Hello everyone, I've just got a quick conceptual question regarding solving circuits using the laplace transform.

See figure.

As my textbook shows, there are two possible transformations of an inductor and/or a capacitor into the frequency domain. One with the impeadance in series with the initial condition voltage source, the other in parallel with the initial condition current etc...

My question is, how do I know which one to pick, and why? Is there certain cases where one representation will simplify the work much more than the other representation? How do I distinguish this?

Thanks again!

 

Is there certain cases where one representation will simplify the work much more than the other representation? How do I distinguish this?

I think you will find that, generally speaking, the current source model faciltates solving via nodal analysis, while the voltage source model works best with mesh. But each circuit requires inspection to determine which will work best.

 

Is there anything in specific that I should be looking for in a circuit that will lean towards one representation rather than the other?

 

Is there anything in specific that I should be looking for in a circuit that will lean towards one representation rather than the other?

Count the number of mesh loops and nodes; whichever is less, that is probably the best method (assuming no other simplifications or methods are available).