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Two thin parallel circular plates of radius 20 mm are separated by 5 mm A material with dielectric constant K =2.5 is filled in the space in between the plates. The...

Question

Two thin parallel circular plates of radius 20 mm are separated by 5 mm A material with dielectric constant K =2.5 is filled in the space in between the plates. The plates are then connected to a 9-V battery:2Calculate the capacitance of the plates ii. Calculate the amount of charge accumulated at the plates. iii. Determine the energy stored in the capacitor: iv. If the battery is disconnected to the plates, predict the voltage across the two plates_ [6 marks]

Two thin parallel circular plates of radius 20 mm are separated by 5 mm A material with dielectric constant K =2.5 is filled in the space in between the plates. The plates are then connected to a 9-V battery: 2 Calculate the capacitance of the plates ii. Calculate the amount of charge accumulated at the plates. iii. Determine the energy stored in the capacitor: iv. If the battery is disconnected to the plates, predict the voltage across the two plates_ [6 marks]



Answers

Find the capacitance of a parallel-plate capacitor with circular plates $20 \mathrm{cm}$ in radius separated by $1.5 \mathrm{mm}$

This question. You didn't. You need to use the capacitance formula? A. Absolutely not divided by D, So the first part asks you to find the capacitance. So area is given to be two meter square, so let's substitute that distance is given three millimeters two times 8.8 times 10 power negative life divided by distances three millimeters so three times 10 power negative, negative three meters even though your units should be consistent. So the answer here is 5.9 times 10 power negative. Nine Better? No. The next part is to find the charge on capacity, which is C Times T. We are given the potential difference, which is 45. So you need to multiply capacitance by 45. You will get the answer as 265 times five times 10 power. They get to nine. Cool. Um, since you want to keep the answer in just two significant digits, it's 2.7 times 10 Power Negative. Seven. Gollum Next part is to find the energy store energy stored. In this case, it's half see the square since we know the sea is 5.9 and applied potential is 45 The answer here is just multiplication. Oh, capacitance on DDE potential different square. So your answer will be given by 59 seven, three 0.7 times 10 Power *** too nine. So let's keep the answer in just two significant digits. So your answer again. Now it's 6.0 times 10 power Negative. Six Jude, this is energy stored. Now there is a part which also asks you to find the electric field now electric field. Let me write it as e f equals me divided by D So the potential difference is 45 distances three millimeters So I need to write in terms of meters. This will give me 15,000 world for meter. See, the units are different for energy is Jules and for electric field It's world for meter No Next buck asks you toe find the same quantity when the slab of plastic is inserted with the dialectic constant off 3.2 So capacitance Now, uh, the final capacitance will be just die electric constant times the initial capacitance The dialectic constant is 3.2 times 5.9, which was initially capacitance. So your unsent is 3.2 times 5.9. That is 1.9 times 10 power. Negative eight. See that I have tried to keep all the answers in terms of two significant digits. In this case, Charge store is also multiplied. But K, that is di electric constant from the initial charge. So okay, time's Q that mean, like zero here. So you understand it is initial charge. Initiate the passage ins. So what? Initial charge Waas 2.7 times 10 587. So if you perform that operation is just 8.6 times 10 power negative seven colon. Now we're supposed to find energy store. Since energy store is half see me square, your energy will also be multiplied by factor of GABA. So your energy now really just be 3.2 times this six point zero. This gives you 1.9 times 10 power negative fight Jewish. On the other hand, electric field will be unaffected because it doesn't have the factor off capacitance because in it, so you will have. It's just very divided by these or 15,000 boat per meter

In this question, It would give it there. Is it Captain stood up. Remember place. And between the there is a strictly law. It quite to four. And don't tend to give our poor bull per meter. And the constant of the blade is you white. Seven. Fight the separation between the makes off the Kappa Studies 1.95 and 10 to the power off minus three meters. If the chart on the place of the captain stories y 775 micrometer, that is a 0.77 pipe into 10 to the power bi six school up that we have to calculate that Kappa skins and area off Beach people, please. Since there is little the electric field with me, that place understands the potential difference. But wind up leads me in Jordan. At cap assistance will be charged. Hold what unit? Potential difference that you about in duty, not substitute. And that is filled with updated eight Quite who for? In tow? 10 to the power six and districted, 1.95 in tow. Tendo de powered by this. Then you saw already on simplify the tapestries we are getting for quite in tow. to tend to the bar minus seven. Parrot, did you read it? My prophetic. No area of the place can be calculated by the bad luck after that, not a appointee. Prosperity played, so your place would be No. We are substituting the value here, Captain Street to be a major. Well, quite a doing. 10 to the power off minus seven. Distance between the plated value of the electric. Constant is 3.7 pipes on. He had it. Okay, 30. So the doing the production here and better club after noughties ate quite a fight. I can't do the by my guest. Well, on solving you will get Aereo. That meant to be 28 23 meters square.

