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Assertion: Capacity of capacitor depends on charge stored on the capacitor. Reason: If capacitance of capacitor is $mathrm{C}$ and potential difference across the c...

Question

Assertion: Capacity of capacitor depends on charge stored on the capacitor. Reason: If capacitance of capacitor is $mathrm{C}$ and potential difference across the capacitor is $mathrm{V}$, then $Q=mathrm{CV}$.(A) $mathrm{A}$(B) $mathrm{B}$(C) $mathrm{C}$(D) $mathrm{D}$

Assertion: Capacity of capacitor depends on charge stored on the capacitor. Reason: If capacitance of capacitor is $mathrm{C}$ and potential difference across the capacitor is $mathrm{V}$, then $Q=mathrm{CV}$. (A) $mathrm{A}$ (B) $mathrm{B}$ (C) $mathrm{C}$ (D) $mathrm{D}$



Answers

In Fig. E24.17, each capacitor has $C = 4.00\mu$F and $V_{ab} = +28.0 V$. Calculate (a) the charge on each capacitor; (b) the potential difference across each capacitor; (c) the potential difference between
points $a$ and $d$.

So in this question, um, we're wondering about the charge that about I would supply if we had a five micro fair capacitor. And then we had one and 1/2 colds. So, um, so voltage is one and 1/2 falls and the capacitance is five. Micro fair. Odd. Q is CV, so we just multiply those. Oh, I could do that. One of my head. Um, just seven and 1/2 micro cruel. Um, and then we want to get the energy stored. And so you is equal to 1/2 c v squared. So it's just gonna be 1/2 times five times 10 to the minus. Six times 1.5 squared. So let's go ahead and put that into a calculator. Um, times I was 10 to the minus six. Oh, has 5.6. Um, micro Jules. And so let me go ahead and label these. So this is a This'd be now to approach. See? Um oh, I guess I was both a Those were both, eh? How much charge? Ah, we're wanting How much charge? If we wanted to add one jule of energy to the capacitor. And so for that, let's use. Um, see. Sorry. So how much charts? So we're looking for Q. We have the and we have C. And we have, um, and we have you. So Q c and you. So let's use you is 1/2 Q squared over. See, not just subbing in C. S Q Burbey into this equation. And so, um, for exude, I guess having V is equal to Q oversee in this equation. Okay, so we want to solve for the charge, so Q is gonna be equal to to see you divided by no division needed. I could just underline it for importance. Okay, so then we want to just take the square root of to see you. So you we said was one Jule. So we want to take the square root. Ah, two in the times. Five times, 10 to the minus six, and then brats 0.0 three. So that was 3.16 times 10 to the minus three. Sorry. That's was to be a one, uh, cool ums. And then what else is asked? I guess this one I got this one would be. And then what would be the potential in that case. So first, let me re label this be so V is equal to Q Over. See? So we want to just divide this charge by the capacitance so divided by five times 10 to the minus six. So let me go ahead and do that. Yeah. No, I got 632 folds. So kind of a lot to get to a full jewel.

So is this question we have Equation 18.19 from the chapter said you equals well, half o que vi and what this is asking that it wants us to express it in terms of U equals a Q Square over to see and half of CB script. So what do we do that just by observing it, you can see that pretty much What we want is we want to be able to convert between Q, c and D. So we wanted between these reporters who want to be able to change from one in terms of the other is this can be done by using that equation of q equals C Times thing. So in part, we what we have is we want to get rid of the V dependence. So what we would do is instead of the we will have cute about it by sea and says, Give us do you see over Hughes Girl just is desired. Second, we have 1/2 of C B Square, and so what again that compares this play's original Well, what we have this week get rid of Q. Over here, so u equals well, heart of we want to express queue in terms of C times fee again terms fee Because this beauty So that is what half of CVI skirt again, just as we want from party.

Everybody. So we need to find the charge and caps it, er and a potential difference across each one and potential difference across A and B. So for before began, this is the Siri's. And we're just gonna kind of solve what we need here. Okay, so we're solving the C one and C two here, Siri's. So for that we have or clients for four. Plus, for in this we have two new open. Now, for a 2nd 1 we have C one plus C three when this whole thing okay, And here we have to you, plus or you, uh, which equals six new up. Okay, now we have to the 3rd 3rd 1 So here we have the 2nd 1 Okay. Times the C four. Now we're doing, you know, the entire circuit here. Okay. And so we have C two times, actually, plus C four. Okay, I and so we have six times board six plus four and we get to point for you. And now we also confined is the charge of the system for a to B. Okay, Bolt may be and we get 2.4 times 10 to the sixth of times 20 e bolts, which gives us a total charge of 67.2 times 10 to negative six. Um, See, Orme, you see you want OK, how we can do a, which was asking s o a was asking as the cap since so it's gonna be the c four, um, or which is gonna be 67.2 times 10 to negative six. Si. OK. And because C two is also is huge you as well, so that also equals this number. Okay. And now you have not. And so we also need find bring it down a little bit. So we have the vote to eagles. Cute. You over cto, Okay. And we get 67 at times, 10 to negative six divided six times, 10 to negative six, which gives Ausubel of 11.2 bolts. Okay. And now we can find the cue. The charge of three, which is C three in a vault too, which is for you. Uh, times 11.2 bolts, Which equals, um, 44.8, you see, And I equals u C three here. Okay. And your, um now we can do you of one, which is your key one equals C 12 equals two times 11.2 volts, which goes 22 point you see. And that is gonna be equal for C one and see to grab and let me address Mark that. So we have C one C two, we have C four. So 1234 accounted for. So we did that. Okay. And now or be And he is asking for, um, the potential differences across. So we have a potential difference here. You won oversee one, which he goes 22 point for. You see, it looks like I forgot the four here, divided by the sea wind, which is for you have being that those cancel out here. Those is only 5.6 bolts with potential difference. And that's not equal to your C one here. Okay. And now we have to be to which is gonna have, um, the same thing, actually. So your bolts of I'm actually going to do your, um v two slash C two is also about equal this crisis we have this and this bad boy are gonna equal this. Okay? And let me put, um, this as and so that we don't be confused. OK, here we go. And now we do the Volt of three, which is gonna be 44. Hello. 44.8. You see, divided by four U F which he calls 11.2 bolts. Okay. And that is for your C theory. And now for the 4th 1 we have 67.2. You see the writer by four you, which gives us 16 point e volts with a potential difference here and as your C four. Okay. And you're see, question is asking us the potential difference between A and E. So we hav potential difference between A and D. And that is equal. Teoh. Um three. So it's gonna be 11.2. Okay. Thank you, guys.

This question today has three parts, so first we'll start with Part A and we know that the charge between each player is given as Q equals C Delta V and the total energy is given by U equals 1/2 que absolute value of Delta V. So now we can move on to part B and by replacing the vacuum between the plates with a dye electric constant K, the capacitance will increase. And we know that it will increase due to this equation, which is C is equal to a all over four pi Kappa deep, and we know that the potential is kept constant. And we know this because of the equation Q equal. See Delta Bi and that the charge will increase on the plates since the capital has increased. Meanwhile, we know that you is equal to 1/2 que absolute value of Delta V. The total energy will also increase as the charge increases so total e increase as charge increases. And next, we know that the increasing energy comes from the fact that work is done by the external agent, and in this case, it's the battery to pump charges into the points in order to keep the potential difference from being


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