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: RLC circuit - Differential equation - Stationary current calculation

  1. Jan 20, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm decent with differential equations for RLC circuits, and I KNOW the stationary current will be zero, but I need help to work it out mathematically, because my maths gets me -2.4A (...)

    L: 0.05H
    C: 0.04F
    R: 3 Ω
    U (source) = 1 V

    I've got the transient solution: c1e-10t + C2e-50t


    i(0+) = 0 (coil prevents instant change in current)
    i'(0+) = u/L = 20

    Once the capacitor is charged up, it will block the current. In other words, the stationary current will be zero.

    3. The attempt at a solution

    So I could simply declare that, on electrical reasoning, but I want to calculate it. The problem is, my calculation is wrong. Something is wrong.

    Been banging my head against this for a while, hope somebody can help me out!

    Differential equation: L*i'' + R*i' +1/c*i = u'

    i''=0, because i'=20

    u'=0, because u=1

    I call the stationary current A:

    L*0 + R*20 + 1/c A = 0

    A=-20*R*C= -2.4

    What have I done wrong? If I lack information, please let me know.
    Last edited: Jan 20, 2013
  2. jcsd
  3. Jan 20, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    i'' isn't 0 because i'=20. i'=20 only when t=0.

    You have two approaches: 1. Solve the differential equation and then take the limit as t goes to infinity; 2. Argue what i'' and i' equal when the system has reached steady state, plug those values into the differential equation, and then solve for the current.
    Last edited: Jan 20, 2013
  4. Jan 20, 2013 #3
    Hmm.. well going with approach 2, that makes sense. There will be no change of i when the system is stable.

    It's real late here, gonna take a look at it tomorrow. Thanks! I will ask again if I am still stumped heh.

    Edit: And yeah, my assumption about i''= 0 because i'(0)=20 is of course flawed.. It's the Christmas break that made me forget some things!
  5. Jan 21, 2013 #4
    Alright, looking at the work again today.

    Well it seems to me I already have the starting values I needed!


    I don't need i'' for that aspect.

    And yeah, if I go with the second approach you outlined, using reason and knowledge of the RLC-circuit, there is no change of i when it is stable, so that means the i''(∞)=0.

    Not sure if using infinity in an argument is sound, but it works!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook