Series and Parallel Basics

Two bulbs wired in a row, one after another, form a series circuit: there's only one path for charge, so every charge that moves anywhere moves through both bulbs. That shared path means the current is identical at every point in the loop. But each bulb still needs a voltage drop to push current through its resistance, and the source only has so much voltage to give. Split between two bulbs instead of one, each gets less, so each glows dimmer. The resistances add directly: R_total = R1 + R2, and that larger total resistance means less current overall too.

Parallel wiring gives charge a choice: two or more branches connect the same two points, so each branch feels the exact same voltage, set by whatever is connected across those points. Current splits among the branches according to each one's own resistance, with smaller resistances pulling more current. Because each new branch is just another route for charge to get through, adding one can only make it easier for current to flow overall — never harder. That's why equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2, always smaller than the smallest individual resistor.

These two patterns are the building blocks for every resistor network you'll reduce to a single equivalent resistance, and they set up the current divider and voltage divider rules used constantly in circuit analysis. Once a circuit mixes series and parallel sections, you simplify piece by piece: collapse parallel branches into one equivalent resistor, then add that to whatever is in series with it, working inward until one number represents the whole network.