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30. Induction and Inductance

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Hey, guys, In this video, we're going to talk about an application off electromagnetic induction to create a circuit element called the Transformer. Now, transformers are very, very important in delivering the power from power generators all the way to the home. Okay, let's get to it now. Power and North America is delivered to the home via an outlet at 120 volts. Okay, this is typically too large for household, a delicate household appliances like Elektronik, such as a laptop toe 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, so I have one coil here with some magnetic field that's changing. It can induce an IMF on a second coil. There's some induced E M f 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 the IMF. 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. Okay, 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. Okay, so I have a picture here of a very classic transformer just to Seoul Annoys placed near one another. Okay, the soul annoys have different numbers of turns, which is going to be very important when we talk about transformers. Now, the one is the voltage at which one soul annoyed operates. Let's call it the input soul annoyed. And V two is the voltage that the second solenoid we can call the outputs Illinois operates at now. If the one is changing continuously, then this magnetic field that I drew here is going to be changing as well. So the magnetic flux through this solo it is gonna be changing as well. And it's going to produce this E m f V two and the relationship between those voltages in the transformer depends upon the ratio off the number of turns of these solar noise. Okay, this equation governs how it transformer works that the ratio off the output voltage to the input voltage equals the number of turns in the output solenoid to sorry. The ratio of the number of turns in the output solenoid to the number of turns in the input solenoid. All right, 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 soul in order to 50 turns made. But you need to make a second soul annoyed to complete a transformer. What is the least number of turns? The second solo we could have. All right, So first of all, let's apply the left half of our transformer equation V two over V one is going to be 15. We said 15 volts is our output voltage divided by 120. This is 1/8. Okay. And now the right hand side of this equation says this is equal to in one over in two now, always said was that we had one soul annoyed with 50 turns, and we needed to make another soul annoyed. We never said which solenoid was the input solenoid in which was the output solenoid. We're free to choose and we want to choose so that we create Ah, second soul annoyed with the smallest number of turns because this equation has two possible outcomes, right? We can say in one is in two divided by eight. That's one output or we can say in two is eight times in one. In either instances, the in that goes into these two equations is gonna be our 50. If it we plug 50 into the top equation, then we're saying that our already made solenoid is the output solenoid into. If we plug it into the bottom equation, were saying that that 50 term solo it is that our input soul annoyed. But either way we can create a transformer. The question is, which one will require a second soul annoyed with the least number of terms. If I put 50 into here, I get 6.25 turns. If I plug 50 into here, I get a hunt. Sorry, 400 turns so clearly 6.25 is a smaller number than so the smallest number of turns. The second solo it could have is six and a quarter. If the second soul annoyed. Okay, is the input Seoul annoyed? Yeah, right. If it's in one, if we want our second soul annoyed to be the output solenoid, it'll need 400 turns, which is not the answer to the question. The question is, what's the fewest number? The fewest Number six and a quarter. And that is, if our second solenoid is the out that's already input solenoid and the soul Lloyd that's already made with 50 turns. Is the output soul annoyed? Alright, guys, that wraps up our discussion on transformers. Thanks for watching.

2

Problem

An outlet in North America outputs electricity at 120 V, but a typical laptop needs to operate at around 20 V. In order to do so, a transformer is placed in a laptop’s power supply. If the coil in the circuit connected to the laptop has 20 turns, how many turns must the coil in the circuit with the outlet have?

A

3 turns

B

6 turns

C

20 turns

D

120 turns

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