5

[-/1 Points]DETAILSCJ10 20.P.018.MY NOTESASK YOUR TEACHERtungsten wire has radius 066 mm and heated from 20 . 1265 Tnc tcmocrature coefficient resistivily a = 4.5* ...

Question

[-/1 Points]DETAILSCJ10 20.P.018.MY NOTESASK YOUR TEACHERtungsten wire has radius 066 mm and heated from 20 . 1265 Tnc tcmocrature coefficient resistivily a = 4.5* 10 3 (CP) hot wire, current of 1.8 Oraduced How long the wire? Neglect any effects due thermal expansion of the wire,When 220applied across the ends of theAdditional HalerialscBook

[-/1 Points] DETAILS CJ10 20.P.018. MY NOTES ASK YOUR TEACHER tungsten wire has radius 066 mm and heated from 20 . 1265 Tnc tcmocrature coefficient resistivily a = 4.5* 10 3 (CP) hot wire, current of 1.8 Oraduced How long the wire? Neglect any effects due thermal expansion of the wire, When 220 applied across the ends of the Additional Halerials cBook



Answers

A tungsten wire has a radius of 0.075 $\mathrm{mm}$ and is heated from 20.0 to $1320^{\circ} \mathrm{C}$ . The temperature coefficient of resistivity is $\alpha=4.5 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1} .$ When 120 $\mathrm{V}$ is applied across the ends of the hot wire, a current of 1.5 $\mathrm{A}$ is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.

Pile. Alex be here with another question on electrical power and resistance from chapter 25 of Jeong Kai's visits for scientists and engineers. So this question tells us that we have a tungsten wire which I have here not drawn to scale, of course. And it's going to be one meter long. It is going to have a current of 15 amps running through it at 3100 Calvet. And the question asked us to find what the diameter D of this wire needs to be such that this is true. So we're gonna use a couple different equations here. The first is gonna be our reliable equation for electrical power. P is equal to ay times be or in terms of just current and resistance, I squared R and we're also going to use the equation for resistance of a wire. Are is equal to row L over a. And since we are going looking for the damn door of the white, we're gonna put a in terms of diameter as pine times d over too. Don't forget the 1/2 squared now. We also furthermore know that resistive ity row is going to be a function of temperature. Such row is equal to rose zero some some inherent property of the material at a reference temperature times one plus Alfa. Another constant of the material times T minus t easier how far away we are from that reference temperature T zero. Now we're also going to have to think back to our equations for black body radiation. We know that the amount of power radiated is going to be equal to Epsilon, some constant, which in this case, is going to be one minute it tells us how efficient the mission is. Cinema, which is just a constant which converts the temperature into power, radiated a the area of the surface. It's radiating times. The surface is temperature to the fourth minuses environments temperature to the fourth, which happens to be the same temperature as a reference structure that we're using up here. Now we know that if we want the wire to be kept at a constant temperature, we want this electric power up here to be the same as this radiant and power down here, in which case we just need to set these two equal and therefore we're going to get the equation I squared Rose zero times one plus Alfa T minus t zero divided by high times D over two squared. This is all just our equation up here for electrical power should be equal to our equation for thermal radiation. Absalon Sigma Never gonna replace the radiating area with this equation in terms of blank to the wire and the diameter pie d l That's the surface area of the wire Times t to the fourth dynasty zero. Before solving this for D, it's gonna take a little bit of algebra. What? After doing it, you should find d The diameter of the wire required to make this true is going to be the third route of four times I squared times rose zero one plus Alfa T minus t zero divided by pi squared Absalon sigma to you forthe minus t zero and forth. Now we're gonna need to use a lot of numbers here which were given to us by the book. We know that Rose Era, which is the resist Avi of tungsten at 20 degrees Celsius, is 5.6 times 10 to the minus e alms times meters. We know that Alfa, which is this thermal change in the resisted Vitti per degree, Celsius is going to be 0.0 45 per degree Celsius. We know that the temperature of her wire is gonna be 3100. Calvin, we know that our reference temperature T zero is 20 degrees Celsius, which is equivalently 293. Calvin, remember, we want to use everything in Kelvin here because of this fourth power we know that Epsilon has given to us is 1.0. You know that I it's going to be 15 abs, we know that sigma is this constant which is going to be 5.67 times 10 to the minus feet watts per meter squared Calvin to the fourth. And I think this is everything. And if we plug all these numbers in, we should find that the diameter of wire required for this is zero point 23 millimeters. They

