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I have this circuit and I have to solve the Thevenin equivalent across the terminals A and B. How do I solve for RTh in terms of the variables present in the circuit?

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The problem is not to have one (or two) variable resistors, because you always take a look at one moment and treat them as fixed during your analysis.

I guess your problem is to see that the variable resistor (potentiometer) actually consists of two resistors (R2 and R - R2). In general they form a voltage divider; in this particular case one of the two "sub"-resistors (R - R2) is shorted so you can forget the (R - R2) part (i.e. treat it as being 0).

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