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LR circuit, book mistake?

  1. Apr 2, 2012 #1
    problem: switch of LR circuit is closed at time = 0; what is ratio of inductor's self-induced emf ( E(L) ) to battery's emf ( E(bat) ) at t = 2τ?

    my solution:
    switch is closed so current begins to build up according to equation:
    i = (E(bat)/R) (1-e^(-t/τ) )
    multiplying R on both sides and plugging in for t = 2τ:
    E(L) = E(bat) (1-e^(-2) )

    E(L) / E(bat) = 1-e^(-2) ≈ 0.865

    But my book says the answer is 0.135, which is just the value of e^(-2), which you would obtain if you used the equation for current decay

    i = (E(bat)/R) (e^(-t/τ))

    instead of the equation for current rise. But the current in this case is clearly rising. So is my book wrong or am I wrong?
     
  2. jcsd
  3. Apr 2, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    R*I is not the voltage across the inductor, it's the voltage across the resistor...
     
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