5

Assuming the potential di fference between points and IO0V, Using the Circuil provided calculate: The equivalent capacitance The total charge The energy stored in t...

Question

Assuming the potential di fference between points and IO0V, Using the Circuil provided calculate: The equivalent capacitance The total charge The energy stored in the circuit The charge on each capacitor (recreate the tablebelow in your blue book; show all work andlor state all assumptions) SmFtop left 5 mF boltom left 2 mFtop middle 6 mF middle middle 3 mF bottom middle 3 mF lelt left 3 mFxight leli 6 mF boltom left

Assuming the potential di fference between points and IO0V, Using the Circuil provided calculate: The equivalent capacitance The total charge The energy stored in the circuit The charge on each capacitor (recreate the table below in your blue book; show all work andlor state all assumptions) SmFtop left 5 mF boltom left 2 mFtop middle 6 mF middle middle 3 mF bottom middle 3 mF lelt left 3 mFxight leli 6 mF boltom left



Answers

Calculate the equivalent capacitance between the points $a$ and $b$ in Figure $\mathrm{P} 26.75$. Note that this is not a simple series or parallel combination. (Hint: Assume a potential difference $\Delta V$ between points $a$ and $b$. Write expressions for $\Delta V_{a b}$ in terms of the charges and capacitances for the various possible pathways from $a$ to $b$, and $\mathrm{rc}-$ quire conservation of charge for those capacitor plates that are connected to each other.)

So the two main branches are in cities. So we have one of us something plus one of us. Something in verse of that. So this is the total capacity ins. In the fourth branch, you have four and two in parallel. So that's force us to in the second round. You also has forced us to in parallel. The unit is Micro Farrell. So you would have see total equals three, Michael.

We have a bunch of capacitors that up something like this with one here, um, one of the middle. This, um So this is between points A and B, and now I'm gonna live thes C one, C two and C three. So this is C one C two C three, and then these two are the same as he wouldn't see too. So as the problem suggests, I'm gonna write the voltage from A to B. Well, let's see. I can take a couple different paths. I can take this path. I can take this path or I can take this path. So for the middle path, that would be, um, I can do. This is some of voltages for each capacitor, so the vultures is charged over capacitance. So cue to oversee two plus Q three, Oversee three plus Q one, Oversee one and then I can do the same for the bottom paths. That's Q one. Oversee one plus another Q one over seat one. I can do the same for the top path. Just Q. Chew over C two, plus another cue to oversee too. All these three expressions have to be equivalent because they all some to the total voltage. Ah, so if I look at the first and second equation, I can deduce Thatch Q one oversee one because I have this and this. So then this Cuban ever see one has equal cute to oversee. Two plus Q. Three. Oversee three That combination and then looking at the first and the last equation, have queued to oversee two. And cue to oversee, too. So this one has to be equal to these two. So cute to oversee. Two Equals Q three Oversee three plus Q one. Oversee one so now on assault for Q three. Oversee three in both cases. So for the 1st 1 this is gonna be Q one. Oversee one minus cute to oversee, too. And for the 2nd 1 we get Q to oversee to minus Q one, Oversee one. But this is just the opposite of the 1st 1 so this equals minus Q three. Oversee three. So if you three over C three equals minus cute, you're of a C three that means Q three oversee three. The only way that could be true is if it's zero. And that's, um, the voltage across C three, which is this middle capacitor. So there's no voltage through the middle capacitor than we can completely disregard it for the equivalent capacitance. And now we have something that looks like this we have, um you have to capacitors in parallel, which these two and then the other two of the Endor also in parallel. So that looks like this. And now we have something that's pretty easy to figure out so that this is four Micro Farage's and the bottom two or each to microfiber words. So we can combine each pair of these because they're in parallel. So for plus two, that's gonna be Six Micro Fareed's. And now we can rewrite this once more with just two capacitors and Siri's. So this is six and six, and now the equivalent capacitance for that is going to be the product of the two. And then divide by the sum Zits were in Siris, and that gives us expectedly three Micro Fareed's. Because whenever you combine two pastors and syriza the equal, you're just gonna get half the tour past them. So the equivalent capacitance of this whole circuit is three micro foods

