1. Not finding help here? Sign up for a free 30min 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!

Electrodynamics: Solve the differential equation

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at the attached circuit, where the current is direct (i.e. DC).

    I have found the following differential equation using Kirchoff's laws:


    I wish to solve this equation, and thus to find Q(t).

    3. The attempt at a solution

    First I differentiate with respect to t to obtain:


    Solving this gives me the following:

    Q(t)=A+B\exp\left( {\frac{R_2+R_1}{R_2R_1C}t} \right),

    where I have used the fact that Q(t=0)=0 to find that B=-A. But how do I find A?

    Thanks in advance.


    Attached Files:

    Last edited: Nov 21, 2008
  2. jcsd
  3. Nov 20, 2008 #2
    Obtain an expression for the current, then find the charge.

    Just use the fact the i = dq/dt and di/dt = d^2q/dt^2 and use separation of variables.
  4. Nov 20, 2008 #3
    You need two initial conditions to find the two constants. One is Q(0), the other one? What is the initial current?
  5. Nov 21, 2008 #4
    I am not told what I(0) is, but I guess it is zero. But how will this help me?

    And if I solve for I instead of Q, then how can I find the particular solution?
  6. Nov 21, 2008 #5
    Ok, I solved it. I just have to find the final charge on the capacitor, and that is the particular solution.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Electrodynamics: Solve the differential equation