Transformer currents & energy losses (intuition)

suppose you have a bulb which requires a 100 volt to power up and let's say if somewhere far away from your city there's a power station which generates exactly that hundred volts then you might think let's just connect them with cables and we'll get what we want right but that's not what we do in real life instead at the power station we use a transformer and step up that voltage let's say by 10 times to make it a thousand volt and then near our house we use another transformer to step that voltage back down to whatever we need how does this make any sense why do we do that well transmission line wires which are so many kilometers long have considerable resistances which you cannot neglect and you might know that current flowing through a resistance heats up causing power loss wait a second how does using transformers help in reducing the power loss that's exactly what we'll explore in this video i want to actually show you what happens to the currents when the voltage gets stepped up or stepped down and once we get that we'll come back over here towards the end of the video and answer our question so since the current everywhere finally depends upon the bulb that we're attaching over here let's start by analyzing the current in this circuit before we look at the currents a quick recap what decides the voltages we've seen in a previous video that the voltage over here and here purely depends upon the number of turns so in this example we are assuming the turns over here is 10 times less than the number of turns over here and as a result the voltage over here will be 10 times less than the voltage over here so this is a step down transformer now if that is not clear or you need a refresher on that feel free to go back and check our video on introduction to transformers anyways now let's think about the currents for example if you look at this circuit how much current do you think will flow over here well that completely depends upon the resistance of the bulb right i know the voltage so i need the resistance to keep things simple let's say the resistance over here was a 100 ohms then from ohm's law the current would be 100 divided by 100 that's going to be 1 ampere so there'll be a 1 amp current flowing it's an alternating current flowing over here but now the question that i want to ask you is how much current do you think will flow here that's an interesting question because this is a different circuit altogether how do we figure that out well we can use one of the basic principles of physics energy conservation we can say that look in a transformer there is energy electrical energy being transferred from here to here so whatever energy is lost by the charges in this circuit must be exactly gained by the charges in this circuit if this is an ideal transformer where there is no energy loss and that's a big if because in reality there will always be energy losses for example you might recall due to the fluctuating current there will be a fluctuating magnetic field in that ferromagnet and turns out the fluctuating magnetic field generates heat in the ferromagnet we call this the hysteresis loss i'm not going to talk about hysteresis what matters is there is heat generated that's an energy loss on top of that this fluctuating magnetic field also generates what we call eddy currents on the surface of the ferromagnet which further heats up the transformer more energy loss and not to mention we assumed all the flux generated over here links over here which is not true turns out in general there will be some flux leakage meaning more energy loss so you get the point no transformer is 100 efficient but let's forget about all of that not for your exams but as of now forget about all of that and let's assume that this is a 100 efficient perfect transformer then energy is conserved my question to you is can you pause the video and think a little bit about by using energy conservation electrical energy can we can you figure out how much current would be flowing in this circuit pause and give this a try okay hopefully you've tried because we are having an energy continuous energy transfer it might make more sense to talk about energy transfer per second which is power and so we can now say whatever is the power input is exactly equal to the power output so power input should exactly equal the power output and how do we calculate electric power we calculate that as the product of voltage and current so the input power would be the input voltage i'm just going to write vi that's our 10 000 or sorry thousand multiplied by the input current which i need to calculate and that equals the output power i'm just going to write as v out which is our 100 multiplied by the output current now instead of substituting let's do this logically it's saying that the product of the voltage and the current must be the same on both sides now because the voltage here is 10 times more than the voltage over here this means that the current over here must be 10 times less than the current over here only then the product will be the same right therefore the current over here don't worry too much about the direction the current direction will have the same direction same sense as this circuit but don't worry about the direction okay the current will be 10 times less so it's going to be 0.1 ampere now i want to spend a couple of minutes over here because this has confused me a lot the equation is telling us for transformers that when you step down a voltage the current increases and similarly if you were to step up a voltage the current would decrease and i'm like how does that make any sense why is it that if the voltage is higher the current should be smaller i mean from the equation it makes sense but why shouldn't be the other way around shouldn't more voltage give me more current ohm's law well we need to be careful ohm's law works for a circuit