Transformers - Online Tutor, Practice Problems & Exam Prep

Transformers utilize electromagnetic induction to convert high voltages to lower voltages, essential for safe household power delivery. According to Faraday's law, a changing magnetic field in one coil induces an electromotive force (emf) in a nearby coil. The voltage ratio between input and output coils is determined by the turns ratio: VV = NN. For example, to reduce 120 volts to 15 volts, a transformer with a 50-turn coil can require a second coil with as few as 6.25 turns, demonstrating the efficiency of transformers in electrical circuits.

Transformers

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.

Example

Hey, everyone. Let's work through this problem together. Here, we're told that we need to build a transformer that drops the 120 volts of a regular North American outlet down to a much safer 15 volts. Now we already have a solenoid with 50 turns, but we need to make a second solenoid in order to complete our transformer. Now here, we want to determine the least number of turns that this second solenoid could have.

So let's go ahead and get started here. Now we know that the ratio of the voltages in our transformer depends on the ratio of the number of turns in our solenoids. That means that \( \frac{V_2}{V_1} \) is equal to \( \frac{N_2}{N_1} \). Now we have both our input and our output voltages here. So this ratio on the left hand side is going to be \( \frac{15}{120} \).

So this will be equal to \( \frac{N_2}{N_1} \). Now we can reduce that fraction. This ends up giving us \( \frac{1}{8} \) is equal to \( \frac{N_2}{N_1} \). Now in our problem, we're told that one of our solenoids has 50 turns, but we're not told which solenoid. So that means that there are 2 possible outcomes here, one in which \( N_1 \) is equal to 50 and one in which \( N_2 \) is equal to 50.

So we need to test both of these outcomes and see which one results in our other solenoid having the least possible number of turns. So let's go ahead and plug these \( N \) values into our ratio here. Now if \( N_1 \) is equal to 50, this then makes our ratio \( \frac{1}{8} \) is equal to \( \frac{N_2}{50} \). Now this means doing some algebra that \( N_2 \) is equal to \( \frac{50}{8} \) or 6.25 turns. Now if \( N_2 \) is instead equal to 50, then this makes our ratio \( \frac{1}{8} \) is equal to \( \frac{50}{N_1} \).

This means that \( N_1 \) will then be equal to 50 times 8 or 400 turns. Now comparing these two values, 6.25 turns is clearly fewer turns than 400. So this means that if \( N_1 \) is equal to 50, this results in our second solenoid having the least possible number of turns, 6.25. Feel free to let us know if you have any questions here, and let's keep going.

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

Here’s what students ask on this topic:

What is the principle of operation of a transformer?

A transformer operates on the principle of electromagnetic induction, as described by Faraday's law. When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field. This changing magnetic field induces an electromotive force (emf) in the secondary coil. The voltage induced in the secondary coil depends on the ratio of the number of turns in the primary coil to the number of turns in the secondary coil, given by the equation:

$\frac{V_2}{V_1}=\frac{N_2}{N_1}$

How do you calculate the number of turns needed in a transformer coil?

To calculate the number of turns needed in a transformer coil, you use the turns ratio formula:

$\frac{V_2}{V_1}=\frac{N_2}{N_1}$

Here, $V_1$ is the input voltage, $V_2$ is the output voltage, $N_1$ is the number of turns in the primary coil, and $N_2$ is the number of turns in the secondary coil. Rearrange the formula to solve for the unknown number of turns.

Why are transformers important in power distribution?

Transformers are crucial in power distribution because they allow the efficient transmission of electrical power over long distances. High voltages are used to minimize energy loss due to resistance in the transmission lines. Transformers step up the voltage at the power generation site and step it down at the distribution end to safe levels for household and industrial use. This process ensures that electrical power is delivered efficiently and safely to consumers.

What is the difference between a step-up and a step-down transformer?

A step-up transformer increases the voltage from the primary coil to the secondary coil. It has more turns in the secondary coil than in the primary coil. Conversely, a step-down transformer decreases the voltage from the primary coil to the secondary coil, having fewer turns in the secondary coil than in the primary coil. The turns ratio determines whether the transformer is step-up or step-down.

How does Faraday's law apply to transformers?

Faraday's law of electromagnetic induction states that a changing magnetic field within a coil of wire induces an electromotive force (emf) in the coil. In transformers, an alternating current in the primary coil creates a changing magnetic field, which induces an emf in the secondary coil. The induced voltage in the secondary coil is proportional to the rate of change of the magnetic flux and the number of turns in the coil, as described by Faraday's law.