solve-the-given-linearization-problemsthe-capacitance-c-in-mu-mathrmf-in-an-element-of-an-electronic

Name: solve the given linearization problemsthe capacitance c in mu mathrmf in an element of an electronic
Uploaded: 2020-07-26
Duration: 3 min 16 s
Channel: Numerade
Description: Solve the given linearization problems.The capacitance $C$ (in $\mu \mathrm{F}$ ) in an element of an electronic tuner is given by $C=\frac{3.6}{\sqrt{1+2 V}},$ where $V$ is the voltage. Linearize $C$ for $V=4.0 \mathrm{V}$.

Question

Solve the given linearization problems.The capacitance $C$ (in $\mu \mathrm{F}$ ) in an element of an electronic tuner is given by $C=\frac{3.6}{\sqrt{1+2 V}},$ where $V$ is the voltage. Linearize $C$ for $V=4.0 \mathrm{V}$.

Manish Kumar · Accepted Answer

So basically in this question to capacitance connector in the cities. So we&#x27;re known drawing suck it first. So for the better of ideologies and so did it. Kappas eater. One more capacitor And there&#x27;s a battery like a potential difference which is also given the capacitance off these two capacity the voltage of the batteries nine gold solicitor for the defender, obviously and didn&#x27;t see one. So you do and C one obviously given, which is Empire Micro, federally and the C two, which is even Ah, yeah, it will my group holiday. So basically, in the first part, we have to clear the equal and capacitance of you know, when the capacitor and the cities So one upon sequel and there will be nothing what one upon see one apart into plus one upon Sito So see gold and comes hard that c one c two upon see one policy toe, which means this will be a storm five plus 12. Which will we like this into five into 12? So this whole thing become 17 upon 60 micro for a day? No. And we can obviously change this and my grandfather to fire day by multiplying train to department six. Now, in the be part, we have to calculate the prudence of defensive because each campus it&#x27;s capacitors. So basically me, every possible that charge total charge flowing to the socket are cruel sods on the capacitors O que you know that you is equal to see Yeah so capacitance C equivalent We have got blurred vision 70 upon this one and we&#x27;ll tell you grow, this is nine given So no, let&#x27;s see Marta going to happen So over the head I&#x27;m gonna be been here reaching there. So this these things over there needed the tart on a capacitor which will comes out Yeah, this will comes out 31 point. I&#x27;d micro clump because capacitor in the macro on your little brother put into difference across its capacitors so I don&#x27;t have anyone will be nothing. What? Q because the oven is the capacitor and the city so that charges on the both think of serving the same. So this will becomes took you, Capellan dark, you who will be cured and do in this Q or their decision? Cuba LBC v took you up on C one, which will be nothing but a 13 point. All right, upon see one vintage, obviously given in the question and then it five pipe. So this over there, this thing will become, comes old. Comes is expiring. 25 world. I was a little easier. Also, Magnum across a mathematical get concealed and killed Abby two over there, which will come upon que upon see too. So they said, with 31 point load up on 12 which comes out to point 65 hold. And now we have to go through the tart and discover city in which we have already discussed. They were. And that teacher, obviously Q one in physical took you to goto you them because they&#x27;re in the city. This is 31 point. I&#x27;d micro column.

Karl Jacob · Answer

Okay, let&#x27;s draw the circuit diagram. First capacity of one capacitor X capacitor three and capacitor to so see to si si point a wouldn&#x27;t be C one on C X and okay. Okay, Now the C one and C X are in Siri&#x27;s See two and see three out in Siri&#x27;s and those these two Siri&#x27;s pairs are in peril, So potential difference across C one and C C X series. It&#x27;s same as potential difference across you. 23 1 more information that is given is that the baby there is potential difference between point A and B zero. That means point A and point B both at the same potential. This implies that potential because see one is equal to potential across see too similarly potential across. See X is equal to potential across Si si, because if potential across see one is same as potential across see, too. Then the Partovi nut is the depositor equally among C one and C two hands to point A and point B will be at the same potential. Now let&#x27;s take an advantage off the given information. No, since the two will see, three are in Siri&#x27;s, You can find the net capacitance off capacity and capacitor to which is equal to see to see three divided by sea to plus C three. Now, if you substitute those values off, see 23 given as 18 microfibers and 4.8 micro fatted respectively. You get the value three point seven eight Michael Barrett. Now you can find the potential across the See two, which is equal to Q divided by sea to know what&#x27;s the value of Q Q equals C 23 which is Ned Capacitance times. We know this is the charge deposited across C two C three series circuit, which is equal to three point 78 We not so it&#x27;s used to find. We see, too. We see two is equal to three point 78 Be not divided by value of C two is 18 now. Similarly, we can find BC Three is equal to 3.78 because in Siri&#x27;s, you have the same charge distributed on each of the capacity. So each capacitor in serious gets the same charge. That&#x27;s the property off serious circuit. So instead of 18 now we have C three value of C three, which is full point eight. Now we have Easy One, NBC three. No, As in page one here, you can see VC one musical too busy too VC one than equals the value of easy to is 3.78 We not divided by 18 30 point 78 We not divided by 18. Now, what&#x27;s the value of the C one that can be given by charge deposited on C one? They were divided by value of C one, which is eight point no equals 3.78 We not divided by 18. You know what? Let&#x27;s not write the value off. See one yet let&#x27;s keep it S e went 3.78 We not divided by 18. This gives you Q equal to 3.78 c one. We not divided by 18. Okay, what&#x27;s the use of the value off cue since we know that capacitor C one and C two are in Siri&#x27;s, So they both have same charge deposited on them so I can use the same thing. Same charge for C X capacitor now charge deposited on the capacitors. See X is given by see X times potential difference across the capacity. See, thanks. No. To use that information, we need to find out the potential across CX, as mentioned before VC X is equal to V. C three on value of V. C. X is BC three now we can make use of that since Josh is given by C x v cx Cute. Now we know Q, which is equal to three point 78 c one. We not divided by 18 equal to see X The value off visit Lee OVC X is given by 3.78 We not divided by 4.8. You can cancel we not on both sides to find out CX equal to C one times 4.8 divided by 18 which is equal to 8.9 times 4.8 divided by 18. So this is equal to two point 37 micro fatted. I hope you understand this.

