Could you please help me develop the intuition on how voltage divider works.
Let me describe the problem with the following example circuit:
As this circuit starts working, the electrons start moving from Vin towards the first resistor having 12 V.
After the electrons have left the first resistor $Z_1$ ($R = 2\ \Omega$) they have lost 4 Volts of energy (according to the voltage divider formula): $$ V_1 = \frac{Z_1}{Z_1+Z_2}\; V_\text{s}.$$
However, if the resistance $Z_2$ had been different, voltage drop at $Z_1$ would be different as well (e.g. if $Z_2$ resistance had been 10 $\Omega$, then voltage drop at $Z_1$ would be 2 V)
So, voltage drop at $Z_1$ depends on resistance of $Z_2$, even while the electrons coming to $Z_1$ do not even ‘know’ there is $Z_2$ ahead (Please let me know if they do know).
So, the question is: how do the electrons ‘know’ how much volts they should drop at $Z_1$, since they have not been at $Z_2$ and cannot know its resistance.
I cannot stop thinking that voltage drop at a certain resistor should depend exclusively on the resistor’s qualities, not other resistors at this circuit.