Resistors in Series

In a series circuit there is only one loop, one path charge can take. Every electron that moves has to pass through resistor one, then resistor two, then resistor three, in line, like cars on a one-lane road. Because there's no fork in the road, no charge can sneak around, so the current is identical at every point in the loop. What changes from resistor to resistor is not the current but the voltage: each resistor drops some of the battery's voltage, converting electrical potential energy into heat, and those drops add up to the total battery voltage.

To find that one shared current, you don't solve resistor by resistor. You add all the resistances into a single total, R_total = R1 + R2 + R3, then apply V = IR once for the whole loop. More resistance in the path means less current everywhere, which is why a second bulb added in series makes every bulb in the string dimmer: the same current now has to push through more total resistance.

This sets up what happens with parallel resistors next, where charge does have a choice of paths and current splits instead of staying constant. It also connects to Kirchhoff's voltage rule: the voltage drops across series resistors must add up to the source voltage, which is exactly how you find the individual voltage across each resistor once you know the shared current.