19.51. So we have this configuration of four capacity for capacitors here, all which have the same value, See? And so we would first like to find the equivalent capacitance between A and B and then, given some applying voltage be we want to figure out the voltages and charges on each of the four capacitors. So to begin with, uh, we look at the diagram here and we see that C one and C two are in Siri's. And so then the serious capacitance there is in parallel with C three and then the equivalent capacitance of the 1st 3 of these are in Siri's with capacity for so the capacitance of one and two in Siri's, their unequal of equal value. So when you have a boat that happening with capacities and syriza resistors and parallel it just have the value. Um, that's then in parallel with three. So the passengers have one too, and three So these just add So you add 1 to 1/2 you get three halves and then these are in a series with four. So see one too 34 So this will be the product. So we have c squared over the some C plus three have C. So the total capacitance between points A and B is 3/5. See? So now for the charges, the charge on this total equivalent capacitance we have, which you can call Q 1234 is equal to the capacitance. There. So one C 1234 Time is B. This is just basically the definition of capacitance. We know that C 1234 is 3/5 c. So this is going to be 3/5. See, time's be so when we have capacitors in Siri's, they have to have the same charge on them. Because looking here, for example, all of the positive charge on the top plate of C two here has to come from moving negative charge to the bottom plate of C one here. So the charge on four is 3/5 see, times V, and this is equal to see four times before. So then the voltage across four is going to be 3/5 speedy, because the sea cancels out setting this C four before, So now we know what we need to know for a capacitor, uh, for so now the voltage across C 123 is Ah, you know the same is the voltage across both of its parallel parts. And also from the preceding week, we can write down Q 123 and cue for the same. This c 123 I'm the 123 So this is three halves, See? Because that was the accidents of one through three. I was the 123 And so then, um, the voltage across 123 is equal to 2/5 v. So looking back at this, uh, C three is going to have the 123 across it because it's in parallel here. So the three is going to be two hits. The you three is see three times B three. So that's going to be to fifth V here and then just see there. So 2/5 CV, Um, and so Q 123 here is going to be Q three plus Q one, too. So if you want to, you want to three minus 23 So if you want to, three is, uh, 3/5 CV. Thank you. Three is 2/5 c. B. So then the charge that's shared between one and two, his 1/5 see and so C one and C two are in Siri's, so they have to have the same charge. So then Kyu Wan is equal to cute, too. And that's equal to the net charge on their equivalent Capacitance, for the reason that we went over before is that this is given a net charge by removing electrons from the positive plate up here and adding them here. And then the same number of electrons have to go from here to here. So the two inter plates, you know, together remain neutral. And then from this week and see that Thea Well, if the charges of the same and the capacitance is air the same, then there will just have to be the same. And then, from this, we can see that's 1/5 of the applied voltage be

