**Concept:** Transformers

Hey guys, in this video we're going to talk about an application of 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 in North America is delivered to the home via an outlet at 120 volts, okay? This is typically too large for household, delicate household 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, so 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 the 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, okay? A transformer is a circuit element, it's something that you place inside of a circuit that does exactly this, it uses FaradayÕs law to convert large voltages into small EMFÕs, okay? So, I have a picture here of a very classic transformer, just two solenoids placed near one another, okay? The solenoids have different numbers of turns, which is going to be very important, when we talk about transformers. Now, V1 is the voltage at which one solenoid operates, let's call it the input solenoid, and V2 is the voltage at the second solenoid being called the output solenoid operate operates that. 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 EMF V2, 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 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. 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 turn made, but you need to make a second solenoid to complete your transformer. What is the least number of turns the second solenoids could have? Alright, so first of all, let's apply the left half of our transformer equation V2 over V1 is going to be 15, we said, 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 N1 over N2. Now, all we said was that we had one solenoid with 50 turns and we needed to make another solenoid, we never said which solar was the input solenoid and which was the output solenoid, we're free to choose and we want to choose, so that we create a second solenoid with a smallest number of turns, because this equation has two possible outcomes, right? We can say N1 is N2 divided by 8, that's one output, or we can say N2 is 8 times N1. In either instances, 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 into, we plug it into the bottom equation, we're saying that, that 50 term 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 terms? If I plug 50 into here, I get 6.25 turns; if I plug 50 into here, I get 800-, sorry, 400 turns. So, clearly, 6.25 is a smaller number than 400, so the smallest number of turns the second solar should have is 6 and a quarter, if the second solenoid is the input solenoid, right? If it's in 1. If we want our second solenoid to be the output solenoid, it'll be 400 turns, which is not the answer to the question, the question is what's the fewest number? The fewest number is 6 and a quarter, and that is if our second solenoid is out-, sorry, input solenoid and the solenoid that's already made with 50 turns is the output solenoid. Alright guys, that wraps up our discussion on transformers. Thanks for watching.

**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?

Consider an ideal transformer consisting of a primary coil of N _{1} = 240 turns and a secondary coil of an unknown number of turns, N_{2} as shown below. The primary coil is connected to a function generator, which is set to produce a sinusoidal peak-to-peak voltage of 16 V. Using Using the oscilloscope, a student measures the peak-to-peak voltage difference across the secondary coil to be 56 V. What is N_{2}?

a) 70

b) 720

c) 840

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You need a transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is completed through a 55 Ω resistor. What is the effective resistance of the secondary circuit?

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You need a transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is completed through a 55 Ω resistor. How many windings should the secondary circuit contain?

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