I would like to know why by adding two resistors in series we would get a sum of it's resistances.I know by Ohm's Law that since $$R=\frac {V}{I}$$ it's certain that you would attain the equation $$R_t=R_1+R_2$$
But I would like to have a practical definition on how resistances in series produce sum of it's resistances.
For example in the image below the point that confuses me is that how does the first resistor's resistance influences the second resistor's resistance. Because if we would try to find the current through the second resistor what I expect is that it (current) of the second resistor should be found by dividing only the resistance of the second resistor with the voltage through the circuit but unfortunately it is $$I_2=\frac{V}{R_1+R_2}$$
Could anyone help me understand why my expectation is wrong?