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: RC Circuit Differential Equation

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the general solution of [tex]L \frac{d^2I}{dt^2} + R \frac{dI}{dt} + \frac{I}{C} = \frac{dV}{dt}[/tex] given [tex]L = 0[/tex] and [tex]V = V_0 cos(\omega t)[/tex].

    2. Relevant equations

    3. The attempt at a solution
    So the equation basically turns into a first-order RC circuit equation [tex] R \frac{dI}{dt} + \frac{I}{C} = \frac{dV}{dt}[/tex], but I'm not sure how to approach it to find a general solution.

    The answer the book gives is [tex] I = Ae^{-\frac{t}{RC}} - \frac{V_0 \omega C (sin(\omega t) - \omega R C cos(\omega t))}{1 + \omega^2 R^2 C^2}[/tex] and I'm not sure how they came to that conclusion, so any help or nudge in the right direction would be greatly appreciated.
  2. jcsd
  3. Apr 2, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi sritter27! Welcome to PF! :smile:

    To find the general solution of R dI/dt + I/C = -ωV0sinωt,

    assume it's of the form Acosωt + Bsinωt, and you get the given result,

    except that you've copied it wrong … it's [tex]V_0 \omega C\frac{ (sin(\omega t) - \omega R C cos(\omega t))}{1 + \omega^2 R^2 C^2}[/tex] :wink:
  4. Apr 3, 2009 #3
    Oh wow I should have been able to see that. My many thanks for the help!
    Last edited: Apr 3, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook