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In Figure $18.46,$ each capacitor has $C=4.00 \mu \mathrm{F}$ and $V_{a b}=+28.0 \mathrm{V} .$ Calculate (a) the charge on each capacitor and (b) the potential difference across each capacitor.

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Cornell University

University of Michigan - Ann Arbor

Hope College

University of Sheffield

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

02:12

In Fig, 24.9 $\mathrm{a}$ …

12:58

In Fig. 24.8a, let $C_1 = …

02:13

$\begin{array}{lll}\text {…

04:43

24.16. In Fig. 24.8 $\math…

02:50

In Fig. $24.8 \mathrm{a},$…

03:51

In Fig. E24.17, each capac…

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07:36

In Fig. $\mathrm{E} 24.17,…

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$\begin{array}{llll}\text …

01:17

In Fig. 24.9a, let $C_1 = …

16:16

24.15. In Fig. 24.25 , eac…

So this question is a relatively complex one because we have four capacitors combined in ways of mixed, parallel and serious combination. So what we have is we have this configuration and we have a passages of each capacitor is for Quinn 00 mu F. But and we have a supposed potential between A and B is 28.0 votes. And we asked what is to charge on each capacitor of what is a potential difference across each book capacitor. So the other two friends a charge we already have the final voting we thought the total voted so funny is a charge we have. Q equals C Total time's feet total. We don't know it's just a speed, but we do not know if see total in terms of see, So which knows that hotel capacitance off the circuit in terms of the individual capacitors that makes it up. So that's the first thing we need to find. Okay, um, he ordered two finds of the past Jin's between A and B. Let's just think of everything, um, from the lowest unit to the highest unit, Celeste girl from a here and there with seizes parallel circuit. And when we see a parallel circuit, we add two. Such you capacity is off. The two branches up is that will be the final capacitors for the Intel circuit. So let's see Top here. Here we have. It's just labels and what to use 34 so that it's easier. So see one too equals well. Oversee went Ugh equals one. Oversee one plus one. Oversee too impossible. Oversee one while oversea to both works. You want seats? Your equals. Who sees officer to oversee? So we have see one too equals C over too. This is one over 70. Okay, uh, then let's look at 12 and three together. See? 123 equal. See wantyou. Plus I see three. So it just adds a month because they're in parallel. So that's just C over two plus C equals three c over too great. So that's hose. This unit has the capacities of what would fancy and finally, this is a serious with C four. So one oversee total. You could swap over see much of three plus one over C for so it's a total equals one over Well, with much of three plus. Will oversee for equals. One over, uh two overs. Three C plus Quantum, Chrissy and this dominator is five over. Species on this hostess is three C over five. Okay, so that's a tragic past Jin's who has been so that we can calculate. Settle the charge because Q equals C Times T C Total trap city. So this is far over. Three c times t. So it's three or five times of the individual. One is four point Seo's knew attempts to into ze deductive six fire int in times of the voted JJ is six is 28.0 boats. Hence, a final answer is 6.626472 times Chanteuse Negative five cooler or in a different unit to 67.2 Micro Colin. So this is a charge. A cross. This city is the church, Um, if Reece across the total capacitance because the next thing we need to know is we want to figure out How does this amount of total charge distribute out? Here's the capacitors. So let's, um, let's go from here. If SIS is plus Q. Since we'll be knocked him cute. So Q for, um, took charge across both sides of Q. We'll be, which was acute. It will be equal to 67 point, um, to my colon. But what about here? If this destructive cute, that means these two place has to add up to positive. Cute. So says Q is being distributed into the two branches off the circuit, hard as it distribute. So we cannot answer that unless we know the voted JJ So the sea will really had eaten. What is that? See? 123 So the next step, this whole circus he went to three is in servicemen. We see for Sam. Do you see what you're saying? Total carries the same about of charge and see for. And that is 67.2 mackerel cooler. But how was the 67.2 Bakula distribute with this? He wants C to an A C three and something. We cannot know it unless we know homage footage it has and supported all the protection office was. Actually, it's also a party, so this is partly and partly and part big, but we will find answers to both questions together. So Okay, so let's first trying to find sir voltage between what is true? Do you find home? And yes, okay, so we don't want to. Three. This is Q. For it's awfully good to see you and history. So the voted JJ, of course. 123 is Cuba to 32 butted by C 123 Q and history is 67.2. Micro coolant Seema to three is 1.5 times C is well 0.0 times 10 to Z Detective six. Married A system. They should also be take protective. Six. Corn says it gives us a total number of so you want to three equals 11.2 votes. Okay, so, no, you finally finds a charge across. See three, because first history we know it's 11.2 votes across it and window it's individual passages, so accuse three equals. He went to three times C, so it's 11.2 boats times. Um, it's individualized. 4.0 times 10 to the negatives ex parent. And that gives us a 40 for 0.8 speculum. Or like it actually gives you 4.48 tops two inches a day. Cliff seven cooler, but I transfer. Use macro column. So is 44.8 times. Uh, for for a microt. Hold on and fun different. Okay, is And finally we find the one for see what I see too. Or we could just do it the easy way because we know C one seat you in total has the same amount of charge is C three. Why? Because sealant c two together as they have the same voltage and together as they have seen voltage ansi. So they have to share the same church. But the charge is distributed. Um, across you one across sit you. So, um, once we will find is that q one too equal. See one too. On terms we want to Bad. Um, if you want to is the same as the 123 and see what you is just half auf sie Because here we have c went U equals Halsey. So this will be half of C C. Three times 12 is sent as the one to Siri says this is hot off QC. So because of that, we know. Q, this is 22 point for Micro kun. This is equals to both kyu won and you, too. Okay. Finally. So stopping here. We knows a charges across all for capacitors says is for Kyu won and cute you. This's for this's for Q three, and this is for Q. For it's part, be asked us to find the potential difference, the potential difference. We know that, says the protector difference across four. If 11 point to Val's, what about the potential difference across C three and identify the potential difference across history? I would say this is it. So this is the three, actually. Sorry. So this is these three, because this is a potential difference across 123 which is the same as the potential difference across these three certified before the four is just a total potential by this fever and his three, so is 28 votes, minus 11.2 votes. SAT gives us 16.8 falls. End the one and feet, too. What happens is every word V two. They're exactly the same, so they will have the same wattage, and this voltage will add up to be the one to seriously worry. Speech equals half off. He went to history equals 5.6 bolts, so yes, so everything is a circle is for the charges in everything. The square is for the potential difference between two different capacity.

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