Here in discussion before calculating the equivalent depositions most. We know about that capacitors. Okay, A passenger is a conductor separated by an insulator and it is close charge when it is connected to have vaulted supply. And these are connecting different combinations like cities connections and very little connection. Now here the or lying figure shows the combination all cities and Caroline combination of capacitors connected between the wine. Mm and me. So now here we are going to calculate the equivalent capacitance, echo, C. And D. And then similarly we calculate the capacitance across the in depth and then A. And B. And then We will get our overall effective capacitance of this. 30. So the if we were in capacitance across see and the is given by sea of city equal to one divided by one divided by six point nine. My prophetic less. one divided by 6.9 micro fabric less one divided by a 6.9 micro fatter. Now we are taking this in the denominator because as we can see that campus, it is connected A close C. And D. Yeah these are in cities so we are taking this and denominator and this will be connected in parallel with these three. So it will B plus 4.6 Michael Ferris. No after simplifying this they get capacitor. Eco city is Equal to 6.9 micro. Betty. Therefore the capacitance or we can say that equivalent capacitance across C. And D. is equal to 6.9 micro fabric. Now similarly we are going to calculate the effective capacitance across N E. N. Yeah so the yeah capacitance a close E. And yeah is given us capacitance of Across E. F. Equals two. One. Do I did buy one divided by 6.9 Micro Ferret less, one divided by 6.9 micro. fatted less one do I did black 6.9 Micro fabric less. 4.6 Micro battered. Therefore the capacitance across E and F is equal to 6.9 micro static. No, we are going to calculate like equivalent capacitance across A and B. So no, if we violent capacitance across A and B is given by episode and across A. B equal to one divided by one, divided by 6.9 micro fabric Plus one divided by 6.9 micro ferric less, one divided by capacitance across E and F. So after a substitute 6.9 micro ferret for capacitance across E and half, we get capacitance across E and B is equal to 2.3 michael saturday. Therefore effective. Their persistence of the given circuit is 2.3 micro, pathetic. No, we are going to calculate the charge on the each captain sitters. So here in part B of discussion, we know that the formula to calculate the charges on the three nearest capacitors between A and B. Is given us U. Equal to see across A be multiplied by we across A B. Now here C. A. B. Is it will do that total capacitance of the circuit and we may be or voltage across A. B. Is the voltage between point A. And B. No. Yeah on substitute two points three micro feathered or Q. and 4 20 walls or voltage across A B. Very good. U. Is equal to 966 micro. Well on no the charge on the epicenter. She even nearest who and A. And me is you want equal to you Or we can say that Cuban is equal to 966 micro. Well or we can longer door the given value. So we can say that the charge on the capacitor seven near us to a N. B. Is approximately equal to 970 micro problem. Or we will consider this valley also now thins All three capacitors are in series in the given circuit. So these three Capacitors have same volt is that is the vault is must be added to 4 20 world. So each capacitor has won. 40 boy. Therefore voltage across the Yes yes it does. C two is given by we do equal to were kids across a B divided by see Now here on substitute 4 20 world for voltage across A B. We get we two is equal to 4 20 divided by three Which is equal to 140 bald after dividing No the charge on the capacitor. C two is You two equal to see to multiple Lava V two. Now here on substitute four six micro ferret for C. Two and 1 40 wall. Or we do we get you do equal to 6 44 micro alarm. Therefore the charge on the capacitor C. Two near us to A and B. Is rounded off to the nearest value and we can consider it 6:44 Microphone or 6 40 micro. Well, long as it is near list you rounded of a laundry figure now comes to part C. So here we are going to calculate the voltage across the N. C. And D. So the voltage across E. And and is the some of voltages across E. And see see and D. And F. And the does we can say that voltage across E. F is equal to voltage across E. N. C. Plus voltage across sea and the plus voltage across F. And the No here as the three capacitors between E and C. C and B and F and G are in cities, so the charge on them must be seen. And the capacitance across these three has the same grant recipients. So as a desire, the voltage close each of these capacitors must also be same. So as a dessert of this, the double equation can be solved as word. It is across E and F is equal to voltage across Cnlee Plus World is a close cnd Plus World is a close C. And D. Or we can say that bolt is across E. And F is equal to three multiplied voltage across c. n. d. Or we can write, the above equation has portage across C&D. Is equal to voltage across E&F divided by three. Now here substituting 1 40 fold for more did across E and F. We get bolted across C&D. is equal to 140 divided by three. Uh After dividing this, we get voltage Echo, is equal to 47 world. Therefore the Voltage Echo, C&D is 47 world.


Similar Solved Questions

5 answers
17. Clasifique los siguientes halogenuros de alquilo como primario, secundario, terciario ninguno, segun correspondaCH,CH,H,C-ch_CH, ,C CH;~Br H,C CH, CH, CH, CH,H,C G_Br
17. Clasifique los siguientes halogenuros de alquilo como primario, secundario, terciario ninguno, segun corresponda CH, CH, H,C-ch_CH, ,C CH;~Br H,C CH, CH, CH, CH, H,C G_Br...
5 answers
An analyst wants to solve a AgCl salt in a beaker: The analyst observed 10 points that if some amount of KNO3 salt is added onto this solution, more AgCl can be solved in beaker: How do you explain this phenomenon?Your answer
An analyst wants to solve a AgCl salt in a beaker: The analyst observed 10 points that if some amount of KNO3 salt is added onto this solution, more AgCl can be solved in beaker: How do you explain this phenomenon? Your answer...
1 answers
Find the arc length of the graph of the given equation from $P$ to $Q$ or on the specified interval. $$ y=\left(2-x^{2 / 3}\right)^{3 / 2} ; \quad[1,2] $$
Find the arc length of the graph of the given equation from $P$ to $Q$ or on the specified interval. $$ y=\left(2-x^{2 / 3}\right)^{3 / 2} ; \quad[1,2] $$...
5 answers
Consider the following national-income model (with taxes ignored): c(Y) I(i) (0 < c' <1; < 0) ky + L(i) M,u positive constant; L' < 0) Is the Tirst equation the nature of An equilibrium condition" What (ie tolal quantity demanded for mOleY this model? Analyze the comparative statics of the model when money supply changes (monetary policy) ad when government expenditure changes (fiscal policy).
Consider the following national-income model (with taxes ignored): c(Y) I(i) (0 < c' <1; < 0) ky + L(i) M,u positive constant; L' < 0) Is the Tirst equation the nature of An equilibrium condition" What (ie tolal quantity demanded for mOleY this model? Analyze the comparati...
5 answers
'62te18] 6 &&6&286 ~ & L 1 L 1 1 L1 0 1
'62te18] 6 &&6&286 ~ & L 1 L 1 1 L 1 0 1...
5 answers
Write an absolute value equation representing all numbers $x$ whose distance from 1 is 5 units.
Write an absolute value equation representing all numbers $x$ whose distance from 1 is 5 units....
5 answers
The figure above shows the graph of $5^{x} .$ What is the sum of the areas ofthe triangles?(A) $32,550$(B) $16,225$(C) 2604(D) 1302(E) 651
The figure above shows the graph of $5^{x} .$ What is the sum of the areas of the triangles? (A) $32,550$ (B) $16,225$ (C) 2604 (D) 1302 (E) 651...
4 answers
Early study results show that 75% of customers are willing to pay an extra dollars on their purchase t0 a local charity: If the margin of error is 0.012 at 95% confidence; find how many customers are surveyed
Early study results show that 75% of customers are willing to pay an extra dollars on their purchase t0 a local charity: If the margin of error is 0.012 at 95% confidence; find how many customers are surveyed...
5 answers
Varhemm 125IThe following data have been collected from a sample of 8 items 10, 8 12, 15 , 13,11, 6 ,5 The Point estimate of tne population meanils 12Yek TarealIeealtlei DFiag IcletepmSelect cne; WTrueFalse
Varhemm 125 IThe following data have been collected from a sample of 8 items 10, 8 12, 15 , 13,11, 6 ,5 The Point estimate of tne population meanils 12 Yek Tareal Ieealtlei D Fiag Icletepm Select cne; WTrue False...
5 answers
2. How many grams of Ba(OHJz are needed to prepare 200.0 mL of 0.0165 M Ba(OH)z aqueous solution: (Mw: Ba(OHJz= 171.34 g/mol)
2. How many grams of Ba(OHJz are needed to prepare 200.0 mL of 0.0165 M Ba(OH)z aqueous solution: (Mw: Ba(OHJz= 171.34 g/mol)...
5 answers
Q 3(a) [5 Marks] Estimate the current volume of the Universe if the Hubble constant is equal to Ho= 72 kmlslMpcQ 3(b) Marks] Explain the flatness problem of the standard model and how inflation solves it: Solve the expansion equation for the vacuum energy dominated case.
Q 3(a) [5 Marks] Estimate the current volume of the Universe if the Hubble constant is equal to Ho= 72 kmlslMpc Q 3(b) Marks] Explain the flatness problem of the standard model and how inflation solves it: Solve the expansion equation for the vacuum energy dominated case....
5 answers
Method of Undetermined Coefficients 2I Find the general solution to the following: D)y" + 3y' + Zy = e ~2t1'2)y" + 9y = cos(3t)3)y" + 16y = tsin t3~.( ( _
Method of Undetermined Coefficients 2 I Find the general solution to the following: D)y" + 3y' + Zy = e ~2t 1' 2)y" + 9y = cos(3t) 3)y" + 16y = tsin t 3~. ( ( _...
5 answers
Ehcatbole of eccentncity 2 has one focUs at (5), The corresponding dlractrix Is the Iine y = - Find an oquation for the hyparbr8in3oe Ine correci aquallon for Ihe hyperbola; OA Ntll? (t8208 0u2_62Oc: KUZ _ (t820d @auZ_ lytu?
ehcatbole of eccentncity 2 has one focUs at ( 5), The corresponding dlractrix Is the Iine y = - Find an oquation for the hyparbr 8in3oe Ine correci aquallon for Ihe hyperbola; OA Ntll? (t82 08 0u2_62 Oc: KUZ _ (t82 0d @auZ_ lytu?...
1 answers
A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 $W$ of electrical power, and keeps its inside compartment at 5$^\circ$C. If you put a dozen 1.0-L plastic bottles of water at 31$^\circ$C into this refrigerator, how long will it take for them to be cooled down to 5$^\circ$C? (Ignore any heat that leaves the plastic.)
A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 $W$ of electrical power, and keeps its inside compartment at 5$^\circ$C. If you put a dozen 1.0-L plastic bottles of water at 31$^\circ$C into this refrigerator, how long will it take for them to be cooled down to 5$^\c...
5 answers
Oscillating arcadesmosLcqinCurfk) = 100 <r<f(){-20 +5 sin / <* < 20_ 5 sindBSMTIO -
oscillating arca desmos Lcqin Cur fk) = 10 0 <r<f(){-20 +5 sin / <* < 20_ 5 sin dBSMTIO -...

-- 0.023560--