the-circuit-above-has-two-resistors-in-parallel-the-first-r_1-will-have-its-resistance-steadily-incr

Question

The circuit above has two resistors in parallel. The first, $R_{1}$ , will have its resistance steadily increased. The second, $R_{2}$ , will have a constant resistance of $R_{2}=4 \Omega .$ Which of the following graphs correctly depicts the total resistance of the circuit, $R_{\mathrm{T}}$ , as a function of $R_{1} ?$
a. IMAGE IS NOT AVAILABLE TO COPY
b. IMAGE IS NOT AVAILABLE TO COPY
c. IMAGE IS NOT AVAILABLE TO COPY
d. IMAGE IS NOT AVAILABLE TO COPY

Linda Winkler · Accepted Answer

Mhm. One of the examples that shows up a lot in circuits is a situation where you look at a circuit with short term behavior with time T. Equals zero, for example after switches closed and then after a long time um when the switch has been closed for a very long time. Um And these are usually a fairly simple to analyze. We&#x27;ll take a look at a simple example here where you have two resistors in parallel and one is just we&#x27;ll call are one and the other is for OEMs and instead of closing a switch, what we&#x27;re going to do is let our one increase as time goes to infinity let&#x27;s say. Um And we we don&#x27;t know where it starts from but we can look at it as a very situation where it starts with a very low value close to zero for example. Um And if it starts with our one very low at T. Equals to zero. So usually what you do is you re draw the circuit at two different times. Um And we&#x27;re gonna start with our one very close to zero, which is we&#x27;ll see is it&#x27;s not a good idea what your circuit is basically going to look like is a short between The two terminals of the battery. Okay. Um Mhm. So it&#x27;s going to act like that total resistance in the circuit Is also very close to zero At T. equals zero. And like I said, that&#x27;s not a very good idea because that could battery out. And of course we know shorted batteries can create fires and whatnot. Um But then as time goes to infinity, we&#x27;re going to let are also that same re sister become infinitely large. And what that will look like then is I&#x27;ll call it the open circuit. Okay. So you might as well have no connection whatsoever between those two points in the circuit. Um and then you&#x27;re, our total is just going to look like for OEMs. Um, so what your total resistance will look like in time, uh, is it will start at a low value. Maybe not perfectly zero. We hope not. And it will approach for OEMs. The larger that are one gets, the more that circuit will approach the Forum limit. Mm hmm. So almost like calculus taking a limit. Mm

Ze-Han Lee · Answer

All right. So in this problem, uh, so we have to resistance connecting parral are one or two. Okay. And our wise, instead of increasing and are too, is a constant. So the equivalent resistance of the circuit is, uh, are equal are one or two developed by our one plus hard to write. And because our two is a constant so we can rewrite this as our two times are one do well by our one plus aren&#x27;t too right. So, uh, we if we show the relation between our and our one, we see that it&#x27;s somehow like this, So Ah, there is Ah, there was a time, no value. So there&#x27;s terminal value is simply able to our one. Yeah. Somebody get this summer. Sorry. Simply go to our two. So there&#x27;s a terminal body off the star. And if our 10 that zero all right,

Shoukat Ali · Answer

in the first part of this question, we are going to kill lead they, Clint Resistance When the resisters are combined in Siri&#x27;s Lord Disick Willard Resistances for serious combination we can right ar e equals two are one plus our two. Let&#x27;s call it equating one now setting that will use into this equation we will get ar e equals to 2.0 plus 4.0 This will give us ar e equals to 6.0 Zittel. So this is the answer. The first part of this question In second part of this question, we have to repeat the calculations for federal combination. We are going to kill. Let Ari for this combination for battle combination we can, right whenever ari equals to one hour are one plus one by our two. So let&#x27;s go to the question, too. Now, setting the values into this equation we will get one by r e equals to one by 2.0 plus one by 4.0 So this is a grand too r equals to 1.330 so I know the question

Elizabeth Xu · Answer

so sorry with Courtney, you simplified the expression for our So be a born father by one. Right about Post Grad, or are one plus one Word of my art too. So one of their own leader. Me too. On the to practice together. Even to do that you can do common denominator are one or two. So we have Our two crews are one in the numerator. We know that one divided by a fraction. It was equal to the This is a tumor is equal to the reciprocal attraction. You are one or two. Bye bye. Are two plus or one. So what&#x27;s your introduced Okay now for B? Well, we have to do is just use the formula that any direct above this one and you can just playing with our values are one or two. So you know you are. What do we equal to? Our one used him times or 2 20 right, Abi? 10. Close 20. So then you have 200 too long. In my 30 you&#x27;re equal to 20 divided by three. Yeah,

Suman Saurav Thakur · Answer

you&#x27;d be have and expression for two resistances connected in parallel equal to one by one by r one plus one by r two. The figure must be Ottawa in and are too connective. Certain potential difference we So that is not our area of concern. First of all, we need to solve this denominator, but taking L City off our own out, it will be our one are to benefit. Divide R one R two with our one. We get out with caution. So it will be wanting to are two bless one into our own. Okay, now it will become one work. I went over our hopeless arwen do right away R one r two. No, please remember, if is divided by me by sea, it becomes in to see the world bags be really used. These concept this concept over here it becomes one into I don&#x27;t know too. Do right by I won&#x27;t preside. Are our becomes Ottawa in our to do right by are one place are too. So this is the solution of our first part. And then we are doing first part part over here. No work barred me foot. Partly you have been given are one the value of our 1 10 homes. And I do 20 films just plugging. These values are on our toe in our question. Our on our tooth anywhere by r one plus r two, our only calls to 10. 20 by and bless 20 it becomes 200 divided by 30. So is there a job? You get canceled out. We will be left with 20 way three own or six Dubai 31 motor. The correct answers. Thank you.

Matt Gibson · Answer

I&#x27;ll start by simplifying the denominator of the fracture on the right. So I will keep the one. And then I find a common denominator on the one here, which we are. One are too. So the top left would be are too Plus, and then the top right would be our one. I&#x27;m gonna change this into the division symbol This so this would be our equals. One divided by r two plus are one over r one are to this should have been our to here. You&#x27;re just using the same numbers here, parts for division I will change at the medication. So I have r equals one. Times are one are to over our two plus are one Anything times one is the same. So my answer would be our equals are one or two over, and it&#x27;s probably better if I put these in order. Most books would just have r one plus or two&#x27;s. That&#x27;s the answer for party for part B. Now it says to substitute in 10 and 20 so the total resistance would be our would be some plugging in. Our one is 10 or two is 20 are one is 10 plus 20 so my total resistance would be 200 over 30. Cancel their zeros so it will be 20/30 which would be about 6.6 repeating or 6.7 homes.

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