# Help with nonlinear resistor

#### bluebird

Joined Apr 8, 2008
1
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!

#### Dave

Joined Nov 17, 2003
6,970
In a complete circuit Kirchhoffs Voltage Law always applies.

Dave

#### scubasteve_911

Joined Dec 27, 2007
1,203
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.

http://www.eas.asu.edu/~holbert/eee202/EEE202_Lect12_DiffEqSolutionTransientCircuits.ppt

Steve