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Homework Help: Charge entering element, current as a func of time

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Over time (0s ≤ t < ∞), charge enters an element according to q(t) = 7.5C · (1 − e(+t/τ)).

    1. What is the current into the element as a function of time? (Find a symbolic answer!)
    2. What is the unit of τ?
    3. Prove that the unit of the result indeed is A.



    3. The attempt at a solution

    Do I need to take the integral of this to get current as a function of time? I don't suppose I cane just separate the coulomb int A*s and get the A by itself or is that not right?

    And I dont know where else to go on this problem...
     
  2. jcsd
  3. Jan 25, 2012 #2
    I suggest you look up the definition of electric current. You should know it already, though.
     
  4. Jan 25, 2012 #3
    yep... what am I missing?
     
  5. Jan 25, 2012 #4
    Perhaps you are missing the concept of a rate (using calculus).
     
  6. Jan 25, 2012 #5
    q(t) = 7.5C · (1 − e(+t/τ)).

    In this equation, the final output is in C, is it not? then would the units of tau be seconds also, so then to have this find current, can I multiply the whole thing by 1/t leaving me with amps as the resultant unit?
     
  7. Jan 25, 2012 #6

    You're supposed to find the instantaneous current. Yes, if you divided by time, your answer would have the correct units. But that answer itself wouldn't be correct.
     
  8. Jan 25, 2012 #7
    so do I need to take the derivative?

    -7.5C/τ*e(t/τ)

    or

    -7.5A*e(t/τ)
     
  9. Jan 25, 2012 #8
    What do you think and why? This is a very basic question. I don't think it's something with which you should struggle this much, if you are studying physics or engineering at the college level.
     
    Last edited: Jan 25, 2012
  10. Jan 25, 2012 #9
    i think that's right, because coulombs is the current coming in over an amount of time. (amps times however many seconds) so derivative would give instantaneous current at a given time.
     
  11. Jan 26, 2012 #10
    current is rate of flow of charge.
    So you need to take a derivative of the given expression.
    exponentials are dimensionless t = unit of time so T = time too :)
    as you take derivative you intitutively divide by DELTA t and take limit 0 so you have unit C/t = A
     
    Last edited by a moderator: Jan 26, 2012
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