# Transformers - Power Transmission

**Transformers** are used to change one current into another current. Step up transformers increase the voltage of the current while step down transformers decrease the voltage. In **power transmission**, which is power transmitted through wires over large distances, there is a power loss due to the resistance caused by ( I^2)R heating. In this process, step up transformers are needed to pump up the voltage using AC.

So let's talk about Transformers and Power Transmission so this is actually a very very important aspect of electricity and magnetism that's only been known since about 1885 maybe a little bit before that when Nikola Tesla really pushed the idea so here's the idea.

When we try to transmit power through long power lines we always suffer a loss. We suffer a loss of power due to what's called I squared r heating and that's because every wire no matter what we make it of is going to have some resistance you know some resistance because that material has a resistavity and that means the longer the wire the more the resistance so if we've got a wire that's 10 feet long, nobody cares. If the wire is 1000 miles long, leads to a problem and so we get this heating associated with I squared r so notice that this heating will become smaller if I can make the current really small so all we need to do is just transmit power at a really low current but we tried to do that with dc we got a major problem because low current means we don't have very many electrons doing anything and with dc power that's what you need you need the electrons doing stuff so if we've got a small current there's no reason to transfer the power anyway because there's not very much power, so alternatively what we can do using alternating current is we can step up the voltage. Now what's beautiful about this is that using ac current and using the electromagnetic induction when we bump up the voltage the power has to remain constant. Now the power that we're transmitting is IV current times potential difference that has to remain constant so if we bump up the voltage say by a factor of a hundred then what has to happen in order for I times V to remain the same, well it means we got to bump down the current by a factor of a hundred. Now when we send that into the transmission line, now I is down by a factor of a hundred so that means I squared r is down by a factor of 10,000 so this is very very very useful and in standard communities you'll use a step up transformer like this to bump up the voltage from a standard household like 120 volts all the way up to standard transmission voltage 450,000 volts and that's the way that it works.

Alright so let's look and see how a transformer is built, so based on the idea of electromagnetic induction but we've got to do a little bit of stuff to make it feasible so here's what we're going to do, we're going to have our primary and we have the wire coming and this is what's carrying the current and he wraps around an iron core alright, we need to use iron or some other soft ferromagnetic material it needs to be magnetic but it needs to also be very transient in its magnetism so it just need to listen to whatever an external magnetic field is telling it do, a permanent magnet would not work as the core of a transformer so let's see why. Alright we've got this incoming current, we wrap it around part of the iron core some number of times the number of times I'm going to call n sub p for number of primary turns alright? And then we send it out. Now this current is going to come through and because it's a current it's going to generate a magnetic field. Now what happens to that magnetic field? Well this is a soft Ferro magnet, so if the magnetic field associated with this guy is pointing up then the whole iron core will generate a magnetic field that circulates around with the magnetic field that the primary is asking it to use and look what happens. Now there's a magnetic field over here that's threading the secondary part of the circuit. Now just leaving it that way nothing happens alright that be like dc alright we got a magnetic field what do you want? There's a magnetic field, in order to use electromagnetic induction or the Faraday - Lenz law, we need to change this magnetic field and the that way we're going to do that is by changing this current that's going into the primary and we're going to do that using ac so we're going to change it 60 times per second, now what that does is it changes this magnetic field therefore changing that magnetic field and changing the flux of that magnetic field through this part of the circuit.

So through electromagnetic induction what that does is it generates a current over here so we had a current over here changing that current changes the magnetic field circulating through the iron core and then that changes the magnetic flux running through here and then through Faraday - Lenz that generates a current over here and it's a bit to think about but it kind of make sense you know it takes a minute to really get into all that you know magnetic field going through here whatever, but what ends up being the case is that the potential difference between these two parts of the wire is proportional to how many wraps of wire we have, and that means the ratio of the secondary potential to the primary potential is equal to the ratio of the number of turns and that's a Geometrical fact how many times did you turn it around, over the secondary side to the number of turns on the primary side. So that means that if come in and I only wrap once and over here on the secondary side I wrap a hundred times then the voltage over here on the secondary side will be a hundred times bigger than the voltage over here on the primary side, and that means that the current's going to be a hundred times smaller. And so this is called a step-up transformer because it steps my voltage up by a factor in this case a four thirds okay maybe this isn't a very good step-up transformer but whatever and then I'll step it up I'll transmit my power over how many hundreds of miles I need to from the power plant to the houses and then at the houses I run this guy backwards stepping on back down and I'm good to go. Again one of the wonders of ac power that we could not get from the old dc system and that's transformers and power transmission.

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