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Figure 18.47 shows a system of four capacitors, where the potential difference across $a b$ is 50.0 $\mathrm{V}$ . (a) Find the equivalent capacitance of this system between $a$ and $b$ . (b) How much charge is stored by this combination of capacitors? (c) How much charge is stored in each of the 10.0$\mu \mathrm{F}$ and the 9.0$\mu$ F capacitors?

(a) $C_{\mathrm{cq}}=3.47 \mu \mathrm{F}$(b) $Q_{\mathrm{nt}}=174.0 \mu \mathrm{C}$(c) The charges on both capacitors are the same for the entire system and equal 174.0$\mu \mathrm{C}$

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

Hope College

University of Winnipeg

McMaster University

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Okay, so for this problem, we have four capacitors. I'm gonna go ahead and draw the system. Um, so let's see. Ton, 589 or 10 95589 Okay, so here's 10 five, and then groups made that a little long. So 10 5 neat and nine. And we're told that the potential difference across a B is 50 volts. So here is a Here's be the Delta Bi is 50 volts. And then our goal is to get first the equivalent capacitance of the system between A and B. So to do that, you wanted, um if you're adding and wanna consider the equivalent resistance rules. So if you're adding and parallel, just add regular soc equivalent of C one pussy too, and then adding in Siri's, you want to do the inverse adding, So let's find the equivalent resistance of C H and C five. That's just gonna be, um, 13. Um, and then one of these has that micro fair odds. Those 13 micro fair, odd and then to find the total. What you want to do is you want to take the this 13 and do this inverse adding thing. So see equivalent is gonna be one over 13 because the network of five and eight is in Siri's with the no, but the nine and 10 capacitors. So you have one over 13 plus one over 10 plus one over nine. And so, if you saw first see equivalent by adding these fractions and inverting them, maybe you'll get what I got, which is one won over nine into a calculator right now. So that's 3.47 groups. Um o Okay, so three 0.47 grand litter. Why, there's some kind of flag where something going on, Press something. Okay, well, that's where I hope that goes away. Oh, sorry. And then that stuff. Why not, Meters, Terry. Right. This so that's C equivalent is 3.4 seven Micro fair ad. Okay, so the next question asks us how much charges stored on this combination. So, um, this I like this problem because it kind of illustrates the use of even finding the equivalent capacitance. So, um, so the charge is just gonna be the equivalent capacitance times the voltage. And so that equivalent capacitance is 3.47 and then the voltage iss um, I think 120. Some putting this into my calculator right now? Nope. No, it's 50. So that the times would be that was 1 74 micro colognes, And then we want to get how much charges stored on each of the capacitors. So what's gonna happen is, um, s o the battery. Like, imagine a battery is like putting this charge on this system. So it's gonna output, charge and put, um And then it's gonna fill up capacitor the 1st 1 the with the value of 10 micro fair odds and so is gonna put all of the charge on that. It's gonna polarize, and then adding the charge to this 10 is gonna polarize it and make this right plate of the 10. Have an opposite sign charge, and then that's gonna pull her. And then that's gonna polarize. Um, these two plates and they have to have a charge that adds up to the charge on this negative side of the plate. So, um, these two are gonna sort of split that charge in some sense, and how they split it is determined by their capacitance. But before I get too far, I'm just gonna write down that The charge on the tens, That's what they want. The charger in each of them. So the charge on the 10. Oh, wait, what is? Oh, it actually only asks for the charge stored on the 10 and nine mere microfiber rod capacitors, so we don't really have to worry about that. So, um Okay, so the queue on the nine is just gonna be this secure in the time. It's just gonna be the, um, charge output by the battery. So that's gonna be the so I guess I can say Q 10 equals Q nine equals 1 74 micro who loans, Um, And then, by the way, you could consider, um 99 The system is, um, is symmetric, at least structurally, with respect to nine and 10. So nine is gonna also have the full amount of charge. The only time the charge is gonna get split. This between five and eight.

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