Sign of the Thevenin resistance equation

[Jonas E]

Here is my problem: when trying to find Rth for a circuit with dependent sources, I excite the circuit a voltage Vo, and then proceed to find the resulting current Io. Finally, I use the equation Rth = Vo / Io, with a plus (+) sign. The way I see it, Io enters the positive side of Vo, so the Passive Sign Convention holds. However this gives me the negative of the correct answer. In my book the author defines Io in the opposite direction (away from the positive side of Vo), and then uses Rth = Vo / Io, with a plus sign.

Can someone please point out the mistake in my reasoning and explain the relationship between the sign of the expression above and direction of the current Io?

Image of the circuit below:

 

[phinds]

You have not given sufficient information. The current could be flowing in either direction depending on the rest of the circuit. What sign you give it when solving the problem is totally arbitrary and irrelevant. If you have signed it the "wrong" way you'll just get a negative answer.

 

[gneill]

Note that you're looking to find the equivalent resistance of the circuit, not the source. So by definition this is determined by the current that flows into the circuit from the applied source: