Using a simple lattice model of conduction, where electrons are accelerated by an electric field, and are slowed down by bumping into the lattice, you get the following equation for current density:
Let's imagine an ideal DC voltage source connected with perfectly conducting wires to a resistor. Just from intuition, as the electrons reach the lattice of the resistor, you'd think that there'd be a pileup of electrons, since they don't have as much mobility in the resistor (almost like a traffic jam at tight roads). Do electrons or other charge carries collect at the end of resistors? If they do, is this what creates a voltage drop across resistors (or equivalently, an electric field across a resistor)? This idea of a collection of charge seems to imply a capacitance to the resistor. Do real resistors display any in-built capacitance?