smaller amount of surface area for this chemical reaction to happen so we're going to learn that electric current is the flow of electrons per second because inside of this thing there's a large surface area for a large amount of the chemical reaction to happen it can physically supply the amount of electrons that Ohm's loss says that should come out of it but in here there is not a large enough surface area to physically produce the amount of electrons that Ohm's law would predict so even though these are both six volts if I hook this up to a load and I hook this up to the same load depending on what the load is we might not get the correct amount of current that we predict ahead of time so these physically larger batteries are going to be used in applications when we require a high current and these small tiny batteries are going to be used in applications when we don't require a large current for instance we might use this in a lantern to supply a very large amount of light or a car battery you've seen car batteries big rectangular thing it's used to supply many many amps to start an engine it has to supply a large current to be able to function but these little batteries or these little batteries they're not used to start a car there might be used in your remote control or to power your calculator the electronics in your calculator do not require much electric current so it's able to function just fine we have smaller batteries even at the same voltage to power devices that don't require a large electric current we have to have physically large batteries to supply current in situations where we need very high or higher electric current now that is the reason and we can talk about the resistance of the batteries and I'll talk about that a little bit later because you know you can think about it different ways but ultimately that is the reason but before I discuss it any further I want to show you that what I'm saying is correct and in order to show you I've devised a little experiment and I want to describe that to you right now all right what I want to do now is describe what we're going to do here I have uh five different resistors they're all a 10 watts which means they can take a lot of power without burning out I just chose large ones to not run into any problems with burning anything up the top one is 100 ohms then we have 50 ohm ohms then we have 20 ohms then we have 10 ohms then we have 1 ohm in general what happens as you reduce the resistance well according to Ohm's law as the resistor gets smaller and smaller and smaller the electric current goes up and up and up so as we decrease the resistance in the circuit if that's the only element in there we expect the current to go higher and higher what I'm telling you is that this physically large battery is going to be able to supply more current for a longer period of time than these little batteries because they're physically smaller even though in theory you would think they would do the same thing they can't because this one is just not large enough to supply the required amount of current so what we're going to do is we're going to start off with only the 100 ohm resistor and we're going to hook it up to a battery here the six volt battery and I have a table on the board that we're going to fill out the first resistor in the list is 100 ohms and we're going to in theory calculate what the uh what the uh current should be in this case what should the current be for 6 volts and 100 ohms how do we find the current according to Ohm's law I is equal to V over R you need to say that you know 50 times I is equal to V over r i is equal to V over R so 6 divided by 100 V over R should be 0.06 amps right now we already said that four AAA batteries right which is what we uh what I was holding up right here this is also about six volts yes I know it's a little more than six volts but I'm rounding to make the math a little easier but this is supplying about six volts So in theory that's what the th is in theory it should Supply also 0.06 amps all right what's going to happen when I change the resistance and cut the resistance in half well it's going to be 6 divided by 50. and I'm going to get 0.12 amps as my theoretical current 0.12 amps as well the reason it's the same is because this is a six volt battery and this is four Double A's Triple A's which is also six volts so across the same resistor it's going to give you the same thing notice this current is exactly double this because I cut the resistor in half what happens when I get to 20 ohms 6 divided by 20 0.3 amps and over here the exact thing 0.3 amps what happens when I get to 10 ohms 6 divided by 10 0.6 amps and over here 0.6 amps what happens over here 6 divided by 1 is 6 amps and over here what happens it's going to be also 6 amps I can tell you right now these little AAA batteries are never going to be able to give you 6 amps uh in fact this I'll be very surprised if this large battery could even do it because you need a physically large battery to supply that many electrons per second to keep up with what Ohm's law is telling you should be happening all right so let's go ahead and do our little experiment what we're going to do is use the 100 ohm resistor and we're going to hook up this battery to it and we're going to measure the electric current now we have to learn how to measure current the way I have this meter set up right now is as a volt meter so your meter uh whatever meter you have might be a little different but you can see that to measure voltage with v right here you have to have it over here to measure electric current the electrons have to flow through the device so you can't uh connect it here you need to connect it over on the other terminal if you're measuring current you have to push the current through the device so it has to be connected over here so I'm going to put this back where it is and what I need to do is I need to I need to let the current flow directly through uh from the battery into the uh into the device there into the measurement device and so on so what I'll do is I'll clip this battery I'll connect it right here and then it will come over and I will connect it to um connecting it right here to my uh ammeter over here measuring the electric current right and then it's going to go through the meter and then the meter is going to come over here where I'm going to connect it back through the resistor again so all I've done I'm still connecting it directly through here I'm connecting it through here but the current is also flowing through my meter so that I can measure and then I got to switch it over to amps right here and so now I'm going to connect it to both sides all right so I'm going to connect this side of the battery here I'm going to connect to the resistor right here and I'm going to connect it over here so all I've done is connected in series where my meter is is also in series with this resistor and I will connect it right here and I realize for this one you have to press this button right here this is trying to measure like AC uh AC current so I need to like press the button until it says DC so now the electric current is flowing through the resistor the 100 ohm resistor but also through the meter and it's telling me 0.06 roughly amps which is exactly what uh I calculated should happen so I'm going to go over here and put 0.06 amps there so Ohm's law is calculating what I should get in terms of the current when I physically measure the current that's exactly what I get 0.06 amps so let me disconnect that over here and I'm just going to disconnect the large battery I'm going to put it to the side and now we're going to connect the small batteries to it and we can use either these just to make it a little more interesting let me grab the double A versions which I think are a little bit fresher I haven't used them at all so here are the AAA batteries again adds up to six volts we already verified that measured that so what I'll do is I'll connect one side over here right and then the other side all I've done is replace the battery uh and we're going to measure over here what's going on what do we get 0.059 amps 0.059 0.059 amps which is very close to 0.06 and the voltage of the batteries is not quite the same so it's basically agreeing with Theory perfectly so I'm going to take this off before we drain our batteries I don't want to drain the battery so when we are not asking the cert the circuit to provide very much current both the large battery and the small battery are able to keep up there's enough surface area and chemical reaction in this little bitty battery to enable to supply this many amps uh through the circuit and that's why it agreed with Theory and there was really no difference so now what we're going to do is we're going to take this resistor out which was 100 ohms I'm going to put it aside so I don't accidentally use it and I'm going to go down to my next resistor this is half the resistance which is going to double the current uh there and we uh this is a 50 Ohm resistor so we said for 50 ohms we expect the current to exactly be doubled 0.12 amps so what I'll do is I'll connect this guy over here and we'll see exactly what it measures right here let me connect it like this what do we have 0.125 amps that's what we're measuring 0.125 so I'll put 0.125 amps it's Bingo right on the money uh able to supply the amount of current as requested by the circuit okay so now we'll disconnect this and now that we know what we're doing it's going to go a lot faster I don't have to explain every single thing we're just going to connect these smaller batteries up to it and see what we get okay now we get 0.110 let me make sure I have a good connection here just to make sure there's no connection problem 0.11 let's round up 0.111 right so we have 0.1111 amps this is still pretty close because a 0.12 0.111 it's a little bit lower but it's actually pretty good I would say that that's still agreeing with that so even asking for double the current it's able to keep up so let me go ahead and take this apart we're going to put this aside and I'm going to take off this 50 Ohm resistor I'm going to put it aside and now we're going to lower the resistance to 20 ohms for 20 ohms same voltage we expect 0.3 amps to be able to be supplied so I'm going to connect this here I'm going to put the battery connect the battery right here and I'm going to connect the other side of this resistor this is a 20 Ohm resistor here and what does it give me it gives me 0.306 so 0.306 is what this guy can supply so they match exactly all right now I'm going to take the large battery off put it aside I'm going to grab the smaller battery right here and we're going to see what it can supply 0.3 amps let's see whoa that's a little different zero it's not 0.3 0.252 0.252 amps so clearly there's I'm going to disconnect it before I start draining the batteries down I don't want to influence our experiment but you can see that right here somewhere between here and here is when the break happened what's going on here is this physically large battery is able to supply enough current in accordance with Ohm's law it's Bingo right on the money but the physically smaller battery even at the same voltage is really unable to do so it's it's not able to keep up and you can start to see it break with what the theoretical value is but let's keep going because I have more resistors and you know I bought them and I want to you know see how far we can take it so we're going to go to 10 ohms here and I'm going to take this one away and we'll get the large battery and let's see uh what the battery is able to supply here the theoretical value the theoretical value at 10 ohms should be 0.6 amps it's starting to actually be quite a bit of current and what we get here 0.562 amps so that's pretty respectable but not quite 0.6 0.562 amps but it's able to supply uh and notice it's going down a little bit here but it's able to supply pretty close I would say to the theoretical value let's go over here and connect the smaller battery and if our theory is correct this thing is not going to be able to keep up basically at all with this 0.418 I'm going to disconnect it so we don't drain anything 0.418 so the small battery was able to provide 0.418 now you might say well wait what's going on I thought he said there was a limit here and this battery can't go above the limit but it's above this one right here what's going on what I'm saying is the resistance that's connected externally is trying to quote ask for a certain amount of current in accordance with Ohm's law and it's able to get as close as it can to that but what's happening is as a percentage it can't get as close as it should get notice the percent between here and here is pretty close the percent difference if you were to calculate it between here and here is quite large so the percent error in what you're able to achieve with a smaller battery is just not going to be