I understand both the current divider formula and why it is mathematically correct. I am curious though why physically this is true. My book provided me the following circuit:
The explanation in the book left a lot to be desired. The physical explanation was basically:
The total current from the source I is split into two currents I1 and I2 at the junction of the parallel resistors. I1 passes through R1 and I2 passes through R2 respectively.
They are recombined at the other side so that the current and voltage across them are made whole again.
From the formula, the current x across a given resistor x is given by:
Ix = It * (Rt)/(Rx + Rt)
and so from the formula it's clear the total resistance (and therefore the other resistors including the branch's resistors) has an effect on a given individual branch of current.
Why physically is this effect true? It seems counter-intuitive in the sense that you might expect only the branch's resistor, rather than both resistors, to effect the current.