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Finding maximal total current for a system

  1. Feb 21, 2014 #1
    1. The problem statement, all variables and given/known data


    a) There are two fuses connected in parallel: fuse A has resistance R_A = 1Ω and
    maximal current (by which it melts) I_Amax = 1A; fuse B
    has resistance R_B = 2Ω and maximal current (by which it
    melts) IBmax = 1.2A. What is the maximal total current for
    such a system of fuses?

    b) What is the total current when the
    fuse B is substituted with a fuse C which has R_C = 2Ω and
    I_Cmax = 1.7A?



    3. The attempt at a solution

    for part (a) we have:

    [tex] R_B/R_A = I_A/I_B = 2 [/tex] because of that fuse A will melt first (the current through it will be 1 A) so we substitute it in the equation and solve for I_B, we get:

    [tex] I_B = 0.5 A [/tex]

    So:

    [tex] I = 0.5+1 = 1.5 A [/tex]

    I'm not sure how to do part B

    Edit: Answers are: a) 1.5 A
    b) 1.7 A
     
  2. jcsd
  3. Feb 21, 2014 #2

    haruspex

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    Looks like a mistake in the question to me. Are you sure you've quoted it correctly?
     
  4. Feb 22, 2014 #3
    Yes, I'm sure.
     
  5. Feb 22, 2014 #4
    Imagine in part (B) current exceeds 1.5 A. What happens then?
     
  6. Feb 22, 2014 #5
    Then fuse A would burn and the current would be redirected to fuse C only?
     
  7. Feb 22, 2014 #6
    Correct.
     
  8. Feb 22, 2014 #7
    So the answer is 1.7A because after changing to fuse C a larger maximal current is possible where fuse A would burn and the current (1.7A) would be redirected to fuse C only.
     
  9. Feb 22, 2014 #8
    1.7 A is possible from the beginning, it is just that fuse A gets blown in the process. This is different from case (a), where the max current is only possible with the two fuses intact.
     
  10. Feb 22, 2014 #9

    haruspex

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    Doh!
     
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