Series & Parallel

Series: one path

Components in series form a single chain — the same current threads through every one of them (there’s nowhere else to go). Each resistor takes its own bite of the battery’s voltage (V_i = I·R_i), and the bites always add up to the full supply. Total resistance simply adds:

Old-fashioned Christmas lights were wired in series — one dead bulb broke the single path and the whole string went dark. Series is also why adding resistance anywhere in a chain throttles the current everywhere in it.

Parallel: many paths

Components in parallel connect across the same two nodes — so they all see the same voltage, and each draws its own current by Ohm’s law. The currents add. More paths mean easier flow overall, so the combined resistance is always smaller than the smallest branch:

Your house is wired in parallel: every outlet gets the full mains voltage, every appliance draws what it needs, and switching one off doesn’t darken the rest.

Intuition for mixed networks

Real circuits mix both. The strategy is always the same: find a purely-series or purely-parallel cluster, replace it with its equivalent single resistor, redraw, and repeat until one resistor remains. Two anchors keep you sane: in series the biggest resistor dominates (it hogs the voltage); in parallel the smallest dominates (it hogs the current).