Eduard Sanchez · Answer

Hi there. So for this problem we need to calculate the value of capacity and see So that the kibble and capacities is 12.4 Micro Colom&#x27;s we are also given they fall you for the other capacity tours in this configuration. So the way to solve this problem is two. See what capacitors are in serious and what capacitors are part of a well to the shorter so that you, you can use the formulas for each case, define the a killing capacities for those two capacitors. So we are working two and 2. So in the first case we are going to find the cabling capacities between The Capacitors one and 2. So we&#x27;re going to call dot see 12 and in this case we can see that both capacitors and half in are submitted to the same potential so that they are in serious going to put that in here. They are in serious so that the cable and capacities See 1 2 is the square root the the embers sorry, of the some of the embarrasses of those of the capacities of those capacitors. So it is this so we substitute those values see want is 8.35 me croak alarms plus one over 12 negro columns. Putting this into the calculator, we obtain a value of 4.9 negro columns. So this is the a key Evelyn capacitance between these two capacitors. So having done dad we now have the following configuration. So capacity tour one and 2 now are there is equivalent And we have in here capacity or three. This capacity four and this you see that&#x27;s the one we want to find so and we can skin here that capacitor uh C 12 and three are at the same potential so that they are in in a part of a configuration so that the equivalent capacitance between these two capacitors is simply the sum of C three plus C 12 so C three is for .25 Grow Cologne Plus C1 to which we have obtained is 4.9 the curriculum. So from here we obtain a body off 9.15 me grow colon so now we have the following We&#x27;re almost there to obtain the body of c. So this is C123, This is four and this is sick. So in this case we can see that capacitors, C and capacitor C 123 are in serious so because they are in serious. The capacitor that we are going to call in this case We&#x27;re going to call it 123 C and this is 1/1 over C plus one over the value of see one 23. We are going to leave it like this because we want this value in here and we are just one more step to obtain the kibble and value so that we can obtain, we can use this condition so know that we found this we are just, we will have this too capacitors, this is once C23C and this is C4 so that and we can see and hear that they are in a parallel configuration so that will attain that the equivalent because we are we have added all of the kid lands. I can um Capacitors so we will have the kibble in which it is the information given but in this case since they are in parallel should be C4 plus See 1 2, 3 c. So this is the final equation. So we need to put what is this, what all of these values so that we can solve for C. So Um we know that this is the equivalent is 12.4 micro colon. So for a girl Colombia We are also given the value of C4 of the for kind of uh capacity which is 7.22 Micro column and The expression for C123C that we just have obtained before. So that will be want over one overseen plus One over C 123. And that value for 1-3 will have it in here so that we can also substitute that. But we are going to rearrange this first so we can right this like this, you can pass this to the other side. We can rearrange this denominator as the following. It should be something like this this with this and with this so we will have the sum times C Times C- 123. So we can see in here that this just will give us these perhaps this ratio and here but when we when we take the inverse of this, just the denominator changes with the numerator. So that worked in this. Okay, so from this we need to solve for C. I&#x27;m going to like so strap these two values so we will have 5.18 Micro columns. So we will have when it passed that sound to hear and we&#x27;ll have this so to solve this, can I put this but this to see it better so we can see in here that we can pass this to the other side and we can characterize see so this will be 5.8 economy critical arms minus See 123 and the order volume point Anger columns. He 123, this is equal to zero and we just simply need to solve for C. It is very straightforward that this is discretion that we are going to obtain. Yeah, of course in here we will have um the value 4 C123 which is 9.15 Micro column. So we just substitute those values in here, we&#x27;ll have this 9.5 then me croak alarms of course we need to obtain um a positive value. So you can see from here that the minus signs council. So putting all this into the calculator, we obtain a body off one point well it is 11 0.9 four micro column, so this is the value for C in this configuration of capacitors. Thank you.

