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In Figure $18.44, C_{1}=3.00 \mu \mathrm{F}$ and $V_{a b}=120 \mathrm{V}$ . The charge on capacitor $C_{1}$ is 150$\mu \mathrm{C}$ . Calculate the voltage across the other two capacitors.

$V_{1}=V_{2}=50 \mathrm{V}$$V_{3}=120 \mathrm{V}-50 \mathrm{V}=70 \mathrm{V}$

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

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

Lectures

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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.

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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.

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Okay, so in this problem, we have this capacitor set up. So we have, um first, the path branches from a to these two capacitors comes back together. Here's B and then here's D here. See one here, see? Two years, see three. We're told the voltage between a B is 1 20 folds, and then we're told C one is equal to ah, 150 or excuse me, three Micro Fahd. And we're told that, um, the charge on capacitor one is 1 50 Micro Cruella Me's so Q one equals 150 micro. Oops. It's a little bit of live here, Um, 10 to the minus six cool homes. And our goal is to find the voltage across the other two capacitors. So let's play around with this one. Um oh, yeah, I'm sorry. This one more thing, it's Q one. So the just kind of zoom out, let's go over the main principles we're gonna use. Um, I'm just gonna state them. I think the video get too long. If I should approve them, there should probably be some nice explanation in the book. Um, capacitors in parallel have the same voltage, just like any two elements in parallel on. Then capacitors and serious have the same charge for networks in Siri's have the same charge more generally. So let's see if we can use those principles to go around and, like, fill in some information. So the voltage a crime to start with C one and C two. So they're gonna have the same voltage. So V one equals B two. So that means V's sees cure her Visa VI's cue over. See? So that's Q one over. Excuse me. That should be C. So be askew. Mercy. So Q one oversee wine equals Q two over a sea, too, so we can get that Que tu is just the ratio of sea to oversee. One times he won. Um oh, do we have? Mm. We don't actually have the, um you don't actually have the capacities of the other f c two. Is that correct? Okay, so we're gonna have to do this more with formulas, so que tu is equal to C one. Oversee too. Um Ah, see to oversee one times Kyu won. And so, um yeah, let's see. So? Well, there's an equation. Let's come up with another one. So let's talk about. I mean, we basically exhausted all the equations we could with these C one and C two. Let's talk about how their religious, you see three. So it was Capacitors and parallel are gonna have. Then serious, they're gonna have the same total charge till the total charge on this plate of sea wind see, two is equal and opposite to the total charge on C three. And so we can say that Q one plus que tu is equal. Two q three. So let's see, um, there's an equation. And then we need an equation that describes the voltage across everything. So we can say the voltage from A to B is equal to the voltage across one or two. But let's do one. Because we have the most information about one post the voltage across, um three. Just kind of going through, like, sort of pick your coughs law type thing, except for we're not gonna set it equal to zero. I guess we could, because we could model. It is like there is a battery here that's creating this voltage from A to B and so you could do a care cost law like on the outer loop. Maybe that's a more believable way to state what I just wrote and Ah, yeah, so I think and then given that we know this, um oh, this is nice. So we know that and we can get the wine because that's Cuban overseas, so we can get the three so we can save the three is equal to, um, b A B minus V one. So that's 100 120. And then V one is gonna be ah que one oversee one. So that's $150 by three. So that's 50 volts. Oh, so satisfying. You don't have to use a calculator. So that's the three s 70 volts. And, um so that's the 3 70 boards. And so, um, must think how we and we know that sequel. Oh, actually, then maybe we don't even have to find the charges. So we have the three and then therefore, um, and then we have few one cause that's equal to Q one over. See, as I discussed. So that's, um, 50 volts. I think that's all a problem actually asked for. And so that's what you want. And that's gonna be the same voltage drop across. Be too. So here's the whole answer. Um, this other charge stuff and he was interesting to know, but not necessary for

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