# Current flow with no resistance

Imagine a simple circuit consisting of a battery with potential $$V$$ connected to a resistor with resistance $$R$$ by a loop of copper wire with $$0$$ resistance. It is obvious that a current $$I=\frac VR$$ will flow through the loop. Now, say that the section of wire between the battery and the resistor bifurcates into two strands which come back together at the resistor, giving the current two different ways to travel through the circuit, like this:

https://freeimage.host/i/HOYyAhl

Intuitively, it seems that a current of $$\frac I2$$ will flow through both the upper and lower strands. Now, one can imagine the wire being shaped into a complicated "spiderweb" arrangement between the battery and the resistor, giving the current many different paths that it can take:

https://freeimage.host/i/HOYyRQ2

My question is, how can we calculate from first-principles how the current will reach the resistor (i.e. what fraction of the current travels through each segment of wire, keeping in mind that the total current must sum to $$I$$)? Kirchhoff's loop law is clearly of no use here, since the voltage over an ideal wire is always $$0$$.