Hi in a given problem, two wires are joined series like this, Two cylindrical vials having different area of cross section. What same length? If this is the wire, see this is the mm The land of wire C. Means L. C. Is equal to L. D. Which is given as 1.0 m. Right or wire C. The resistive Itty is 2.0 into 10 days for -6. Um into meter and it raises hundreds radios of section that is half of the diameter and diameter is 1.00 mm. So The radio says 1.00 millimeter by two. Reach me also bigger than a 0.50 into 10 for minus we meet her then or via P the resistive Itty is 1.0 into 10 days, 4 -6. Home into meter and its radius of prosection will be Half of its diameter, which was 0.50 mm divided by two. All can also be written as 0.25 In to Tenders for -3. Meet up. No as the wire C and B are in series. So current passing through them will remain same in I. C. Will be equal to I. D. And that is given us 2.0 am here. So in the first part of the problem we have to find a potential drop taking place across the first wire here. This is terminal one. This is terminal two. This is terminal three. So we have to find the potential drop across a terminal one and 22 is we want to using home. So will be given as I into our is this is I. C. And R. C. Or I see it will remain sane but for RC it is given as we'll see Into L. C. divided by 5RC Square. So plugging in all known values here for current this is 2.0 ampere multiplied by the sensitivity 2 to 10 days par -6 Own centimeter for length. This is 1.0 m invited by 3.14. The value of I and three years 0.50 Into Kentish par -3 m to the whole square. So finally this potential difference between the terminals one and 2 Some south will be 5.1 Cool. Which is the answer for that first part of this problem. Now, similarly in the second part of the problem, we have to find The potential difference between the terminals two and 3, which will be given by again using arms law ID into R B. All we can say this is I'd into raw B L E invited by five are key to the whole square. So here also plugging in all known values for current 2.0 Progress sensitivity, 1.0 into tended bar -6 length is also saying 1.0 m invited by five which is 3.14 but radius is 0.25 to 10 for -3 m the whole square. So finally this week to three Comes out to be 10.2 paul. Which the answer for that 2nd part of the same problem. No, In the 3rd part of the problem we have to find the rate of dissipation of electric energy in wire steve and their trait of dissipation of electric energy means power, electric power dissipated will be given by the expression he is going to be into. I for me this is given to but I this is I see so or even to. We have already found it will be 5.1 world Multiplied by current which was two MP. ER this pc Himself to be 10.2. What answer for the second for the third part of the problem And finally at last In the 4th part of the problem. Electric power and doomed in the fire. P 30. That will be given as we 2 3 into ivy 42 3. This is standpoint of all Friday again. This 2.0 ampere. So finally, the speedy here comes out to be 20.4. What? Which is an answer for the 4th? The last part of this property. Thank you.

Our system is mad up off two wires they are joined together. Joined together to calculate the electric potential difference between the two points. You first calculate their resistance. The potential difference between a point 0.1 and two is Delta. We want to their physical toe i r c where are sees the resistance off. Why are seeing similarly the potential difference between potential difference between the two and three points His i r d where these there are resistance off Weir d They're cross morning rates off energy dissipation will be P 12 musical toe I square R C and the p 23 physical toe I square rd What ails the problem? Ah, we write our see resistance ofwar seasonable to roll See time's LCD Bye bye. I r C square That is a two times 10 to the power minus six times one divided by by time 0.50 meter square. This uses 2.55 homes. Then we could find a Delta V 12 is equal to i r c. That is to em piers times 2.55 homes Excuse us 5.1 walls but be off the problem. Similarly, we confined it Resistance off Hawaii, which will be our D, is equal to roadie times l d Divided by bi rd square This is one times 10 to the power minus six times one meter. Divided by pi times 0.25 meters square This will you, us our de resistance off 5.9 homes from here. Then we can find the potential difference between Delta v 23 points going by I r D. That is a two MPR times 5.9 homes that isn't called thio talk 10.22 walls which is approximately tin walls but see off the problem. The power dissipated between the points one and two is given by P one to that is I square times r c thirties a 10 wolves body off the problem. The power dissipated between a bob 0.213 is Batou fees I square rd that is 20 walls