Hi. The given problem We are discussing a battle unpaid capacitor before inserting that electric slam between ex players and after inserting the dialectics left between it splits its initial capacitance before inserting the electrics left. I've been given as well 0.5 people that it or you can say this is 12.5 into 10 days apart minus well about it. This capacitor is made using the circular place and the radios off. These circular place has been given as free 100 centimeter. Or we can say this is 3.0 in tow. 10 super minus two meter. No, the charge over the place Initial charge without the dialectics left between the place the charge waas 20 by 10 p coholan and opera Inserting the electrics left discharge becomes Kudisch is going to 45 10 bqool The back three remains connected between the plates off capacitor in the act off, inserting the Gallup licks lead between the place. No. In the first part of the problem, we have to find the directory constant of the medium as we know on inserting that electric slept between the plates of the capacitor, then the Berkeley still remains connected. The charge become skate time so we can say the delivery constant cape is nothing but because Tokyu dish by you so putting these values there 45.0 PICO Coolum divided by 25.0 PICO column We get expression for you get the value for this Alec Constant as 1.8. And this is the answer for the first part of the problem? No. In the second part of the problem, we have to find the potential applied between the players off this capacity for which never used a simple relation between potential and charge. And capacitance, which is week, was took you by sea. So initially, charge WAAS 25.0 Equal alarm and the capacitance waas WellPoint by fecal matter. So this potential here comes out to be just 2.0 volt and it becomes answer for the second part of the problem. No, in the lower part of the problem re Yeah, do fine. In this time you have to find electric field at a point midway between the place. But as you know, electric field remains uniform at every point between the plates of the capacitor. So in order to find this electric field as electrical is given as the potential Grady in and we know the value potential. So first of all, we should know the spacing between the players off the capacitor. So I find this is busy. The use the expression for the passage ins off a parallel political passenger, which is absolutely not a by D capacitance. The doubt that I'll appliques lag between the place we know. The capacitance is well, 15 into 10. Dish for minus 12 is equal to absolute not, which is 8.8 by four in tow, 10 days to par, minus well multiplied by area, which is spy into our square and divided by D. And this D is not given to us. So to find it the make across multiple vision. So this is a gap between the plates comes out of the 8.854 into Dan Bishop ar minus well into 3.14 for the fine, and for areas, this is three into 10. Best par minus school for the whole square, divided by capacitance, will 0.5 in tow. 10. Dish for minors will So finally this be comes out to be approximately 20 into 10 day super minus four Nita So electric field midway between the plates of the capacitor comes out to be leave I d we know the value. Be stupid zero divided by 20 into tender for minus four. Finally, this electric pre meditated in the plates of the capacitor comes out to be one house in boy 4 m. Now we have to find the same expression, same value off electrical intensity Midway, bring in the players. But after inserting the electrics left and s, the back agreements connected. So we needs the potential difference as the list we like different e really dancing whether we are finding these values before connecting the before inserting the electric or after inserting that electric. So there are two answers ritual in insane one for this electric here and other for this potential potential loss going insane before inserting the electrics left between the pillars of capacitor and after inserting the analytics left Thank you

So the capacitance is found from Equation 17-7, with the voltage given by 17-4. So Q here is equal to see Time's V, which is equal to see Time's the electric field times the distance. D Therefore, the capacitance, uh, go ahead and write that down here C is equal to Q divided by the electric field. E times the distance D, Which queue here is equal to 0.6 75 times 10 to the minus six. Cool ums. The electric field e is equal to 8.24 times 10 to the fourth. And that's gonna be volts per meter that's gonna be multiplied by the distance D, which is equal to 1.95 times 10 to the minus three meters. Oh, so plugging those values in this expression, we find out the capacitance C is equal to 4.2 times 10 to the minus nine fair acts so we can box it in this part of our solution to the question. Okay, so now the play area here is gonna be found from Equation 17-9, which says that the past in C is equal to the dialect. Her constant K of the material times? Absolutely not. The vacuum permeated the of free space times, the area divided by the distance between D. So the area A is equal to the capacitance See which we've just found times D same distance in the previous part when we solved for the capacitance divided by the dye electric constant K, which were told, is equal to 3.75 times Absalon not which is the Vacuum Perm utility of free space. It's equal to 8.85 times 10 to the minus 12 Coolum squared times Newton per meter squared and this is equal to 0.247 This is gonna be meter squared weaken box. That in is the solution.


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