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Homework Help: How a heating element is connected to increase power

  1. Oct 6, 2016 #1
    1. The problem statement, all variables and given/known data
    An electrical heating element is to be designed so that the power dissipated will be 750 W when connected to the 240 V mains supply.

    (a) Calculate the resistance of the wire needed.

    (b) The element is to be made from nichrome ribbon 1.0 mm wide and 0.050 mm thick. The resistivity of nichrome = 1.1 * 10-6 Ω m. Calculate the length of ribbon required.

    (c) Draw a circuit diagram to show how a second heating element would be connected to increase the power dissipated to 1.5 kW.

    (d) State one important property of a conductor used to make heating elements.

    Answers: (a) 76.8 Ω, (b) 3.49 m.

    2. The attempt at a solution
    (a) P = V * I and R = V / I. So we find I = P / V = 750 / 240 = 3.125 A and find R = 240 / 3.125 = 76.8 Ω.

    (b) Area = (1 / 10 / 100) * (0.050 / 10 / 100) = 5 * 10-8 m2. L = (R * A) / ρ = (76.8 * 5 * 10-8) / (1.1 * 10-6) = 3.49 m.

    (c) This is the part I'm not sure. This is how I see the question:

    d436c2931327.jpg

    I would say that if we add another 76.8 Ω heating element the current would increase to 6.25 A (1500 W / 240 V). And then I just put the second element above or beneath the given one. And then we will have a series circuit with I = 6.25 A, two elements with R = 76.8 Ω each and V = 240 V. Is this correct?

    (d) This thing I don't know. Maybe it has to do something with it's dimensions or resistivity or something else?
     
  2. jcsd
  3. Oct 6, 2016 #2

    cnh1995

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    Are you sure it is a series circuit?
     
  4. Oct 6, 2016 #3
    If you wanted two 750 watt elements to generate 1.5KW, would you hook them up in series?
    Would nichrome ribbon be a better heating element than copper? murcury? sodium?
     
  5. Oct 6, 2016 #4

    Bystander

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    ?
     
  6. Oct 6, 2016 #5

    Bystander

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    "Cokes ... 1, 2, 3, 4, ...."
     
  7. Oct 6, 2016 #6
    Ah, yes, they should be done in parallel. We can check it by: V = 240 V, I = 6.25 A so R = 240 / 6.25 = 38.4 Ω total resistance of the circuit. And this goes in hand with 1 / R = 1 / 76.8 + 1 / 76.8 → R = 38.4 Ω.

    No idea on this topic. What should be of particular interest in analyzing this?

    Cokes?
     
  8. Oct 6, 2016 #7

    Bystander

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    Simultaneous, or nearly so, responses that are so similar as to be indistinguishable, in the days of the dinosaurs was followed immediately with a chorus of "Cokes (the beverage) and some locally agreed upon enumeration (the count)."
     
  9. Oct 6, 2016 #8
    Alright, looks like (c) is solved : ).

    Any suggestions on this part:
    ?
     
  10. Oct 6, 2016 #9

    Bystander

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    What's the most relevant property?
     
  11. Oct 6, 2016 #10
    Maybe current?
     
  12. Oct 6, 2016 #11

    Bystander

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    Current is not really a property of conductors, since it does vary with voltage; you're so close.:nb)
     
  13. Oct 6, 2016 #12
    Maybe resistance? It should not vary with voltage.
     
  14. Oct 6, 2016 #13

    Bystander

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    Closer.
     
  15. Oct 6, 2016 #14
    It should be resistivity of the material, right?
     
  16. Oct 6, 2016 #15

    Bystander

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    :partytime:
     
  17. Oct 6, 2016 #16
    Don't you mean 4,3,2,1,....cokes ?
     
  18. Oct 6, 2016 #17
    Would nichrome ribbon be a better heating element than copper? mercury? sodium?
    That was my attempt to help you with that last question.
    Copper isn't very resistive. Mercury is a liquid in most heating applications. Sodium is pretty reactive.
    How about gold, sulfur, arsenic?
     
  19. Oct 6, 2016 #18
    Gold, sulphur and arsenic........interesting alternatives, what physical properties of these elements make you suggest them??
     
  20. Oct 6, 2016 #19
    Gold is too expensive and too conductive - but provides a good electrical connection. Sulfur is too resistive. Arsenic begins to sublimate at 615C and would produce AsO3 before that - either would be very toxic.
    So you want something that is solid, inexpensive, resistive, but not an insulator, non-corrosive, not lethal, etc. All properties of a good heating element.
    Also, ideally it would become more resistive as the temperature increased.
     
  21. Oct 7, 2016 #20
    Nichrome (specific resistance / resistivity): 1.1 * 10-6 Ω m
    Copper: 17 * 10-9 Ω m
    Mercury: 960 * 10-9 Ω m
    Sodium: 47 * 10-9 Ω m
    Gold: 22 * 10-9 Ω m
    Sulfur: 1 * 1015 Ω m
    Arsenic: 3 * 10-7 Ω m

    So the higher is the resistivity of an element, the better it fits for the purpose of a heating element? In case we don't consider things like cost, toxication, melting properties and so on like in this question.

    And it looks like sulfur has the largerst resistivity, so solely based on this property it is a good fit?
     
  22. Oct 7, 2016 #21
    I was trying to introduce problematic choices - to assist with an answer to that OP's question #4. In each case, there is a reason that these are not good choices. So, each demonstrates a potential answer to question 4.
     
  23. Oct 7, 2016 #22
    As I said in an earlier post, sulfur is too resistive - it's basically an insulator. In order to get it to carry significant current and thereby generate significant heat, you would need to apply a very high voltage.
     
  24. Oct 7, 2016 #23
    If the resistance of the heater is halved then the current is doubled (assuming same voltage power supply).
    This means that the power is doubled....doesn't this suggest that lower resistivity is an advantage?
     
  25. Oct 7, 2016 #24

    Nidum

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    It's not only the electrical properties that matter .

    The element material has to have a high melting point , adequate mechanical strength and be resistant to oxidation ..

    The material also has to be workable .
     
  26. Oct 7, 2016 #25

    cnh1995

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    I may be wrong here but does 'specific heat' count? Would 'lower specific heat' be a desirable property for a heating element?
     
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