Can RLC circuits with DC voltage supplies be solved using superposition?

ex. attached.. sorry its not rotated!

 

Is the circuit linear? If so, then you can use superposition.

 

I think so. Basically the question becomes: at what point in time do you want the solution?

Example.
Let say the circuit is ON for a long time. This means two things:
* inductor is a short
* capacitor is open
So all you have are two voltage sources and two resistors in series. Very simple circuit.

 

I'm solving for V(T) I(T) etc. SO the circuits not linear, and supposition wont help (I have never been able to understand this intuitively.) I tried a solution that involved mesh current and some other trickery and got a second order differential equation for for the current in the right loop except it's not one that I know how to solve. Can anyone point me in the right direction?

 

Check your textbook.

RLC in dc environment are not really that interesting.

 

I'm solving for V(T) I(T) etc. SO the circuits not linear, and supposition wont help (I have never been able to understand this intuitively.) I tried a solution that involved mesh current and some other trickery and got a second order differential equation for for the current in the right loop except it's not one that I know how to solve. Can anyone point me in the right direction?

Why are you saying the circuits are not linear? Which component in the circuit is a nonlinear component?

Saying that you tried a solution tells us nothing. Show us your work. How else can we see what you have done right and what you have done wrong? For instance, how are you handling initial conditions?

When you say you have DC supplies, that means that those supplies are assumed to have been providing their outputs for a really long time, are continuing to provide that output, and will continue to provide that output for a really long time to come. That being the case, you have no driving input signal that is changing and hence all of the voltages and currents in the circuit will have reached steady state a long time ago and will not be changing. What does that tell you about the voltage across any inductors and the currents through any capacitors?

Usually in this type of circuit at least one thing in the circuit will change, usually at time t=0. Are you sure that is not the case here.