A model-train transformer plugs into 120-V ac and draws 0.35 A...

Question

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.5 A to the train.

(a) What voltage is present across the tracks?

(b) Is the transformer step-up or step-down?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight the key pieces of information that we need to use in order to solve this problem. What voltage is supplied to a toy car? If its power adapter plugs into a 230 volt ac outlet draws 0.45 amps and supplies 9.0 amps to the car. Is the adapter a step up or step down transformer. OK. So for this particular prompt, it appears our end goal, the final answer I should say answers that we're ultimately trying to solve for is our first answer. We're trying to figure out what the volt, what voltage is supplied to this particular toy car, considering that its power adapter is plugged into a 230 volt ac outlet. And considering all the conditions set by the pro itself, considering that it draws 0.45 amps of current and supplies 9.0 amps occur to the car. So considering these key pieces of information, we're trying to figure out what the voltage is supply. So considering this, we're trying to figure out what voltage is supplied to the car. That's our first answer. And then our second answer, we're asked to determine whether the adapter is a step up or step down trans. So now that we know that we're trying to solve for the voltage for this particular problem and determining whether or not this adapter is a step up or step down transformer. Let's read off our multiple choice answers to see what our final answer might be noting that all of our answers for the voltage are in units of volts. And of course, our second answer would either be a step up or a step down transformer in order to save time. I'm just gonna say step up or step down, we know we're talking about transformers. So A is 12 and step down B is 22 and step up C is 34 and step down and D is 55 and step up. OK. So our first step, what we need to do first off is we need to write down all of our known variables. So we know right off the bat that our primary voltage which we'll call VP, our primary voltage is equal to 230 volts. We also know our primary current, which we're gonna call IP and our primary current is equal to 0.45 amps. And we're also, we know what the problem tells us. We're told that the secondary current which we're gonna call is and our secondary current is equal to 9.0 amps. Awesome. So now we're at the stage where we need to identify and use the relevant formula that we're gonna need to use in order to help us solve for our final answer. And the final answer that we're ultimately trying to solve for us, we're trying to figure out what the secondary voltage value is. That's the value that's unknown to us. So now that we know that we're trying to solve for the secondary voltage, we need to recall and use the relationship between voltage and current inside of a transformer, which as we should recall, we could write this relationship equation as vs divided by VP, which means the voltage, the secondary voltage vs divided by the primary voltage VP is equal to the number of secondary turns divided by the number of primary turns. And we also know that the we also know is which is the secondary current divided by the primary current IP is equal to the number of primary turns divided by the number of secondary turns. So this these two relationship equations will help us determine or you know, will help us determine also lead us to the following piece of knowledge. So this will lead to the voltage current relationship. So as we should recall, the voltage current relationship states that vs divided by VP is equal to IP divided by is awesome. So now we need to take this equation and we need to rearrange it to isolate and solve for vs which is the final answer we're ultimately trying to solve for. So using a little bit of algebra, we will find that vs is equal to VP multiplied by IP divided by is awesome. Fantastic. So now all we have to do is we just need to plug in all of our known variables into this equation to solve for the numerical value of vs which is the first final answer that we're trying to solve for. So we know that vs is equal to, we know the value for VP because we know our primary voltage which is 230 volts. And we need to multiply this by our primary current which is 0.45 amps. And we need to divide it by our secondary current which is 9.0 amps. So when we plug that into our calculator, we will find out that vs is equal to 11.5 volts, which will be round to two significant figures or to the nearest whole number, which is approximately equal to 12 volts. And that is our final answer. Hooray, we did it or for our first answer, but we're not quite done yet. We need to determine the type of transformer. So we need to note this is important to write down, this might be a really important thing to know later on. So in order to determine the type of transformer, we need to note that since vs the secondary voltage is less than the primary voltage because this me me this is very important because we know that the secondary voltage is less than the primary voltage. This has to be a step down transformer. And that's it. That's our final answer. For our second answer that we were asked to solve hooray, we did it. So the voltage that is supplied to the toy car is approximately equal to 12 volts and the adapter is a step down transformer. Awesome. So looking at our multiple choice answers, the correct answer has to be the letter A which once again is 12 volts and step down transformer. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.5 A to the train.
(a) What voltage is present across the tracks?
(b) Is the transformer step-up or step-down?

Key Concepts

Ohm's Law

Transformer Basics

Power Conservation in Transformers

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