My question is about the variation of conductivity in a volume of material and its effect on measured current. A volume is comprised of two metals joined symmetrically in a cuboid shape as in the image below. These metals have different conductivities: $\sigma_{1}$ and $\sigma_{2}$. Does $A_{1} = A_{2}$ or $A_{1} \neq A_{2}$?
From what I’ve read so far it seems to me that the average local charge density and drift velocity vary inverse with each other to keep the current density constant throughout the entire sample such that $A_{1} = A_{2}$. However, a friend suggested that diagram 1 is topologically the same as diagram 2 and therefore measured currents $A_{1}$ and $A_{2}$ would be different, where $R_{1}$ and $R_{2}$ are some function of the conductivity of each material and geometry (where $R_{1} = f \left( \sigma_{1}, \sigma_{2} \right)$, $R_{2} = g \left( \sigma_{1}, \sigma_{2} \right)$). I am confused what approach is correct: that $A_{1} = A_{2}$ or that $A_{1} \neq A_{2}$? I'm also wondering the best way to calculate the current measured at $A_{1}$ and $A_{2}$.
Apologies in advance, this is a relatively new topic to me, so my understanding is lacking. If you have any suggestions on books or literature to read or look at that would be really appreciated. Many thanks for your help!