Josh Broderick Phillips · Answer

never taking to pastors that they&#x27;re the same as the last problem and this time there in a Siri&#x27;s connection like this. So this is the C one. It&#x27;s five Micro Farage&#x27;s, and this one is 12 Micro Fareed&#x27;s. Connect them to the battery, Um, with nine volts. Okay, so the first part we want to find equivalent capacitance and capacitors air the opposite of resistors. So if you want capacitors in Siris, that&#x27;s like resistors in parallel, where the reciprocal of Theo equivalent capacitance is the sum of the two reciprocal to the individual capacitance is, and you could just plug in the numbers and, like, take the inverse. But you do a little algebra, you get C one C two over C one plus C two, which is five times 12/5 plus 12. You get 3.53 Micro Fareed&#x27;s equivalent capacitance. And now the potential difference is going to be tricky without the charge. But we know that the charge for passengers and Siri&#x27;s the Charter Age capacitor is gonna be the same. So that tells us that Q. Since we know the the entire voltage across both capacitors must be nine volts. We can combine these into one capacitor and say that Q is the equivalent capacitance times the entire voltage. So this is 3.53 Micro Farage&#x27;s times nine volts, which is 31.77 Cool OEMs, which is a few round 31.8, should be micro, micro cool rooms. And this charge is the same as the charge on the plates of the first capacitor and the second capacitor doesn&#x27;t matter. So now that we know that QUE also has to be C one times the potential difference on C one so called B one and how also has to be C two V two So voltage one, it&#x27;s que oversee one. So 31.77 micro cool ums over five Micro Farage&#x27;s So the microbes go away. We get six point 35 volts for that one. Same thing for the second capacitor, so Q over seat to which is 31.77 micro columns over 12 Micro fair words, which gives us 2.65 volts for the 2nd 1 and 6.35 plus 2.65 adds up to nine volts. So our answer makes sense

Guilherme Barros · Answer

in this problem. We&#x27;re gonna talk about capacitors in Siris. So I consider that we have a situation has shown here on the figure we have three capacitors in Siris connected to a battery. Um, all the three capacitors have the same charge. Q each are. They&#x27;re charged with the same charge. And, um, we can describe the system as if instead of three capacitors in Siris there were There are only one capacitor with the capacitance C such that one oversee is equal to one over C one plus one. Oversee two plus one, oversee three, and this capacitor this only one capacitor has the same charge Q as each off the three other capacitors. And in our problem, we have a situation where V is equal to 15 votes. C one is 4.5. Faraday C two is 12 for a D and C three is 30 to 40. Um, and our goal is to find what is the potential difference in the third capacitor, given the information that we have. So what I&#x27;m gonna do first is to calculate what is the the equivalent capacity and see going calculated with C, we can calculate what is the charge in each capacitor. Q. And then we can calculate what is the potential difference in on Lee, the third capacitor by calculating charge and then then divided by the third capacity capacities. Okay, so let&#x27;s start with So we have one. Oversee is one over C one C one is 4.5 far day, plus one overseas to choose 12 far They wasn&#x27;t oversee three. C three is 30 too far away. So the capacitance is one over 1/4 0.5 fara day. I&#x27;m sorry. It&#x27;s, um, actually should be micro fired a road here without the micro sign. I&#x27;m sorry for that, but all it&#x27;s gonna change is a factor of 10 to the minus six. Eso There should be 10 to the six and overall tend to the sixth year. So it&#x27;s 4.5 micro far they worse. I won over 12 micro far day plus 1/32 micro far day, and this is equal to 2.97 micro Faraday. Now the potential difference v actually, before I have to calculate que so cue is the total potential difference times the equivalent capacities. It&#x27;s 2.97 micro for ITI Times. Um, the potential difference off 15 votes. So this is equal to 44.55 columns. And then we have to calculate the three the capacitance. I&#x27;m sorry, the difference of potential in the third capacitor, and that is the charge Q divided by C three. So it&#x27;s 44.55 microfilms. I wrote films up here, but should have been microscopes divided by with passage ins off 32 micro farming, and this is equal to 1.4 votes, which is the answer to your exercise.

Problem

Solve the given linearization problems.A $16-\Ome…

Problem 43 Easy Difficulty

Solve the given linearization problems.The capacitance $C$ (in $\mu \mathrm{F}$ ) in an element of an electronic tuner is given by $C=\frac{3.6}{\sqrt{1+2 V}},$ where $V$ is the voltage. Linearize $C$ for $V=4.0 \mathrm{V}$.

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Anna Marie V.

Heather Z.

Kayleah T.

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

Anna Marie V.

Heather Z.

Kayleah T.

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

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus