5

1. (20 pts:) Two parallel plates of 120 cm2 are connected to a battery that provides them with a voltage of 12 volts. The plates are separated by a 1.0 mm thick lay...

Question

1. (20 pts:) Two parallel plates of 120 cm2 are connected to a battery that provides them with a voltage of 12 volts. The plates are separated by a 1.0 mm thick layer of air. If the space between the plates is filled with oil, with a dielectric constant it is 4 and a dielectric strength of 12x106 V / m; and then the battery is kept connected: a) How much is the capacitance? b) How much is the voltage across the capacitor? Explain c) How much is the charge now? d) How much is the electric field?

1. (20 pts:) Two parallel plates of 120 cm2 are connected to a battery that provides them with a voltage of 12 volts. The plates are separated by a 1.0 mm thick layer of air. If the space between the plates is filled with oil, with a dielectric constant it is 4 and a dielectric strength of 12x106 V / m; and then the battery is kept connected: a) How much is the capacitance? b) How much is the voltage across the capacitor? Explain c) How much is the charge now? d) How much is the electric field? Can the oil be ionized? Explain: e) How much is the stored electrical energy?



Answers

A parallel-plate air capacitor is made from two plates 0.200 m square, spaced 0.800 $\mathrm{cm}$ apart. It is connected to a $120-\mathrm{V}$ battery. (a) What is the capacitance? (b) What is the charge on each plate? (c) What is the electric field between the plates? (d) What is the energy stored in the capacitor? (e) If the battery is disconnected and then the plates are pulled apart to a separation of $1.60 \mathrm{cm},$ what are the answers to parts (a), (b), $(c),$ and $(d) ?$

Right In the given problem, there is on your capacitor off parallel plate capacitor a plate separation. In the past, it has been given as 1.50 millimeter, or we can say this is 1.50 into 10. Dish for minus 3 m. The charge stall over the plates of the capacitor is 0.18 zero. Michael Fulham Potential Ukraine cycles the place off the capacity just to 100 ball in first part off the problem, we have to find the capacitance off this parallel plate capacitor, for which we use a simple relation for the President's, which is Sequels to Cuba by the So here it becomes 0.180 in tow. Turned issue par minus six along forwarded. This is 200 world. Finally, the capacitance here comes out booby 90 in tow, 10 days apart. Minus Well, had it. Or we can say this is mine. D Geico Parrot, This is the answer for the first part of the problem. No. In the second part of the problem, we have to find the blade area as the police separation is given post. So find this. He used the expression for capacitance, which is upside and not a by D. So from here, the expression per plate area will come out of the sea into D divided by the absolute primitive ity. Absolutely not. So putting all these values here for capacity and this is 90 into turned eight for minus well, for separation between operate, This is 1.50 in tow. 10 Dish a par minus three were upset and not this is the 8.854 in tow. Standish par minus 12. This standish one minus 12 will be cancelled. And finally this Lydia becomes 15 point toe fight in tow. Standish Bar minus three Niedere Square. Or we can say area is your 0.1 I do Meter square. This is the answer for the second part of the problem. No, in the part part of the problem, me have been given the electric breakdown for here. And this starlet breakdown for here occurs. Yeah, and left click field, Or he is equitable. Pre 10 in tow. 10 patients. Barber. Thanks for Amita. This is a maximum applicable electric field. So for this electrical, a maximum applicable potential will be given by Okay, in beauty, the lining pickerel of electric field is the key factor behind this expression. These were don't into the or we can say for me this is 3.0 into 10 days for six world for a meter. And for Blake separation, this is 1.50 into inundation. Par minus street Mito This meter got cancer, so the maximum potential difference that can be applied across the place I'm so to be 4.5 in tow tenders apart tree world it becomes the answer or the third far off the problem. Now, for the fourth part of the problem, we have to find the energy store in the capacitor or that given judge for this job. So the expression poor energy sporting the capacitor you can use here. This is half senior swept. It becomes hard into the passage since which is 90 in tow. Tend a super minus 12 that it multiplied by the potential which is 200 Clint. So this is enjoys and finally, energy scalding Such a capacitor comes out Bobby 1.8 in tow. 10 dish par minus six jewels for we can say you is equal to one point it Micro Joe's. This is the answer for the last the four. The last part of the problem. Thank you.

In this question we have to capacities connected in series C. One and C. Two. Okay. Uh yeah connected to uh 36 boards. Power supply king C one, C two. Okay. In C. Two. Um they have that's a dielectric. He was slain. You dielectric constant 7.0 Okay. So there are three parts in this question. Uh you want to find that after charging by the charges, the total energy stored in the capacities and the electric fuel in C. Two. So given that they have the same area, the area is one cm square. We also have the same place separation which is 0.1 mm. Yeah so to do a the charge on each capacitor are the same. And so to do this easily we can find equivalent capacities. So uh for capacitors in series the the girl and capacitance. The real estate broker of the capacity uh equivalent capacitance. Yes I some not there. Price of progress of the capacitance. Yeah. So um and see one is able to S. M. A. A. D. And then see two. Yes papa excellent on a over the so the equivalent capacitance is one of the C. One last one overseas too. And take the recipe about that. And so you can simplify when you simplify this is what you get. That's not A. Or D. Times one less. One over par pa and the whole thing this whole thing reciprocal. So you can substitute the values. Yes. So the area is 10 to the negative formula square. That is also uh 10 to the negative four. Yeah one plus 1/7. And to the negative one in these two cancer out and you get 7.74 times tend to die. Maybe the Charles. All right okay. So the charge on each capacitor, the one with the Q two is equal to the equivalent times we. Uh huh. So does modify the equivalent capacitance victor Boteach which is 96 all the potential difference. And you guys there were 27 43 There are no questions. Okay, so this is the answer for part a the property. I want to find out a little energy starting the both capacitors. Okay. So we're using U. Equals to have C. B square. In this case you would just be half tons of equivalent capacitance and sweet square. So half times seven points out four and stand to the negative trough times 96 square. Then you get 3.57 times 10 to the negative eight juice thing. Then I see we want to find electric fuel between the place and see too. So first we find C. Two. Is he going to cop are excellent I E D. Yes. We're just putting the numbers and you get 6.2 zero times 10 to the negative 11 carat. Then, uh we can find V two, which is you see two and E two is E O. D. Vito E. So we have Q over. Uh see too hasty. Okay, So you can just substitute given members. Okay? So just yourself calculator. Okay? And you get 1.2 zero times 10 to the five volts per meter. Think. So this is the answer for Patsy, and that's all for this question.

In this problem. On the topic of capacitance, we have a parallel plate capacitor which have plates of an area of 0.12 m2 and separation 1.2 cm. A battery charges the plates to a potential difference of 120 fold vaults before being disconnected. And we then place a dielectric slab which has a dielectric constant of 4.8 and thickness 4mm symmetrically between the plates. We want to find the capacitance before the slab is inserted. The capacitance with the slab in place, the free charge before and after the slab is inserted, the magnitude of the electric field, firstly in the space between the plates and then the between the plates and dielectric. And then in the dielectric itself, the potential difference across the plate with a slab in place. And lastly the external work that is involved to insert the slab. Now, initially the capacity capacitance is C. Not, which is absolutely not times the area A Over the plate separation D. Which is the constant capsule or not, which is 8.85 Times 10 to the -12. Cool um squared new two metre squared Have the area 0.12 m2 divided by 1.2 Times 10 to the -2 m, which gives the initial capacitance to be 89. Pickle Ferrets. Now for part B. We find the capacitance C to be absolutely not times a James camper of uh coppa into d minus B. Mhm plus b Putting in our values. This is 8.85 Times 10 to the -12 in S. I. units which are suppressed Times the area of 0.12 m2 times the dielectric constant 4.8, Divided by the dielectric constant. Kappa 4.8 Into D -B which is 1.2 -0.4 Times 10 to the -2 m. All of this plus B, which is four times 10 to the -3 m. And so calculating, we get this capacitance C to be 1.2 Times 10 to the power to PICO ferrets mm. Do now before part C. Before the insertion we have the charge Q. To be see not times V which is 89. Pickled Carrots, times 100 and 20V, which gives a charge of 11 Nano columns In party. Since the battery is disconnected, Q will remain the same after the insertion of the slab. And so Q remains as 11 nana columns mm. Now for part E. Field strength E is equal to Q over. Absolutely not times A which is 11 times 10 to the minus nine columns divided by 8.85 times 10 to the -12. Cool. Um squared for newton meters squared Times The area. 0.12 m2 which gives the electric field To be 10 kilovolts per meter mm For part F we have the electric field the prime in the dielectric to be the electric field E over the dielectric constant kappa which is 10 Kilovolts Permata divided by 4.8, which gives the electric field in the dielectric slab to be 2.1 kg balls per meter. For part G. The potential difference across the plates, V is equal to E into d minus B plus E. Prime times B. Putting in the values, we get this to be 10 kilovolts. Permata time zero point 012 m zero four m mhm plus 2.1 kg balls Permata time zero 0.4 Times 10 to the -3 meters, Which gives a potential difference v across the plates to be 88V mm. Now, lastly for part H, the work done W is equal to change in energy dealt to you and this is q squid over to Into one over C -1 over. See not So again, if we put our values in this is 11 Nana columns or 11 times 10 to the -9 columns squared, divided by two into one over 89 times 10 to the -12 carats minus one over 120 times 10 to the -12. Farage's, Which gives the work done to B -1.7 Times 10 to the -7 jules,

