In a series resistor circuit, the current remains constant because the total resistance increases, which adjusts the current output from the voltage source according to Ohm's Law. When additional resistors are added in series, the voltage source compensates for the increased resistance by altering the current supplied to the circuit. The concept of conservation of energy is key, as the current, or flow of electrons, must pass through each resistor, resulting in a voltage drop across them. This drop represents the energy lost due to resistance, but does not change the overall current flowing through the circuit. Thus, while resistance opposes current flow, it does not affect the uniformity of current in a series configuration.