able to keep up it's going to get as close as it can what's going to happen it's going to drain faster and faster and faster as you start asking for that current because the chemical reaction will deplete faster all right let's go down and do uh our last resistor which is a single 1 ohm one tiny little ohm resistance and so we're going to do that one and we're going to find out that basically neither one of these batteries is really going to be able to keep up with it six amps the current is is a very dangerous amount of current you have to be careful uh with this kind of thing let's see what it can uh Supply so here we have 2.8 amps right 2.8 amps so I'll write it down 2.88 two point it's going down notice it's going down down down down because it's draining the battery so I'm going to put it I didn't see the exact numbers I'm going to call it 2.8 amps roughly speaking and let's see let's disconnect this one and connect the small battery to it right here and see what this thing does and I have to be really fast because it's going to drain this super super fast so when I connect it 1.31 notice it's going down down down down because it's draining the battery I'm going to call it 1.31 amps so 1.31 amps now notice the percent difference right if you look at the percentage between this and this obviously it's not able to get proportionally as close to the theoretical value as was able to get here so it's not like there's this like hard barrier Beyond which the batteries can't uh well there is always a physical barrier but what I'm trying to say is the point of this experiment wasn't trying to show you you know aha there's a physical barrier Beyond which these barrier these batteries can't go what I'm saying is that as you hook a load of a lower and lower resistance then the battery is going to try to push as much current out as it can to satisfy Ohm's law with that load but what happens is that as it asks for more and more and more current it can't keep up with what is demanded so these small batteries even though they have the same voltage a six volt Source they cannot Supply a high enough current and notice that the current was literally bleeding down the whole time because you're literally depleting the chemical reaction in the process and so it's not able to keep up the large battery was not only able to keep notice the break point was here for this battery it was able to keep up longer but also even when it started to diverge notice this is pretty close still but when we got it to here is when we we saw a huge Divergence but even this is almost able to supply half the current requested this is not even close so the larger batteries can get closer to supplying the theoretical amount of current for a longer period of time and of course they'll take longer to deplete as well because there's more reactants inside and so they can not only do that but they can supply the current for a longer period of time so you use large batteries when you need a higher current Source or if you just need to supply current for a longer period of time physically larger battery can supply current for a longer period of time you use these tiny batteries for very low current applications like a remote control a remote control and a television might take a milliamp or even a microamp it's it's just not going to require very many electrons to to power those little transistors inside your remote control so a small battery is sufficient and you can even get away with these very tiny batteries for these very low current applications now there's one more thing I'm going to talk about here that usually is is we save it for a little bit later when we get more detail with circuits but another way of thinking about this I've described it in terms of how many electrons it can supply but actually if you I don't want to get into it now because it's a little bit too early but if you draw the kind of the circuit equivalent of an actual battery you can model it as a voltage source but also with some internal resistance in other words this device has physical objects inside of it that have resistance and this device in the chemistry the chemical reaction and also the the the the wrapped uh foil inside of it has resistance as well which one of these things do you think is going to have the bigger resistance actually it's going to be this one smaller objects have bigger resistance because the electrons just have to cram through a smaller place to go anywhere this thing has a lower resistance so some of this effect can be described in terms of the resistance of the batteries I'm actually going to do a lesson later on that process but we have to get a little farther Beyond Ohm's law to understand how that predicts what we're doing here but for now I just want to say that Ohm's law is a linear relationship between the voltage and the current given a resistor as the load which is a linear circuit element right different than transistors and and diodes will get to later which are non-linear right and Ohm's law calculates the theory the theoretical the power supply that I'm using over here can supply enough current it can adjust itself to supply enough current uh depending on whatever is asked of it because it's coming from the wall electricity and there's a limit to that as well I can't uh you know you have a megawatt of power coming out of this thing but for anything I'm doing on the bench it's going to be able to supply enough current in accordance with Ohm's law even though this is six volts and this is six volts the theoretical currents that are requested are not always able to be uh honored for lack of a better word so we have to ask ourselves the question okay if it's true that that uh Ohm's law is always true then what's actually going on if I so if I'm uh supplying a six volts as a source and I'm doing it across a 1 ohm resistor right um then I'm calculating 6 amps this is what Ohm's law tells me but I'm not actually getting that much current doesn't that mean Ohm's law is violated doesn't that mean Ohm's law doesn't work sometimes the answer is no what's actually happening is if I were to measure the voltage on these terminal without anything connected I'm going to get the six volts but if I'm trying to demand too much current of it and I measure the voltage while that's happening I'm going to get something less than 6 volts in other words the voltage will be drooped or dropped on this thing when it's unable to supply the correct amount of current I