So in this problem we're considering a capacitor that is charged to a potential difference of 120V and then you place a slab of dielectric material between the plates. Um and so we want to start off by trying to figure out what is the capacitance of the capacitor Before we add the dielectric before the dielectric is added, capacitance would be given by epsilon, not a divided by D. And so that's just going to be 8.85 times 10 to the negative 11 fair ads for part B. We now want to figure out what the capacitance is after you have added in the dielectric and in that case we want to consider the capacitors as two capacitors in series would that is the air filled capacitor in one that is dielectric filled. So our air filled capacitor, I'm going to call see one and it's going to have a capacity is equal to epsilon, not a divided by d minus T because 80s amount of its thickness is now taken up by the dielectric. Um and then the dielectric capacitor has a capacitance of kappa, absolutely not A over T. And so to find the capacitance of the entire capacitor we would find the equivalent capacities and if these are in series that would be one, oversee one plus one over c two, take the inverse Which would end up being equal to 1.2 times 10 to the -10 fair ads mm hmm For part C. We want to figure out what the charge is on the capacitor before you introduce the dielectric. So Q. Is just going to be C times V. Where again C. Is the capacitance without in parts A. And B. Is the voltage 120 volts. And that result in a charge of 1.06 times 10 to the -8 coup loans for part D. We want to find the charge after you have added in the dielectric. But it said in the problem that you have disconnected the battery and so there's nowhere for charge to come from or go to. So the charge is going to stay the same. We're still going to have a charge of 1.6 times 10 to the negative eight Cool albums for part B. We want to find the electric field between the plates and the dielectric. So in the gap of air and in general the electric fields between the plates of a parallel plate. Capacitor is given by Q over epsilon. Not A. So if we use the charge that we found in part, excuse me. In part C, you would get that the electric field is 9981 volts per meter for part F. We want to now find the electric field inside the dielectric. We're going to use that same formula. But now, instead of just absalon not you have to multiply by the dielectric constant. Um and so that would change the electric field and you would get 2000 and 79 volts per meter inside the dielectric for a part G. We want to know what the voltage drop is across the capacitor once the dielectric is added. Um And so that's easy using the relationship that V should be equal to Q divided by C. In this case we want to use that C equivalent that we found in part B. Um and we would get that the voltage drop should be 88V and lastly for part H squeezing it in at the bottom. Here we want to know what is the work that's done in inserting the slab. So work done is going to be equal to the change in potential energy. And we know that the potential energy can be found by Q squared over. Sorry? Yeah Q squared over to see. So changing potential energy would be cute squared divided by two times one, oversee -1, oversee not where C not is the capacitance we found in part A. And C. Is the capacitance we found in part be. So when you plug in those values you get negative 1.7 times 10 to the negative seven jewels of work done


