5

The parallel plate capacitor of plate area 4210 1n? is filled with wwo dielectric slabs; each with thickness 3 mm as given in the figure below: One slap has dielect...

Question

The parallel plate capacitor of plate area 4210 1n? is filled with wwo dielectric slabs; each with thickness 3 mm as given in the figure below: One slap has dielectric constant 2 anc the other 6. How much charge does tne 10 V pattery store on the capacitor? (15 points) '0 8 8 1 Monamed f~ /^ 4 1 { 1 0 14 '

The parallel plate capacitor of plate area 4210 1n? is filled with wwo dielectric slabs; each with thickness 3 mm as given in the figure below: One slap has dielectric constant 2 anc the other 6. How much charge does tne 10 V pattery store on the capacitor? (15 points) '0 8 8 1 Monamed f~ /^ 4 1 { 1 0 14 '



Answers

In Fig. 25 -56, the parallel-plate capacitor of plate area $2.00 \times 10^{-2} \mathrm{~m}^{2}$ is filled with two dielectric slabs, each with thickness $2.00 \mathrm{~mm} .$ One slab has dielectric constant $3.00,$ and the other, 4.00 . How much charge does the $7.00 \mathrm{~V}$ battery store on the capacitor?

In this problem, there is a capacitor filled with to die electrics um and connected to a battery and we want to figure out what is Q. The charge that will be stored on the capacitor when you have a seven volt battery connected to it. So Q in general for capacitors is going to be see time's V. Um and because we now have a capacitor that's filled with two types of dielectric, we're going to consider that as two capacitors that are in series with each other. And so we'll need to use the equivalent capacitance to find the charge. And the equivalent capacitance would be one, oversee, one plus one, oversee to inverse see one do this in a different color. C. One, the capacitance of capacitor, one would be Kappa one. Absalon not a over D. C. two would be capital to absalon, not a over D. And so when you plug it in you can simplify and find that Q would be epsilon, not A over D. Times one over capital one plus one over capital too in verse. And again you're multiplying by the voltage. So plugging that all in, you get you should get a charge of 1.06, 2 Times 10 to the -9 columns

So this question they're asking for a lot the capacitance, the charge, the electric field, the potential energy and the potential energy after and after we're including a di electric. So let's just write down our givens. We have a an area of two point zero meters squared and then we have a separation distance of three point zero millimeters. We can say this is equal to point zero zero three meters. Ah, and we have niece of oh equaling three five volts. So the first thing we should find, the capacitance, the capacitance, Sisa Bo is going to be equal to Absalon, not the electric primitive ity of free space times area divided by the separation. So this would be equal to eight point eight five times ten to the negative twelfth and then times two, divided by the separation distance of point zero zero three. So this is going to give us five point nine times ten to the negative ninth carrots. So this would be one answer for party. Ah, we could probably do que ce of theirs. The charge, Q subzero something any people to see subzero about the times he's observed. So this would be five point nine times ten to the negative nine and then times thirty five VOCs. So this is going to give us two point one times ten to the negative seventh. Um, cool ums. So this would be your second answer for party. We need e subzero. So this would simply be equal to the subzero over the separation distance. So this would be thirty five volts, divided by point zero zero three. And we're getting one point one seven times ten to the fourth volts per meter. So this would be our third answer for party. And then our final answer for party would be the potential energy. So this would be equal to one half a cease abo times Visa Bos, where this would be one half and then this would be five point nine times ten to the negative and ninth. And then this would be thirty five squared. So we have a potential energy of three point six one times ten to the negative six jewels. So this would be our final answer for part A. Now, for part B, they're asking us to include the dialect trick. So include Die electric and the dye electric constant K is going to be equal to three point two. So we can say that the new capacitance is equal to the dye electric, constant times the sea. Not so. This would be a three point two times five point nine times ten to the negative nine and we're getting this is equal to one point eight nine times ten to the negative eighth Claridge's and we know that the voltage doesn't change. So essentially, voltage V rather, cue the charge. Rather is going to be equal to see the um, at this point, we found both of these, so we can have one point eight nine times ten to the negative eighth and then the voltage doesn't change again. So this is only thirty. So this is only thirty five bolts once again. And this again equal six point six one times ten to the negative seventh Cool arms. So this would be one answer for me. This would be your second answer for me again. The battery's still connected. The voltage is current Stant. So the electric field e does not change on the separation distance hasn't changed as well as the voltage. So the electric field doesn't change. So e equals e not equals one point one seven times ten to the fourth of Volts Premier again, This would be your third answer for Part B. Um, And then your final answer for part B would simply be equal to half. And then this would be C V squared. So be won over to and then one point eight nine times ten to the negative eighth. This would be thirty five squared. So our final answer for part B the potential energy would be one point two times ten to the fifth. Rather tends to the negative fifth. Jules, this would be our final answer for part B. That is the end of the solution. Thank you for watching.