So to start, we're looking to find the resistive ity of theologian um, wire at T equals 50 degrees Celsius. So the equation we're going to use here is resistive ity is equal to the initial resistive ity times one plus alfa, which is the temperature coefficient of resistive ity times the final temperature minus the initial temperature. If you plug in, the values were given for all that, we find that the resisted ity is equal to 3.15 times 10 to the negative eight oh meters. So that's part a for part B. We're looking to find the current density. And so we have current density is equal to the electric field times the conductivity. But connectivity is just equal to one over the resisted Vitti that's equal to the electric field over the resisted ity. Using our reasons to be we got from part A. You find that the current density is equal to 6.3 times tend to the six and over meters squared and then for part c, we're looking forward the total current And so for that, we know that the current density is equal to the total current over the area. And so the current is equal to the current density times the area. We can just rewrote the area as pi r squared using our diameter. And so you find that the current is equal 2.5 amperes. And so then, for part D, we need a couple more values I have written here the molar mass of aluminum, the density of aluminum not to be confused with the resisted viddy, the charge of an electron and avocados number. So for part D, the equation we only used to find drift velocity is current times molar mass over the charge of an electron times the area times of a god rose number, times the density and plugging in our values. For that, using the current you found in part C, we find this is equal to about 6.6 times 10 to the negative four meters per second for our drift speed. And then finally, for Part E, we're looking for the potential difference. We know that potential difference is equal to electric field times the distance. And since the distance is two meters, we just need to multiply the electric field by two to find a potential difference until that's going to be 0.4 volts


