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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 simplycharacterized 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...
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...
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