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Find resistance, inductance, and the time constant for an RL circuit.

  1. Apr 6, 2014 #1
    1. The problem statement, all variables and given/known data

    A 5.0V battery is attached to an RL circuit. The current is given by the formula: I = V0/R(1-e-t/τ), where I0 is the steady-state current, and τ is the time constant for the circuit.

    Using the data table provided, determine τ, R, and L for this circuit.

    Code (Text):
     I(mA) | t(μs)
    ---------------
       0   |   0
     3.94  |   1
     6.32  |   2
     7.77  |   3
     8.65  |   4
     9.18  |   5
     9.50  |   6
      ...  |  ...
     10.0  |   ∞
    2. Relevant equations

    I = V/R
    τ = L/R
    εL = -ε0e-Rt/L
    I = ε0/R(1-e-Rt/L)

    3. The attempt at a solution

    So I started by concluding that ε0 = V0 = 5 V and I0 = 10 mA.

    Using that I determined that R = V0/I0 = 5/0.01 = 500 Ω which gives me resistance.

    I know that once I find τ or L I can easily find the other one, but I can't figure out how to find either of them. At first I thought I could simply work I = V0/R(1-e-t/τ) algebraically to give me τ, but I end up getting undefined from using the natural log with a negative number.

    I feel like I have to use the data to find one of them (probably τ?) by using the relationship between two of the data points but I'm sort of stuck at this point.
     
    Last edited: Apr 6, 2014
  2. jcsd
  3. Apr 6, 2014 #2

    rude man

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    Homework Helper
    Gold Member

    When t = 1 time constant, what is the current?
    Then, what is the time constant?
    Then, expess the time constant in terms of L and R.
     
  4. Apr 6, 2014 #3
    Ah, so when t = τ, I = 5/500(1-e-1) ≈ 6.32 mA.

    So τ = 2 μs from the data and therefore L = 500*0.000002 = 1 mH.

    That seems correct, right?
     
  5. Apr 6, 2014 #4

    rude man

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    Homework Helper
    Gold Member

    It does to me! :smile:
    Good going.
     
  6. Apr 6, 2014 #5
    Thanks a lot! Can't believe the answer was so close, lol.
     
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