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!

Energy Dissipated in an RL Circuit

  1. Nov 5, 2017 #1

    Drakkith

    User Avatar

    Staff: Mentor

    1. The problem statement, all variables and given/known data
    In the circuit shown in (Figure 1) , the switch makes contact with position b just before breaking contact with position a. As already mentioned, this is known as a make-before-break switch and is designed so that the switch does not interrupt the current in an inductive circuit. The interval of time between "making" and "breaking" is assumed to be negligible. The switch has been in the a position for a long time. At t = 0 the switch is thrown from position a to position b.

    What percentage of the initial energy stored in the inductor is dissipated in the 90 Ω resistor 1.4 ms after the switch is thrown from position a to position b?

    Figure 1:
    pr_7-3.jpg

    2. Relevant equations
    ##i(t) = 0.5e^{-500t}##
    ##i(0) = 0.5 A##
    ##p(t) = i(t)^2R##
    ##W_i=\frac{1}{2}LI^2##
    3. The attempt at a solution
    I found the equation for the current after ##t≥0##. To find the power dissipated in the 90 ohm resistor, I thought I was supposed to find the integral of the power from 0 to 1.4 ms.

    Initial energy is ##W_i = (0.5)(0.32)(0.5^2) = 0.04375 J##

    Power is:
    ##p(t) = i(t)^2R##
    ##p(t) = (0.5e^{-500t})^2(90) = 22.5e^{-1000t}##

    The integral of power is: ##\int_0^{1.4ms} 22.5e^{-1000t}\, dt = 22.5 \int_0^{1.4ms} e^{-1000t}\, dt = \left. \frac{-22.5}{1000}(e^{-1000t}) \right|_0^{0.0014} = -0.0225(e^{-1.4}-e^0) = -0.0225(-0.7534) = .01695 J##
    ##W(1.4ms) = 0.01695 J##

    The percentage of initial energy is: ##\frac{0.01695}{0.04375}(100) = 38.75##

    Unfortunately it appears that answer is incorrect. Any ideas where I might have gone wrong?
     
  2. jcsd
  3. Nov 5, 2017 #2

    phyzguy

    User Avatar
    Science Advisor

    How did you get the .04375? 0.32 / 8 = 0.04, not 0.04375. The rest looks OK to me.
     
  4. Nov 5, 2017 #3

    Drakkith

    User Avatar

    Staff: Mentor

    Whoa... I have no idea. I must have typed something in incorrectly in my calculator.
    Correcting that gives me 42.375%, which is the correct answer.

    Thanks phyzguy.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Energy Dissipated in an RL Circuit
  1. RL Circuit (Replies: 3)

  2. RL circuit (Replies: 7)

  3. RL Circuit (Replies: 3)

Loading...