Heating effect of current

you may already know that when electricity passes through any material like say this wire over here then it starts producing Heat this is the same reason why your mobile phones tend to get hot when you play games on them so on one hand we could say this is a wastage of electricity because some of the electrical energy is getting converted into unwanted heat but on the other hand this means we can now create heat from electricity we don't have to depend on fire anymore and so this is the principle behind your iron boxes today or maybe electric toasters or even light bulbs the light that we get is because of the heat that is generated due to electricity and of course an extreme example would be when lightning strikes a tree the heat produced is so much that it catches fire so whether it's for good or bad or worse in this video you'll see why this electric current which is just a full of electrons produce heat and we'll also learn how to calculate the amount of heat generated due to the electricity all right so let's first begin with the name of this phenomena this is simply called the heating effect of electricity but it's also often famously called Joule heating and that's because it's this guy James zhu was the first person to study the relationship between electricity and heat in detail and if you're wondering then yes the SI unit of energy jus is named after the same person but let's come back to our question what causes Joule heating in all these cases well the main reason for this is coalition cohesion between electrons and atoms so let's look at that in a little bit more detail so to understand where this heat comes from let's zoom into this wire and let's say we zoom in all the way to the atomic level so that we can see the individual atoms that make up the wire now when we have an electric current basically there are electrons flowing through this material now here's the important thing these electrons don't flow in straight lines instead whenever they encounter an atom in their path they bounce off of these atoms so these electrons are continuously colliding and bouncing off of different different atoms as they move forward and during the collision these electrons transfer some of their energy to the atoms think about it it's like a very small stone coming and hitting a big stone it transfers some energy to that big stone isn't it similarly the electron transfers some energy to the atoms and as a result the atoms start shaking they start healing and now you can imagine what would happen if we had lots and lots of electrons you know going and colliding with these atoms these atoms start jiggling a lot and whenever the atoms of them of any material start jiggling that's when the material heats up so basically whenever we have an electric current whenever we have electrons flowing through any material because of the collision between the electrons and the atoms the electrons transfer some of the energy to the atoms making those atoms jiggle and as a result the material gets heated up okay now that we have some idea behind how Joule heating works let's go ahead and see if we can figure out a connection between the amount of heat generated and electricity and for that let's get rid of this picture and consider a filament of light bulb let's say that the current through the light bulb is I and let's assume that the potential difference across the filament is V viii now to calculate the amount of heat generated all we need to do is use energy conservation you see we know that it's the electrical energy that's being converted into heat so for example if we find out that hundred joules of electric energy is being lost every second then it means hundred joules of heat is being produced every second so you see all we need to do is calculate how much electrical energy is lost over here every second and then we are done and we've already seen in a previous video how to do that we've seen that the amount of electrical energy that is lost or gained per second which we often call electric power turns out to be just the product of voltage and current and current and if you're interested in knowing where this comes from then we have discussed this in great detail in a previous video so it would be a great idea to go back and watch that video for this but anyways this number tells us how much electrical energy is being lost every second and since it's being converted to heat it also means this tells us how much heat is being generated over here for a second so this number so let's write that now this number okay this represents heat produced per second so in one second this is the amount of heat generated in ten seconds well the heat generator will be ten times this number and so in general we can now write the amount of heat generated will be this number the amount of heat generated per second per second times T times T and there we have it it's not a new formula because we already knew how to calculate electric power lost or gained so this formula tells us that if we have more current then we have more heat generated and that kind of makes sense if we have more current then there'll be more electrons passing for a second and as a result we will have more collisions happening per second and so we'll have more heat generated per second the formula also says more voltage means more heat why is that well remember both it is potential difference which is an indicator of how much potential energy these charges have these electrons have and so more voltage means they have more energy and I'm pretty sure you agree if something were to come and hit these atoms with more energy the atoms would vibrate more rigorously more violently and as a result we would expect more heat to be generated when lightning strikes a tree the voltage and current are both super high and as a result the heat generated is incredibly high enough to burn that tree all right what if we don't know the voltage and the current but maybe we know the voltage and the resistance or maybe the current and the resistance can we still calculate the amount of heat generated the answer is yes because we know what's the connection between voltage current and resistance Ohm's law it tells us that voltage is current times the resistance and so what we can do is in this formula substitute for V as IR and then we'll get IR times I and so that will give us I squared R times T so this is another formula in terms of current and resistance and similarly over here we can substitute for I as we all are in that case what we would get is V over R so V squared over R V squared over R times T and this is a formula that tells us how much heat is generated in terms of voltage and resistance and these are not really different formula these are all identical formula they all come from the same one so don't think about them as two three different ones basically this is our formula and we just substitute Ohm's law and we get the other two so that's pretty much it but before we conclude I just want to talk about a couple of technical details one is whenever we have heat generated due to electricity we often term it as power dissipated dissipated so if you're ever asked to calculate the power dissipated we basically have to calculate how much heat is generated for a second and the second thing is when Joule was doing the experiment to figure out the relation between electricity and heat he figured out this formula experimentally without doing any mathematics and it's for that reason this formula is often called joules law joules law of heating but back then we didn't know where this formula came from but today we know that this formula is identical to this and this as well and so today we can treat any of these three formulae as joules law of heating