want to show you that right now I think the simplest way to show you is to reconnect the six volt battery to it so what I'm going to do is connect this here and I'm we've got going through our meter over there right and we're going to verify again what's going on we're only getting a little bit less than the uh the three volts or the six volts that we were getting a little bit less than three volts so what I'm going to do now is actually disconnect the probe so I can actually measure the voltage while I'm going to reconnect the circuit but without the meter in place and I'm also going to go here notice I told you I had to connect it over here to measure current I'm going to go back to measuring voltage I want to show you what the voltage on this battery is when it's in operation so I'm going to put this up over here right and then what I want to do is I want to hook this thing up so I don't think I'm going to need this I think all I really need is to hook it across the battery right so we're doing the same thing I'm just hooking it across and we already know it's it's about uh two almost three amps something like that and now what I'm going to do is while this thing is an operation actually let me disconnect it while there is no current flowing what is the voltage across here the voltage is if we look up we've got to switch it over back to voltage so we're going to go to voltage what is the voltage the open circuit voltage when nothing has happened notice it's already a little bit drained because I've been using it a lot to supply a lot of current but it's at 6.2 volts but when I'm unable to supply the current right and uh I'm now asking I'm getting about three amps flowing through that what is the voltage right now the voltage is not six volts anymore it's dropped to 4.3 volts and it's dropping even more so let me disconnect that let me explain that when you have a battery not connected to anything you have What's called the open circuit voltage we saw that it was a little bit over six volts we were using the battery a little bit so originally it was 6.4 but then it was just 6.2 when I'm asking the battery give me six amps and it's like I can't this is all I can give you you think it's violating Ohm's law because it should give you this but it's not it's giving you something lower and what happens is the voltage across the battery terminals also drops because it physically can't keep up and you can also explain this in terms of the internal resistance of the battery in a future lesson I will draw that picture for you and show it to you but it's sufficient just to say that when the battery can't keep up Ohm's law is never violated the six volts that you thought you had you didn't really have it because as soon as you start asking too much current of it then the chemistry just can't keep up inside the battery voltage drops and that's why it can't Supply the correct amount of current now since we're talking about voltage I can't end the lesson without talking a little bit about AC versus DC direct current alternating current this battery all of these batteries and including the supply that I'm using here are what's called direct current and if I were to use an analogy if you look at this piece of string here with these lines on it this these little dots are meant to uh meant to be the electrons in a circuit and so if I use my imagination and say okay it's connected like this direct current is something that flows like this it comes out of one terminal and it just goes and goes One Direction over and over and over again and it just keeps going the voltage is only in One Direction and the electrons are only going one way over and over and over and over again direct current but in alternating current what's happening is things are alternating Direction what happens is the current might flow out of one terminal of the battery for a little bit and then switch directions and then start going the other direction the other direction like this and then stop and then switch Direct questions and then come back the other direction like this and then stop and then go back the other way and then go back the other way and it alternates back and forth back and forth back and forth back and forth back and forth over and over again forever now in the United States the frequency of the switching back and forth is 60 hertz which is the switching happens 60 times every second right but in other countries it's 50 hertz and other countries has different frequencies and it's related to how the electricity is generated at the power plants basically what you have is some sort of steam generator usually from coal or from nuclear and the steam is turning a generator the generator is a coil of wire and a magnetic field and it's rotating and because of the rotation the you get the backwards and forward motion of the electrons I'm not going to get into it here but it's because of the rotational motion of the generators in the large power plants that's really why we have AC current also it's much more efficient to transmit AC electricity over long distance says if you try to do it with DC you you'll have a lot of losses due to heat it's not very practical so we have the generation and transmission in terms of AC when we get it down into our walls we also are using AC coming right out of the walls but our portable devices like our batteries are all what we call DC only one direction of the voltage and of the current flow I hope you've enjoyed this deeper dive into the concept of voltage I really wanted to focus on voltage of course using Ohm's law as well next lesson will be on a little deeper dive look at current and a little deeper dive looking at resistance and then we'll get into more complex circuits so I hope you've enjoyed this please drop me a note let me know what you think follow me on to the next one learn anything at mathandscience.com

Channel: Math and Science

Views: 56,341

Keywords: Ohm's Law, voltage, current, resistance, electrical circuits, electrical engineering, electric potential, electric charge, Ohm's Law formula, circuit analysis, circuit design, circuit theory, electrical components, electrical power, electrical energy, electrical units, electric circuit calculations, circuit simulation, electric circuit examples, electric circuit problems, electric circuit projects, electrical basics, electrical tutorials, what is voltage, what is ohms law

Id: Z_jthQa9xtc

Length: 53min 42sec (3222 seconds)

Published: Thu Apr 13 2023