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RL Discharge Derivation

  1. Apr 18, 2017 #1
    1. The problem statement, all variables and given/known data
    After a long time, an inductor is disconnected quickly from the battery and then attatched to a resistor.

    2. Relevant equations
    V = Ldi/dt
    V = ir

    3. The attempt at a solution
    KVL: voltage across inductor - voltage across resistor = 0
    Ldi/dt - ir = 0
    di/i = rdt/L
    ln|i| from i(t) to i(0) = rt/L + C
    i(t)/i(0) = e(rt/L +C)
    i(t) = i(0)Cert/L

    At time t= 0, i(t) = initial current i(0). Plugging in i(t) = i(0) and t = 0 gives C =1.

    Now we have i(t) = i(0)ert/L

    The correct equation is i(t) = i(0)e-rt/L, different from what I have; I have a positive time constant r/L.

    I know i(t) must be smaller than i(t) when time increases, and usually this is taken care of by a negative constant of integration, but as C = 1, the only way I can account for i(t) < i(0) is to use negative time.

    Derivations I have seen started off KVL with -Ldi/di - ir = 0, but I don't understand why my method doesn't also work.

    Is my method incorrect?
    Last edited: Apr 18, 2017
  2. jcsd
  3. Apr 18, 2017 #2


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    Please state the problem fully including what you are asked to find.
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