1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook