Parallel Resistance Confusion
think about what series and parallel mean, resistors in parallel, they share the voltage while the current is split in each branch and for series the voltage divides while they all share the same physical current.

First think what it means to measure R1 in this arrangement you apply the voltage to AB and measure the current through it. You never measure resistance directly you apply voltage and measure current or apply current and measure voltage, so you have to be careful how that happens.







simulate this circuit &ndash; Schematic created using CircuitLab

Now in your case you gotta think about R2 and R3 in series first, they share a current let's call it I23 and their voltage added up I23(R2+R3) gives you the voltage between AB or Vab correct? So you can see how the current that runs I23 is not the same as current I1 so it cannot be in series in this arrangement. Actually if you measure the source current you get the equivalent resistance, parallel of 1 and 23 series.

Now if you apply the voltage like this and measure the source current you get the equivalent in series. You can see there is only one current and the voltage V is split between all 3 resistors, conditions for series connection are met.

This is why most people recommend disconnecting resistors when you measure them in a circuit, because depending on how you apply voltage the resistance measurement can change. This case is easy to see, but others can be much harder to follow.







simulate this circuit

edit: mistake on the definition of series and parallel, had series written twice.