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

For the given problem In about a, we can find electric field E a is equal to be divided by de Louise. The potential difference. These the distance between the plates, then substituting a value 600 worlds divided by three times 10 to power minus three meter. Use us two times 10 to the power five walls per meter, but be off the problem since the distance here is 0.300 meter and voltage res 600 walls in the capacitor be as well we write e b is equal to we Divided by d student Those values we get e B to B two times 10 to the power five walls or meter But see off the problem For airfield capacitor we ride Sigma is equal to Q a divided by a that is a cool See a times we divide by a substituting the value of expression for C s. Sorry, so long times A divide by D times re divided by a a cancels out. We are left with an expression that is keeps long We divide by d where we do our bodies equal Thio e So here we have this is e a so shooting value for its alone. Andy. We get sick my to be 1.77 times gentle power minus six Coolum per meter square for body off. The problem for a die elected field capacitor for a dialectic. Philco pastor for D Sigma be charged into B is equal to copper dialectic constant times alone times e b Some student values. 2.60 times 8.85 times dental power minus 12 times two times into the ball or five walls. For Peter, this gives our signal be Sigma B to B 4.60 times 10 to the power minus six Coolum per meter square for a party off the problem. They're induced charged density induced charged density is given by Sigma A minus Sigma Be so shooting manning for sick. My answer it Maybe we get here minus 2.83 times Stendhal Former minus six, Coolum Core meter square


