5

A metallic conductor is 10.0 m long and it is made from amaterial having a resistivity ρ = 2.00 x10-8 Ω·m. The potential differencebetween its ends is 2...

Question

A metallic conductor is 10.0 m long and it is made from amaterial having a resistivity ρ = 2.00 x10-8 Ω·m. The potential differencebetween its ends is 2.00 V. There are 1028 freeelectrons per cubic meter, and these electrons are the chargecarriers. What is the drift speed of the electrons in the conductor(in mm/s)? (A) 3.00 (B) 0.784 (C) 6.25 (D) 8.21 (E) 11.4 (F) 0.163

A metallic conductor is 10.0 m long and it is made from a material having a resistivity ρ = 2.00 x 10-8 Ω·m. The potential difference between its ends is 2.00 V. There are 1028 free electrons per cubic meter, and these electrons are the charge carriers. What is the drift speed of the electrons in the conductor (in mm/s)? (A) 3.00 (B) 0.784 (C) 6.25 (D) 8.21 (E) 11.4 (F) 0.163



Answers

The free-electron density in a copper wire is $8.5 \times 10^{28}$ electrons $/ \mathrm{m}^{3} .$ The electric field in the wire is $0.0600 \mathrm{~N} / \mathrm{C}$ and the temperature of the wire is $20.0^{\circ} \mathrm{C}$. (a) What is the drift speed $v_{\mathrm{d}}$ of the electrons in the wire? (b) What is the potential difference between two points in the wire that are separated by $20.0 \mathrm{~cm} ?$

In this question, we are given information about um aluminum wire. Okay. And he has a diameter of 0.1 00 And then the issue is 0.2 Per meter. And temperature is 50 degrees C. Okay, so I want to compare the resistive itty current density in the wire to the current wire, crispy of the electrons and the potential difference that's present in the wire. Okay. So in part in to calculate our sensitivity, can you be using um our goal is to or not Times one plus how far T minus T. Not so uh same L. And same A The resistive itty. Okay. Also changes. We have temperature. Mhm in the same way. Okay. Actually say assume L N A. Ln A. Uh that's not change. Okay then the resistive Itty changes with temperature the same way. So we have really close to run on on one to alpha team and seen on Okay. Mhm. So uh roll not is given to be 2.82 times 10 to the power of -8. So this one can check from the book. Uh the resistive itty of aluminum, aluminum, 20°C.. And then one plus 3.9 times 10 to the negative tree. I'm 15 -20. Mhm. Yeah, Resistive 83.15 times 10 to the power negative eight old meter. Okay, so this is the And so for party. Mhm. Okay. Then in part B went to calculate the current density to be using jay equals to stick my E. Which is one of our role. Thanks. E. Okay. Yeah sigma is the conductivity and it's the rest of broker of receptivity. Okay, so jay is um your room 0.2 by 3.15 times 10 to the Power -8. And you get 6.35 And sent to the power of six ampere Per meter Square. So this is the current density for part B. And then perceiving to calculate the total current. Okay. Current. Just be current density times the area which is chase and Pay Rs way. And just J times pi over four the square. So substitute the numbers and you get 0.0 fall 99 mps. Okay, so this is the answer for Patsy. And then paddy. We want to find a true speed. So be using jay equals two and Q. V. D. So you first need to calculate the church care identity and he goes to charge their identity. King is equal to the density times the abogados constant by mullah mess. Mhm. He the density of aluminum is 2700. Did you commit a cube and then multiplied by our graduates constant And then divide by the Salamis which is 0.027 kg per mo. and the answer is 6.02 times 10 to Power of 28 per meter cubed mm. And so we d that crispy is jail over and Q. Mhm. Putting their numbers. Okay. And the answer is 6.59 times 10 to the power of -4 m/s. Okay? So this is the answer for party and in party trying to calculate the potential difference. So using delta P equals two E. Data X. So potential difference is equal to 0.2 times two. Which is Your .50. What's so this is the answer for party and that's all.