within a circuit so over here if the voltage increases current will increase voltage decreases current will decrease but here we are comparing voltages and the currents of two different circuits they can have whatever values they want so don't compare voltages and currents of two different circuits and think about ohm's law okay but still this equation did not make much intuitive logical sense to me and i struggle with this for for years but i think i think finally i have a decent explanation to understand why in a transformer if you have more voltage you'll end up with less current so for this let's go back to the basics and ask ourselves what's the meaning of a voltage well remember voltage basically means joules per coulomb and so 1000 volts basically means thousand joules per coulomb what does that mean that means that if there was a coulomb of charge that moved from here to here then it would lose thousand joules of energy to transfer that to the blue circuit so let's say here is the coulomb of charge and this cloud represents thousand joules when it moves down it would lose that thousand joules to the blue circuit okay and on the other side we have hundred volts potential difference here what that means is 100 let me write that over here 100 joules per coulomb and since here we are gaining energy this means that if a coulomb were to move from here to here it would gain 100 joules of energy again here's our coulomb and as it's moving it will gain only a hundred joules of energy and so now the question is how can this coulomb lose a thousand joules but this coulomb only gains a hundred joules how can that be ah here's the here's how i like to think about it this coulomb talks to this coulomb and says hey because you're giving me a lot of energy and i can't take all of that in one go maybe i'll take multiple rounds maybe i'll just take 10 rounds and in each round i will take only 100 joules and that's what it does and that's why the coulomb over here has to travel 10 times faster than the coulomb over here now of course the animation is not perfect first of all i'm not showing 10 rounds i'm only showing five rounds and the current is supposed to be alternating i'm not showing any of that just to keep things simple but you get the idea right because we are stepping down voltage we are forcing this coulomb to accept less energy and as a result it has to go faster and take multiple rounds and that's why stepping down voltage increases the current and of course something similar is happening near the power station side as well because we are stepping up the voltage this time it's the coulomb that is receiving the energy that is traveling slower because it is receiving way more energy than the coulomb over here can give and so stepping up the voltage has to decrease the current so now we can look at the big picture without the transformers the transmission lines would have had one amperes of current but with the transformer by stepping up the voltage by 10 times we have reduced the current in the power lines by 10 times and so now if we factor in the resistance of these transmission lines which is very real then remember the power dissipated the amount of heat dissipated per second in the transmission lines is given by i square r and since the current over here is 10 times smaller than the current over here the power dissipated over here would be a hundred times smaller than the power that would get dissipated over here which kind of makes sense because the charges are flowing very slowly over here less collisions are happening and so you would expect low power dissipation now at this point i had one more confusion yeah i used to be a confused kid see people always say power loss or heat dissipated is i square r i square our losses but hey power can also be written as v square by r and so if i look at this equation with more voltage i would get more power loss so doesn't that mean stepping up the voltage actually increases the power loss what's going on over here can you pause the video one more time to see and see if you can explain this yourself all right remember where this comes from this comes from ohm's law by substituting v is equal to ir and ohm's law is always applied across a resistor so this voltage is not this voltage or this voltage this is the voltage that would come across the resistor and that voltage is basically i times r which means over here since the current is 10 times smaller even that voltage across this resistor has also reduced by 10 compared to the voltage over here and so yeah because there is some voltage drop happening not all the thousand volts will appear over here some of the voltage drop will appear over here but that amount is much smaller than what you would get here a lot of that hundred volt would get appeared over here does that make sense so even voltage wise if you look at it power dissipated has reduced stepping up voltage helps in efficient power transfer and now you may ask well then why just step it up to a thousand volt why not say 10 000 volt and and you're right uh in in reality the transmission lines carry currents at very high voltages hundreds of thousands or sometimes you step it up to even millions of volts and finally you may be one of those people who might say why million when we can do a billion i mean if you step it up to a billion world then the current would be almost negligible you'll have almost perfect power transmission right well yeah theoretically yeah but remember to step up voltage you'll have to put more windings appropriately so good luck with that but even if you do that well there are other problems now with a billion volt voltage potential difference we can ionize the air and that will start giving us lightning everywhere that's not good so yeah there are practical limitations to how you can go but if you keep that in mind then yeah higher you go better would be the power transmission