Help with nonlinear resistor

Discussion in 'Homework Help' started by bluebird, Apr 8, 2008.

  1. bluebird

    Thread Starter New Member

    Apr 8, 2008
    Hi all,

    I'm trying to solve the following problem:

    "A resistor R and a capacitor C are in series with a battery of constant voltage V0. Suppose that the gate is closed at t = 0, and that there is no charge on the capacitor initially. Let Q(t) be the charge on the capacitor at time t >=0. Derive the circuit equations."

    The twist is that there is a nonlinear relation between voltage and current, that is, the current flowing through the resistor is given by the general function I = g(V) rather than the usual I = V/R. My question is, can Kirchoff's voltage law still be applied in this case, or does that only work for a linear problem? Thanks for any help you can provide!
  2. Dave

    Retired Moderator

    Nov 17, 2003
    In a complete circuit Kirchhoffs Voltage Law always applies.

  3. scubasteve_911

    Senior Member

    Dec 27, 2007
    Yes, Dave is correct, you can always apply a circuit analysis law, since it is true for all of time.

    You're right about the non-linear relationship. This calls for a "time-domain solution" where t is the input to your final equation. Whatever variable you choose to isolate, you should be able to find it as a function of t. Your time domain solution will consist of two parts: transient and steady-state.

    The transient solution will disappear as t approaches infinity, unless it is an unstable circuit. The steady-state solution will be left.

    Since I don't wanna get into the math on here, I found something that will help you.