In this question, we're told we have a strip of silver, it is not point not five thick and 20 wide. It is in a magnetic field of 9.8 Kessler's and there are 5.85 times 10 to the 28 free electrons per cubic meter. There is a current of 10 amps through the strip. So what we want to find first is the drift velocity of the electrons. In order to do this, we need to use the expression I the current is equal yeah. To A. And a V. D. Which is the drift velocity, is the charge of the electron and is the number of them present and A is the area of the strip. So we know all of these values. We want to find the drift velocity. So what we need to do is rearrange his expression to the drift velocity is equal to the current over A. N. E. We've been given all of these in the question, we know that A. is equal to the thickness times the width. So we can just substitute this into here. And what we can say is that as a result A is equal To one times 10 to the -6 meters squared. And we can use that in this expression here as T. W. So now we've got this, we can substitute into the original expression for V. D. We know the current is 10 Amps has given in the question and we divide this theory by this area. We just calculated equal to T. W. So the thickness times the width. So 1.6, one times 10 to the -6. Rather Multiplied by N 5.85 times 10 to the 28 as given in the question, Yeah. Multiplied by the charge on an electron. So 1.6 times 10 to the -19. Yeah. Okay, This gives us an answer for the drift velocity equal to 1.07 Times 10 to the -3 m/s. Yeah. In the next part of the question, we want to calculate what the hall voltage measured by the meter is. We know that the expression for the hall voltage Is equal to V eight equals B. The magnetic field strength multiplied by the current over the thickness times a number of charge carriers, times a charge on the electron. So, plugging in the values we've got we know again the B field the magnetic field is equal to not .8. The current is equal to 10. The thickness is equal to not point not five. And the number of child carriers is 5.85 times 10-28. And E is again 1.6 times 10 to the -19. So we can sub in these values. So not .8 for B. Not applied by 10 for the current over, Not point not five times 10 to the -3 as it's needing to convert into meters. Multiplied by M. 5.85 times 10 to the 28. Yeah, Multiplied by the charge 1.6 times 10 to the -19. Which gives us a value equal to 17.1 μv as the whole voltage. Yeah, the final part of this question wants us to calculate which side of the volt meter would be at the highest potential. So we know that the Lawrence force is given by F equals Q V cross B. In the case that these vectors the velocity is V and B is the magnetic field. Again, we know that as a result of the right hand factor product rule. so crossing these two vectors, the force on the electron will be towards the left, and as a result, the direction of the hall current will be towards the right, leaving the left side of the volt meter to have a higher potential reading. Therefore, the left of the volt meter will be at the highest potential. Mhm. Yeah. Mhm. Yeah.

Okay, so we know the current density was just J here. Can we go to currently about my area? So therefore current, I should be good j A. So current density in this case is given as 1.5 times 10 to par six MPR per meter square and the area should be equal to pi times the diameter divide by two to the power to and I'm during this case is a good one point. Also millimeter if we call into meter is he with the one point 0 to 10 to the power of 93 meter, so eventually have errors. You go to a 2.6 year old one pie test into a power opening. Seven meters were so now it's fucking better The equation to determine occurrence which is equal to 1.50 times 10 to the power of six MPR for a meter, score multiple by 2.601 pie times 10 to the power of Negus seven meters square and this will give us the occurrence is equal to one point 23 m Pierre. So not it's determine the drivel last the so we know current committee Goto on q b d a is the electron density, which is evil. The one I'm sorry, a point by 10 to 10 to the power between the A premier, a cube in his question. And one of the current is he with 1.23 m. Pierre And we know que Here is the charge of the chart carriers, which is the charge of electrons, Things Charles Caris veterans and another charge of the Lateran is 1.6 times 10 to the power of neck. 19 columns in the area is you go to a 190.601 attends 10 to the power of the next seven years, for it does not arrange me here with the drivel drivel. Last DVD is a good guy over on the way, So now that's plugging better. The equation. To determine the drift velocity, which is equal to 1.23 m. Pierre, divided by a point by tens 10 to the power of 28 per meter cubed and times 1.6 has tend to the power of the neg knighting Coolum and Mobile by 2.601 high times 10 to the power of the next seven meter square. And then he moved. Uh, I'm here to the middle. Also look better. Okay, so, uh, this will give us the dreadful. Last year is equal to one point 11 times. Tend to the power off. Negative for meter for a second. We can worry too. Millimeter per second is equal to 1.1 war times 10 to the power off connective. One millimeter per second, which is equal to zero point. We don't want one millimeter for a second, and these are the answers for this question.

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
'AssignmenLLuzoSearch[Review Topicse [References] Use the Rcferences Tccn important values if needed for this question.For the decomposition of ammoniaplatin Um surface at 856NHy LM +the avcrage ratc of disappcarance of NHz over the lunc period fiom 0 $ to t = 3926 18 fouud bc 1.S0xlO € Ms"1Ihe averageof formation of Hz OVet thc #an Wmc perod Ms70 t
'Assignmen LLuzo Search [Review Topicse [References] Use the Rcferences Tccn important values if needed for this question. For the decomposition of ammonia platin Um surface at 856 NHy LM + the avcrage ratc of disappcarance of NHz over the lunc period fiom 0 $ to t = 3926 18 fouud bc 1.S0xlO â...
5 answers
Is the proposition roblem Write the truth table of the proposition p ^-(q 5 p): ^-(q p) tautology, contradiction, Or & contingency?Are the propositions (q^=r) ~ p and rV (q - + p) logically equivalent Problem 3 Provel (Show work) _
Is the proposition roblem Write the truth table of the proposition p ^-(q 5 p): ^-(q p) tautology, contradiction, Or & contingency? Are the propositions (q^=r) ~ p and rV (q - + p) logically equivalent Problem 3 Provel (Show work) _...
2 answers
For the matrix, list the real eigenvalues, repeated according to their multiplicities_9 1The real eigenvalues are (Use comma separate answers as needed )
For the matrix, list the real eigenvalues, repeated according to their multiplicities_ 9 1 The real eigenvalues are (Use comma separate answers as needed )...
5 answers
(8 pts) 13. Find general solution to the differential equation y" +Ty" + 16y' + 10y = 0(11 pts) 14. Find particular solution to the differential equation+5 G +6y = xe' .
(8 pts) 13. Find general solution to the differential equation y" +Ty" + 16y' + 10y = 0 (11 pts) 14. Find particular solution to the differential equation +5 G +6y = xe' ....
4 answers
What is the defining characteristic of a geometric series? Give an example.
What is the defining characteristic of a geometric series? Give an example....
5 answers
A uniform line charge with linear density ^ lies along the Y-axis. What flux crosses a spherical surface cantered at the origin with r = RZRNJEOD. None f the aboveRAEoNco
A uniform line charge with linear density ^ lies along the Y-axis. What flux crosses a spherical surface cantered at the origin with r = R ZRNJEO D. None f the above RAEo Nco...
5 answers
45. State Kepler s Third law; explain what the law means in your own words:
45. State Kepler s Third law; explain what the law means in your own words:...
5 answers
Question Let Z be the number of red marbles obtained when two marbles are drawn WITHOUT replacement from a bag contain four red marbles, three green marbles and three blue marbles What is the expected value of Z?Select one_a. 1.0000b0.90000.8000Correctd_1.10001.2000
Question Let Z be the number of red marbles obtained when two marbles are drawn WITHOUT replacement from a bag contain four red marbles, three green marbles and three blue marbles What is the expected value of Z? Select one_ a. 1.0000 b 0.9000 0.8000 Correct d_ 1.1000 1.2000...
5 answers
You hang a mass from the end of a vertical steel wire = 2 X 1011 Pa): The steel mass stretches the wire 0.20 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long: 0.05 mm0.20 mm0.10 mm0.40 mm
You hang a mass from the end of a vertical steel wire = 2 X 1011 Pa): The steel mass stretches the wire 0.20 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long: 0.05 mm 0.20 mm 0.10 mm 0.40 mm...
5 answers
Assume that A and Bare 3 X 3 matricesIndicate which of the following are true. (Select ALL that are true:)(A(3A + SB)) SBT A + 3AA:OA' B' (BA)A' Ais 3 symmetric matrix
Assume that A and Bare 3 X 3 matrices Indicate which of the following are true. (Select ALL that are true:) (A(3A + SB)) SBT A + 3AA: OA' B' (BA) A' Ais 3 symmetric matrix...
2 answers
Find a power series solution in powers of x for the differential equation y" + y = Ogiven that y(0) = and y'(0) = 0
Find a power series solution in powers of x for the differential equation y" + y = Ogiven that y(0) = and y'(0) = 0...
5 answers
The circuit shown has battery and resistors 6ov (12 pts_ Find current voltage for each resistor (3 pts) Find the power delivered by the battery consumed by the strongest resistor 528 3150 38 } 52 45
The circuit shown has battery and resistors 6ov (12 pts_ Find current voltage for each resistor (3 pts) Find the power delivered by the battery consumed by the strongest resistor 528 3150 38 } 52 45...
5 answers
Consider Pi, the Lincar space cf polyuctnials f (t) of degree nt Dsst 2. [bri] What is the dimeusion of P;?(6) [Spt] Show that the map T P+ Pz given by TU(C)) = /()- f(-0},ia Zicizn: Crcruionnitko[Spe] Pird the watrix of T , uer the rais {L1+61+t+P} o R:
Consider Pi, the Lincar space cf polyuctnials f (t) of degree nt Dsst 2. [bri] What is the dimeusion of P;? (6) [Spt] Show that the map T P+ Pz given by TU(C)) = /()- f(-0},ia Zicizn: Crcruionnitko [Spe] Pird the watrix of T , uer the rais {L1+61+t+P} o R:...

-- 0.019744--