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Current Decay in an R-L Circuit

  1. Aug 4, 2010 #1
    I was trying to solve this problem the other day for my physics class and I keep getting the wrong answer. The problem is as follows:

    An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with a 15 ohm resistor, a battery of internal resistance ohms and open-circuit terminal voltage of 25 V, and an open switch. (Note u = 4*(pi)*10-7 T *m/A)

    How long after closing the switch will it take for the stored energy in the solenoid to reach 1/2 of its maximum value?


    So this is what I did:

    L = (u0N2A)/l

    where L = inductance in Henry
    N = number of turns
    A = area of cross-section
    l = length in meters

    L = (4*(pi)*10-7 )(5452)(3.8*10-4)
    .185

    L = 7.66 *10-4 H

    Then I found the current I:

    I = emf/R

    where emf = electromotive force/voltage
    R = resistance

    I = 25 Volts/(15 ohms + 5 ohms) = 1.25 Amps

    Next I used the energy equation to find the maximum energy:

    U = 0.5*L*I2

    where U = energy
    L = inductance
    I = current

    U = 0.5*(7.66 *10-4)*(1.252)
    U = 5.99*10-4 J


    Then I don't know where to go from there to find time. I already tried an equation I found in my textbook....

    U = U0e-2*(R/L)*t

    t = -ln(.5)*L/(2R)
    t = -ln(.5)*(7.66 *10-4)/(2*(15+5))
    t = 1.32*10-5 sec

    and solved for t that way, but I keep getting 1.32*10-5 sec, when the answer should be t = 4.71 *10-5. I know t = 4.71 *10-5 is the correct answer because it came off of the answer sheet for a review.

    Can anyone shed some light on what I am doing right/wrong?
     
  2. jcsd
  3. Aug 4, 2010 #2

    vela

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    You need to find the current as a function of time and use it to calculate the energy stored in the inductor as a function of time.

    The equation you tried doesn't apply to this situation. For one, it starts at U0 and decays to 0, but in this circuit, the energy starts at 0 and increases to the max value you found as t goes to infinity.
     
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