Hey guys. In this video, we are going to talk about an application of electromagnetic induction to create a circuit element called the transformer. Now transformers are very important in delivering power from power generators all the way to the home. Okay? Let's get to it. Now power in North America is delivered to the home via an outlet at 120 volts. This is typically too large for household delicate appliances like electronics such as a laptop to operate. And in fact, the power generated at power stations isn't even at 120 volts. It has to somehow decrease by the time it gets to your house in order to arrive at your house at 120 volts.

Now remember, whenever a coil has a changing magnetic field, I have one coil here with some magnetic field that's changing, it can induce an EMF on a second coil. There's some induced EMF on the second coil if the magnetic field is changing. This is just what Faraday's law tells us. This is a process of electromagnetic induction. This induced EMF, if we choose these coils carefully, can be tuned to be as small as we need. This is the concept of what a transformer is. A transformer is a circuit element. It's something that you place inside of a circuit that does exactly this. It uses Faraday's law to convert large voltages into small EMFs.

So, I have a picture here of a very classic transformer, just 2 solenoids placed near one another. The solenoids have different numbers of turns, which is going to be important when we talk about transformers. Now v1 is the voltage at which one solenoid operates, let's call the input solenoid, and v2 is the voltage that the second solenoid, we can call it the output solenoid operates at. Now if v1 is changing continuously, then this magnetic field that I drew here is going to be changing as well. So the magnetic flux through this solenoid is going to be changing as well, and it's going to produce this EMFv2. And the relationship between those voltages in the transformer depends upon the ratio of the number of turns of these solenoids. Okay? This equation governs how a transformer works. That the ratio of the output voltage to the input voltage equals the ratio of the number of turns in the output solenoid to the input solenoid.

Alright? Let's do a quick example of this. You need to build a transformer that drops 120 volts of a regular North American outlet to a much safer 15 volts. You already have a solenoid of 50 turns made, but you need to make a second solenoid to complete your transformer. What is the least number of turns the second solenoid could have?

Alright. So first of all, let's apply the left half of our transformer equation. V2V1 is going to be, 15, Right? 15 volts is our output voltage divided by 120. This is 1 over 8. Okay? And now the right-hand side of this equation says this is equal to n1n2. Now all we said was that we had one solenoid with 50 turns, and we needed to make another solenoid. We never said which solenoid was the input solenoid and which was the output solenoid. We are free to choose. And we want to choose so that we create a second solenoid with the smallest number of terms. Because this equation has two possible outcomes. Right? We can say none is ntwo divided by 8. That's one output, or we can say ntwo is 8 times none. In either instance, the n that goes into these two equations is going to be our 50. If we plug 50 into the top equation, then we're saying that our already made solenoid is the output solenoid n2. If we plug it into the bottom equation, we're saying that that 50-turn solenoid is our input solenoid. But either way, we can create a transformer. The question is, which one will require a second solenoid with the least number of turns? If I plug 50 into here, I get 6.25 turns. If I plug 50 into here, I get 400 turns. So clearly, 6.25 is a smaller number than 400. So the smallest number of turns the second solenoid could have is 6.25. If the second solenoid is the input solenoid. Right? If it's none. If we want our second solenoid to be the output solenoid, it will need 400 turns, which is not the answer to the question. The question is, what's the fewest number? The fewest number is 6.25, and that is if our second solenoid is the input solenoid, and the solenoid that is made with 50 turns is the output solenoid.

Alright, guys, That wraps up our discussion on transformers. Thanks for watching.