Similar Solved Questions

5 answers
Value of thc Uim"t? T Xn Lim 7y0 n (n+1) zan-1
Value of thc Uim"t? T Xn Lim 7y0 n (n+1) zan-1...
5 answers
Calculatc thc indicated limit-DNECalculute thc indicated linut lim 24_ siru)URE
Calculatc thc indicated limit- DNE Calculute thc indicated linut lim 24_ siru) URE...
5 answers
Il you (uvd solution of KCI hatthas #pH 105.what /s Ute I1bo | Mwr solun?Vicr Infett FonnatPafAE#p
Il you (uvd solution of KCI hatthas #pH 105.what /s Ute I1bo | Mwr solun? Vicr Infett Fonnat PafAE#p...
5 answers
Use the ALEKS calculator to solve the following problems_(a) Consider distribution with 2 2 degrees of freedom. Compute P '(-1.21 <1< 1.21). Round your answer to at least three decimal placesP(-1.21<1<121)- ] (b) Consider distbuton with 11 degrees of freedom_ Find the value of such that P (t < c) = 0.10 Round your answer to at least three decimal places
Use the ALEKS calculator to solve the following problems_ (a) Consider distribution with 2 2 degrees of freedom. Compute P '(-1.21 <1< 1.21). Round your answer to at least three decimal places P(-1.21<1<121)- ] (b) Consider distbuton with 11 degrees of freedom_ Find the value of suc...
5 answers
Is it possible to express the zero vectorlinear combination ofandmore-3than one way? Justify your answer.
Is it possible to express the zero vector linear combination of and more -3 than one way? Justify your answer....
5 answers
4. Solve and show each step using Scientific Notation LO0251150001L.0Z52 (150)(.000025)(2500)Hint Convert into numbers with exponents and solve accordingly.
4. Solve and show each step using Scientific Notation LO0251150001L.0Z52 (150)(.000025)(2500) Hint Convert into numbers with exponents and solve accordingly....
5 answers
(2 points) Find values of A and r that make the function P(t) = Aert match the data:a) P(O) = 4 and P(5) = & P(t)b) P(O) = 7 and P(11) = 4. P(t)c) P(2) 10 and P(6) = 15. P(t)d) P(3) = 15 and P(6) = 11. P(t)
(2 points) Find values of A and r that make the function P(t) = Aert match the data: a) P(O) = 4 and P(5) = & P(t) b) P(O) = 7 and P(11) = 4. P(t) c) P(2) 10 and P(6) = 15. P(t) d) P(3) = 15 and P(6) = 11. P(t)...
1 answers
According to the U.S. Department of Education, $42.8 \%$ of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
According to the U.S. Department of Education, $42.8 \%$ of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?...
5 answers
You have two boxes. Box A contains mole of water (HO) and box B contains 1 mole of hydrogen peroxide (HzOz):Which box contains more formula units? Select ][Select / Which box contains more atoms?Select |Which box contains more hydrogen atoms?Select / Which box contains more oxygen atoms?Which box contains more grams . of matter?Select ]
You have two boxes. Box A contains mole of water (HO) and box B contains 1 mole of hydrogen peroxide (HzOz): Which box contains more formula units? Select ] [Select / Which box contains more atoms? Select | Which box contains more hydrogen atoms? Select / Which box contains more oxygen atoms? Which ...
5 answers
(p)6 Use convergent the integral JO test divergent: 6 X{ne"} determine whether the series
(p) 6 Use convergent the integral JO test divergent: 6 X{ne"} determine whether the series...
5 answers
For the following sample 35, 45 , 30, 35 , 40, 25 . Findthe standard deviationSelect one:a. 12b. 50c. 7d. 40
For the following sample 35, 45 , 30, 35 , 40, 25 . Find the standard deviation Select one: a. 12 b. 50 c. 7 d. 40...
5 answers
Transferred heat being Is due to the on the watct- the ice cubes
transferred heat being Is due to the on the watct- the ice cubes...
4 answers
The blood typing antigens are located:Oa. In serum Ob. RBC surface Oc. WBC surface
The blood typing antigens are located: Oa. In serum Ob. RBC surface Oc. WBC surface...
5 answers
Pont) Sketch the vector Ileld F(x,Y) = 3/+ Sjand calculate the Iine Integral of F along the line sogment from (~2,~5) to (-3.5) .
pont) Sketch the vector Ileld F(x,Y) = 3/+ Sjand calculate the Iine Integral of F along the line sogment from (~2,~5) to (-3.5) ....
3 answers
3x8lim I00 x + [
3x 8 lim I00 x + [...
5 answers
Part DDetermine whether the image is upright or invertedBoth images are uprightThe image of the first object is upright and the image of the second object is inverted_The image of the first object is inverted and the image of the second object is uprightBoth images are inverted.
Part D Determine whether the image is upright or inverted Both images are upright The image of the first object is upright and the image of the second object is inverted_ The image of the first object is inverted and the image of the second object is upright Both images are inverted....
5 answers
The adjacent ligure shows a wave whose speed is 280000 m/s. Calculate the amplitude; period, frequency, and wavelength of the wave.80 cmnS
The adjacent ligure shows a wave whose speed is 280000 m/s. Calculate the amplitude; period, frequency, and wavelength of the wave. 80 cm nS...

-- 0.062277--