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Electrodynamics: Solve the differential equation

  1. Nov 20, 2008 #1
    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.

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