Similar Solved Questions

5 answers
Find the length of the curve Vzti + etj + e-tk; 0 < t < 8
Find the length of the curve Vzti + etj + e-tk; 0 < t < 8...
5 answers
Hw6: Problem 14Previous ProblemProblem ListNext Problempoint) Let F(x) = f(f(x)) and GC) = (F(1))? and suppose thatf(8) = 2, f(2) = 2, f'(2) = 15, f'(8) = 14Find F' (8) and G'(8).F'(8)G' (8)Note: You can earn partial credit on this problem.Preview My AnswersSubmlt AnswersYou have attempted this problem = timos Your overall recorded score Is 0%_ You have unlimited attempts remaining_Email instructor
Hw6: Problem 14 Previous Problem Problem List Next Problem point) Let F(x) = f(f(x)) and GC) = (F(1))? and suppose that f(8) = 2, f(2) = 2, f'(2) = 15, f'(8) = 14 Find F' (8) and G'(8). F'(8) G' (8) Note: You can earn partial credit on this problem. Preview My Answers S...
5 answers
HAND WRITTEN pdf file show all the work/steps/FORMULAS MUST fit THESE PAGES). Must have the name no- named exams will not be graded!1) (12 points) Determine if the series converges Or diverges: Ck=1 kvk2+1
HAND WRITTEN pdf file show all the work/steps/FORMULAS MUST fit THESE PAGES). Must have the name no- named exams will not be graded! 1) (12 points) Determine if the series converges Or diverges: Ck=1 kvk2+1...
5 answers
93 aitempts IenCheck my workBe sure t0 answer all partsWrite an cquilibriuni constant expression for the reversible concentrations, and use exponents where neededBrzlg} Ch(g)2ErClg)Boo kKeqfenced
9 3 aitempts Ien Check my work Be sure t0 answer all parts Write an cquilibriuni constant expression for the reversible concentrations, and use exponents where needed Brzlg} Ch(g) 2ErClg) Boo k Keq fenced...
5 answers
You are t0 verify each question using Mathematica: Snapshot the codes for cach question and paste below thc question:polr _ coordintes, polar function exists by the enmstrophoid, with equation Consider the equation of this strophoid that bounded as <0 < 1 Plot the strophoid convert the strophoid equation t0 rectangular coordinates Find the area enclosed by the loopsec & Zcos 0.
You are t0 verify each question using Mathematica: Snapshot the codes for cach question and paste below thc question: polr _ coordintes, polar function exists by the enm strophoid, with equation Consider the equation of this strophoid that bounded as <0 < 1 Plot the strophoid convert the strop...
5 answers
An Erlenmeyer flask weighs 125.4 density of water is 0.997 gmL_ g empty and 225.1 g when filled with water. If the tetrachloride is 1.59 glmL Whal isthe volume of the flask? If the density of how much does this same flask carbon liquid? weigh when filled with thisA mass Of mercury occupies 0.750 L. What The density Of mercury iS 13.546 Ivolume would an equal mass of ethanol occupy? glmL and density of ethanol is 0.789 g/mL.
An Erlenmeyer flask weighs 125.4 density of water is 0.997 gmL_ g empty and 225.1 g when filled with water. If the tetrachloride is 1.59 glmL Whal isthe volume of the flask? If the density of how much does this same flask carbon liquid? weigh when filled with this A mass Of mercury occupies 0.75...
5 answers
'large company is hiring for 3 different positions and gives preference to candidates who can perform any tasked listed in any of the positions A pool of 21 candidates equally quallfied applied to any position available In how many ways the company can select the candidates?a. P(21,3)b.2143C(21,3)d.none of the listed answers
'large company is hiring for 3 different positions and gives preference to candidates who can perform any tasked listed in any of the positions A pool of 21 candidates equally quallfied applied to any position available In how many ways the company can select the candidates? a. P(21,3) b.2143 C...
1 answers
Let p > 10 be the prime number closest to the last two digits of your student number: Let G = Ap be the alternating group on p letters. Compute Inn(G), the group of inner automorphisms
Let p > 10 be the prime number closest to the last two digits of your student number: Let G = Ap be the alternating group on p letters. Compute Inn(G), the group of inner automorphisms...
5 answers
Why do we use the absolute value of $x$ or of $g(x)$ in the derivative formulas for the natural logarithm?
Why do we use the absolute value of $x$ or of $g(x)$ in the derivative formulas for the natural logarithm?...
5 answers
Find and simplify the difference quotient$$ rac{f(x+h)-f(x)}{h}, h eq 0$$for the given function.$$f(x)=-x^{2}-3 x+1$$
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=-x^{2}-3 x+1$$...
5 answers
Plants and animals whose young die in great numbers often producemany small offspring (r-selection)b. few large offspring (K-selection)c.few large offspring (r-selection)d. many small offspring (K-selection)
Plants and animals whose young die in great numbers often produce many small offspring (r-selection) b. few large offspring (K-selection) c.few large offspring (r-selection) d. many small offspring (K-selection)...
5 answers
Using properties of determinants compute det   −1 −2 2 4 3 1 −1 2 5  (Mention each property used in each step )
Using properties of determinants compute det   −1 −2 2 4 3 1 −1 2 5  ...
5 answers
Point) The Ispnng Tlex exercise system ccnsistssorina vnth pne end flxed anonancon the other end The idea that YOU exerc se your muscles Dy stretching the spring from its natural length, which is 37 cmIfa 180 Ncwton lorce equinedkcep Inc {gorng Stcelchcdengin 52 cm, how much work (CqtgCcstretch from 48 cm t0 77 cm?Your answer must includa tha correct ynits:Work =
point) The Ispnng Tlex exercise system ccnsists sorina vnth pne end flxed ano nanc on the other end The idea that YOU exerc se your muscles Dy stretching the spring from its natural length, which is 37 cm Ifa 180 Ncwton lorce equined kcep Inc {gorng Stcelchcd engin 52 cm, how much work (CqtgCc stre...
5 answers
Suppose the joint density of Yi and Yz is given as e-Y1 0 < y2 < y1 < 0 f(y1,Y2) = 3 0 elsewhere(3 points) Find the marginal density function of Yz4 points) Find the conditional density function of Yi given that Yz = Y2_3 points) Find P(Yi < 2Y2 = 1).
Suppose the joint density of Yi and Yz is given as e-Y1 0 < y2 < y1 < 0 f(y1,Y2) = 3 0 elsewhere (3 points) Find the marginal density function of Yz 4 points) Find the conditional density function of Yi given that Yz = Y2_ 3 points) Find P(Yi < 2Y2 = 1)....
5 answers
The human circulation system has approximately 1 x 10 capillary vessels_ Each vessel has diameter of about um_ Assuming cardiac output is 8 Llmin, determine the average velocity (in cm/s) of blood flow through each capillary vessel: 0.00115 cm/s
The human circulation system has approximately 1 x 10 capillary vessels_ Each vessel has diameter of about um_ Assuming cardiac output is 8 Llmin, determine the average velocity (in cm/s) of blood flow through each capillary vessel: 0.00115 cm/s...

-- 0.021934--