in-the-following-exercises-solve-the-given-maximum-and-minimum-problems-when-two-electric-resistors-

Question

In the following exercises, solve the given maximum and minimum problems.
When two electric resistors $R_{1}$ and $R_{2}$ are in series, their total resistance (the sum) is $32 \Omega$. If the same resistors are in parallel, their total resistance (the reciprocal of which equals the sum of the reciprocals of the individual resistances) is the maximum possible for two such resistors. What is the resistance of each?

Yaqub Khan · Accepted Answer

he&#x27;ll be held to Our sisters are one equal to kinda sick. So home second wrister are two equal to 47 home and the harvester. It is our three equal to 51 home. So we get maximum reticence when the lannisters are committed in cities. So the effect your reticence you call too are one plus our to bless our tree by putting the values Here are one is 36 home are two is 47 home and our three is you doing home. So be hell The maximum reasons equal do wanted before Oh and affect you re since in minimum when the researchers are committed in battle So in bruhn combination re hell this is broken off equal and resistance is equal Do reciprocal off for citizens apostasy local up second instance Plus this broken off I thought this is no By putting different world lives Here we get one Our article unt is equal to one of our 36. So home bless one hour 47 home plus one over 51 home So we good Ari Clint he called to 14 point fight six This is the minimum value mystery can achieve when that is Tercel committed in Britain

Yifan Xu · Answer

all right. So the total electrical resistance are of two resistors connected in parallel with resistance are one in archery is given by one over R because one overall, one plus one of our two. All right, So the question is, when we&#x27;re given that one resister has a resistance of 2.3, let X be the resistance of the second register. Expressed a tutor resistant are as a function of X, so it&#x27;s gonna be all over our recourse. That&#x27;s suppose our want us knowing as 2.3 and the 2nd 1 is X and we want to express our as exit. It&#x27;s gonna be 2.3 acts over X plus 2.3. All right, so that&#x27;s question, eh? Are the question beers. Find the resistance in the second register if the total re distance off the peers at least 1.7. So we want our to be a list 1.7, which means 2.3 over 2.3 acts over experts 2.3 sweeter than or equal to 1.7. Since negative resistance does not make any sense in the context, we can assume that excess quitter, Oregon zero and thus X plus 2.3 is greater than zero. So we can multiply both side by experts to 0.3. So it&#x27;s gonna be 2.3 acts quicker than 1.7 next post 2.3. So we will arrange everything together and we&#x27;re gonna have a point six x square then or you could to 3.9 I want. And thus we can have acts being greater than where you&#x27;re good. Too fine. Point 6.52 All right, so that&#x27;s the resistance of the second resistor If the total resistance of the pier is at least 1.7 as long as exit sweeter than or equal to 6.52

Caelan Thomas · Answer

If we take partial derivatives of the equation, we get negative. One over R squared times d r equals negative one over r one squared times tr one plus negative one over our two squared times d r. Two plus negative one over our three squared Tim&#x27;s d. R. Three And we can approximate this with negative Don&#x27;t our over r squared equals negative Delta are one over r one squared plus negative don&#x27;t are too over our two squared post Negative. Don&#x27;t our three over our three squared? So now we&#x27;re going to need to find are don&#x27;t our one don&#x27;t are too until two are three so that we can solve for what we really want Which is Delta are so are we can calculate from the given equation Rearranged, as are one our to our three. All over our to our three plus r one r three was R one R two. And if we plug in are known values, we get 25 times 40 times 50 over 40 times 50 plus 25 times 50 post 25 times 40 And that&#x27;s going to give us our equals 200 over 17. So now what about don&#x27;t are one. Thoughts are too, and tilt are three. We know that there&#x27;s a 0.5% Massimo her, so we&#x27;ll just multiply 0.5 by each. Our value. So for our one, we can&#x27;t tell to our 10.1 to 5 for Delta are, too. We get 0.2, and for Delta R three, we get 0.25 and now we&#x27;re ready to plug in and sulfur Delta are so we get negative. Delta are over 200 over 17 squared because negative 0.1 to 5 over 25 squared minus 0.2 over 40 squared, minus 0.25 over 50 squared. And that will give us Delta are it&#x27;s approximately 17 squared. Sorry, 200 squared over 17 squared times 0.1 to 5 over 25 squared plus point 2/40 squared plus 0.25 over 50 squared, Which gives Delta are I have approximately one over 17 or as a decimal, about 0.59 Holmes

Jayashree Behera · Answer

let the resistance off to resistors be Ireland and I do and it&#x27;s a zoom. Are one Toby, the smaller sister. Now, from the statements off the problem, we have our went over. I want lists are to the parallel equivalent assistance off our one and are to be equal to three rooms on the series. Vicky Valent to be 16 arms. So now, as you can see, we have to. We questions and two unknowns. Armament are too, so we can use a method off substitution and elimination in order to solve this to the first leg. First, let&#x27;s take the simpler question and express one variable in terms off the other. So now we have Olivant domes off are too. So now we can plug this expression in place off our one over here and solve for Artoo. So doing. So we find our toe be equal to drugged ones and then lugging this value off our back. Over here we find our way to the equal to fort loans. Therefore, for party that we have to find the smaller resistance of the smaller resistances are one and the physical to four rooms on dhe. The larger resistance is our true and that is equal. Go, Dr Holmes. Thank you

Robert Leedy · Answer

okay were given the equation to find resistance. We were told one resistor has a resistance of 2.3 owns like that in for our one good one over R is equal to one over 2.3. Plus, the other resistor has a resistance of X one over. Now it wants us to first expressed the total resistance. Are is a function of X. So we need to solve this equation for our pretty straightforward when you find a common denominator on our left side, which of course, is going to be 2.3 acts we have one over R is equal thio X over 2.3 eyes plus 2.3 over 2.3. That&#x27;s giving us the new equation. One over. R is equal to x plus 2.3 over 2.3 x when you solve this for our So, in order to do that, we are going to multiplied by our and divide by the fraction giving us our new equation, R is able to 2.3 acts over X plus 2.3. Next Part B tells us to find X. If our total resistance is 1.7 owned. So we&#x27;re gonna plug 1.7 for arms. Self correct. You know, a solve for X. We&#x27;re going to multiply our denominator across. Giving us 1.7 s plus 3.91 is equal to 2.3 X. We were all the access to one side or Constance to the others. We end up getting an equation. 0.6 X is equal to where you 0.91 starving friends way get a resistance of 6.52 homes.

Problem

In the following exercises, solve the given maxim…

Problem 16 Easy Difficulty

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Heather Z.

Samuel H.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 24

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Heather Z.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Grace H.

Heather Z.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Heather Z.

Samuel H.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus