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Homework Help: Series Circuit DIfferential Equation - My answer is coming out to be wrong

  1. Feb 14, 2010 #1
    Series Circuit DIfferential Equation - My answer is coming out to be wrong......

    1. The problem statement, all variables and given/known data

    A 6.5 amp current is necessary in order to start the motor for a certain factory appliance. The circuit for the appliance is designed with a 2 ohm resistor and a 1.5 henry inductor. If there already exists a steady current of 2 amps in the circuit at time t = 0, what electromotive force is necessary to achieve the desired current in 1.25 seconds?

    The answer should be 15.1 volts.

    2. Relevant equations

    1) L di/dt + Ri = E(t)

    or

    2) R dq/dt + q/C = E(t)

    3. The attempt at a solution

    It makes sense to me to use Equation (1):

    L di/dt + Ri = E(t)

    1.5 di/dt + 2i = E(t)

    => di/dt = [E(t) - 2i ] /1.5

    => di/[E(t) - 2i] = dt/1.5

    => ln[E(t) - 2i) = t/1.5 + c

    => E(t) = Ae-t/1.5 + 2i

    i(o) = 2

    A = E - 4

    => E(t) = (E-4)e-t/1.5 + 2i

    i(1.25) = 6.5

    => E(t) = (E-4)e-1.25/1.5 + 13

    => E - (E-4)e-0.83333 = 13

    => Ee0.83333 - (E-4) = 13e-0.83333

    => Ee-0.83333 - E + 4 = 29.9126

    => E(e-0.83333 - 1) = 25.9126

    => E = 19.9178 Ans.

    The answer should be 15.1 volts. PLease help!!! What is the thing that I am doing wrong!!!

    Thanks!!
     
  2. jcsd
  3. Feb 14, 2010 #2
    Re: Series Circuit DIfferential Equation - My answer is coming out to be wrong......

    First off, Your entire method could not possibly work if E(t) is not simply a constant, but thankfully in this case it is. You only made one simple mistake when you integrated di/[E-2i]. you're missing a -1/2 in front of the ln|E-2i|.
     
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