Similar Solved Questions

5 answers
Let X be random variable with mean bud For P(xi 2 5)and variance 02 = 2. Find an upper
Let X be random variable with mean bud For P(xi 2 5) and variance 02 = 2. Find an upper...
5 answers
Question I: Consider a function f(1,y) which is differentiable at (a,6) , with Duf(a.6) 3 and Dvf (a,6) = 1 where u = 7(1, 1) and v = 7(1,-1)- Find fx(a,b) and fy(a,b). (b) If f(z,y) represents the temperature of an object at the point (1,9), find the rate of change of temperature of an object with velocity (3,2) at the point (,6).
Question I: Consider a function f(1,y) which is differentiable at (a,6) , with Duf(a.6) 3 and Dvf (a,6) = 1 where u = 7(1, 1) and v = 7(1,-1)- Find fx(a,b) and fy(a,b). (b) If f(z,y) represents the temperature of an object at the point (1,9), find the rate of change of temperature of an object with ...
5 answers
(5 points) Find the radius of convergence and interval of convergence of the series 2 (6-2x)" 3"+2" n=
(5 points) Find the radius of convergence and interval of convergence of the series 2 (6-2x)" 3"+2" n=...
5 answers
Question 10 (1 point)Consider the following differential equation (c _ 5)2 (2 + 6)2y" + (x _ 5)(r + 6)y' + 9y = 0. How many irregular singular points ?a) 3b) 2c) 4d) 0e) 1
Question 10 (1 point) Consider the following differential equation (c _ 5)2 (2 + 6)2y" + (x _ 5)(r + 6)y' + 9y = 0. How many irregular singular points ? a) 3 b) 2 c) 4 d) 0 e) 1...
5 answers
Use the data in Table $7-1$ to predict the energy difference between 2,3 -dimethyl-but- 1 -ene and 2,3-dimethylbut-2-ene. Which of these double-bond isomers is more stable?
Use the data in Table $7-1$ to predict the energy difference between 2,3 -dimethyl-but- 1 -ene and 2,3-dimethylbut-2-ene. Which of these double-bond isomers is more stable?...
5 answers
Which solutior has a higher percent ionization of (he acid, 10M solution ol HC H,O aq) or J D.DIDM solution of HC, H,Oaq) ? Justily your answer Including the calculatlon of percent ionization far each solution: Ka for HC,H,O,151.8*102 HC?H3O2 (aq) H2o ( ~
which solutior has a higher percent ionization of (he acid, 10M solution ol HC H,O aq) or J D.DIDM solution of HC, H,Oaq) ? Justily your answer Including the calculatlon of percent ionization far each solution: Ka for HC,H,O,151.8*102 HC?H3O2 (aq) H2o ( ~...
1 answers
Let $S=\{(u, v): 0 \leq u \leq 1$ $0 \leq v \leq 1\}$ be a unit square in the uv-plane. Find the image of $S$ in the xy-plane under the following transformations. $$T: x=v \sin \pi u, y=v \cos \pi u$$
Let $S=\{(u, v): 0 \leq u \leq 1$ $0 \leq v \leq 1\}$ be a unit square in the uv-plane. Find the image of $S$ in the xy-plane under the following transformations. $$T: x=v \sin \pi u, y=v \cos \pi u$$...
5 answers
Second and the thrra row o} A; respectively. Find the correct raw aperctlan _ apeked to A Ehn? Civcs 8he Mairlx
second and the thrra row o} A; respectively. Find the correct raw aperctlan _ apeked to A Ehn? Civcs 8he Mairlx...
1 answers
Identify the variable and write an inequality that describes situation. Rita will not take less than $\$ 12,000$ for the car.
Identify the variable and write an inequality that describes situation. Rita will not take less than $\$ 12,000$ for the car....
1 answers
True or False? In Exercises 69 and 70 , determine whether the statement is true or false. Justify your answer. The vectors $\mathbf{u}=\langle 0,0\rangle$ and $\mathbf{v}=\langle- 12,6\rangle$ are orthogonal.
True or False? In Exercises 69 and 70 , determine whether the statement is true or false. Justify your answer. The vectors $\mathbf{u}=\langle 0,0\rangle$ and $\mathbf{v}=\langle- 12,6\rangle$ are orthogonal....
16 answers
What is the oxidation state of Cl in each ion?a. ClO- b. ClO2-c. ClO3- d. ClO4-
What is the oxidation state of Cl in each ion? a. ClO- b. ClO2- c. ClO3- d. ClO4-...
4 answers
Find the particular solutiondilterentin cquadion that ctieioc tno inicia cquatons7"(1)
Find the particular solution dilterentin cquadion that ctieioc tno inicia cquatons 7"(1)...
5 answers
310 224 240 20W is an orthogonal set and thereby basis for Span{W}_ Use the dot product to write Xwith coordinates relative to W .28 33W[xlw
310 224 240 20 W is an orthogonal set and thereby basis for Span{W}_ Use the dot product to write X with coordinates relative to W . 28 33 W [xlw...
5 answers
One of the following states is not allowed In the Hydrogen atom:[41,0,0)[42,1,1)[03,4,1)[432,-1)[431-1
One of the following states is not allowed In the Hydrogen atom: [41,0,0) [42,1,1) [03,4,1) [432,-1) [431-1...
5 answers
Whatis the major organic product for the following ' reaction?OH,4"NH;"
Whatis the major organic product for the following ' reaction? OH,4" NH;"...
5 answers
Provide complete synthesis of the following desired product from the given starting material and any other reagents you need: You do not need to show any mechanisms: (12 points) Starting Material: BenzeneDost ( mochia:
Provide complete synthesis of the following desired product from the given starting material and any other reagents you need: You do not need to show any mechanisms: (12 points) Starting Material: Benzene Dost ( mochia:...
5 answers
Rownte the equation shown below in one of the standard forms of the conic sections and identify the conic seci2 p4x+2y4 16y =Which equation below is equivalent t0 the given equation?
Rownte the equation shown below in one of the standard forms of the conic sections and identify the conic seci2 p 4x+2y4 16y = Which equation below is equivalent t0 the given equation?...

-- 0.034290--