Thevenin isolates nonlinear element

[JessicaHelena]

Homework Statement

If we want to study the behavior of a circuit with linear resistors, independent sources, and an unfamiliar, perhaps nonlinear, element, it is to our advantage to package up everything but the unfamiliar element into a Thevenin or Norton model, so we can concentrate on the interaction of this simply-characterized circuit with the unfamiliar element. For example, the circuit on the left of the diagram can be summarized, from the point of view of the unfamiliar element, by the circuit on the right. (Please refer to Fig 1.1)

Write the algebraic expressions for the Thevenin voltage and resistance.

Relevant Equations

V/I = R

I have no problem getting the $R_{TH}$ since from the special element's POV, the resistors are in parallel, and that's the answer.

However, I don't really understand how to get $V_{TH}$.

Ignoring the special element, it seems that I have the resistors in series this time. But I'm not too sure how to move forward from there.
So going back to the resistors in parallel idea, I can get the overall current by doing $i = V_s / R_{TH}$. Since the special element and $R_p$ are in parallel, multiplying $i$ by $R_p$ will give me the voltage, which gives me $V_s(R_s + R_p)/(R_s R_p)$, which isn't quite right, apparently...

 

[hutchphd]

The equivalent voltage Vth is the voltage obtained at terminals A-B of the network with terminals A-B open in the original circuit. I note that your result is also not dimensionally consistent ( which is a crime where I live !)

 

[gneill]

Note that $R_p$ and your mystery device are in parallel, so that you may swap their locations without altering the circuit.

Break the circuit where indicated and reduce what's to the left of the break to its Thevenin equivalent. You should be able to find the voltage A-B without too much difficulty