I'm new in electronic and I want to know the exact definition of equivlant circuit. My trouble is that we know for example that a resistance equivalence has same current of the resistances in series for a same tension. If we substitute the resistance in series with the equivalent resistance we obtain another circuit and then we calculate the tension in to the poles of the equivlent resistance. At this point we use this voltage in original circuit, but how we know that in the orginal circuit the tension is the same? I don't see explanation maybe it follows from linearity but textbooks I had read don't say anything about this question.
Suppose we have a circuit C and a subcircuit A and let be K the complement circuit of A in C so C=K+A. Now I say that A' is equivalent to A if we consider C'=K+A' calculate the currents and voltages of K in this case and they are the same of K in the original circuit C. If my definition is correct then we must proof that proposition in all cases we want to show an equivlant circuit such as equivalent resistance. Correct me if I'm wrong. I gave that definition because it is what we do in exercises.
I have these two circuits:
I solve the second circuit and I find the voltage on R23, then usually in exercises I use that voltage in first circuit to compute current in R2 and R3 in first circuit. My question is: why the volatage in the second circuit can be used for the first (I want a rigorous proof)? Is there a theorem concerning equivalent circuits (in this case R23 is quivalent of R2, R3 in parallel) embedded in other circuits?