Series vs Parallel Circuits

Series Circuit

Components connected end-to-end so the same current flows through each one. The total resistance is the sum, and one break stops everything — like old Christmas lights.

$R_{total} = R_1 + R_2 + \cdots$

Unit: ohm (Ω)

Example: Two bulbs (60 Ω and 120 Ω) in series on 12 V: total 180 Ω, current 0.067 A through both — the 120 Ω bulb gets twice the voltage and glows brighter.

Parallel Circuit

Components connected across the same two points so each gets the full voltage while current divides among branches. One branch can fail without affecting the others.

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$

Unit: ohm (Ω)

Example: House wiring is parallel: every outlet gets the full 230 V (or 120 V), and unplugging one lamp doesn't dim the rest.

Key differences

Aspect	Series Circuit	Parallel Circuit
Current	Same through every component	Divides among branches
Voltage	Divides among components	Same across every branch
Total resistance	Sum — always larger than any one	Reciprocal sum — always smaller than any one
One component fails	Whole circuit goes dead	Other branches keep working
Used for	Fuses, simple sensors, strings of LEDs	House wiring, car electrics

Why students confuse them

Adding a resistor in parallel lowers total resistance — it feels backwards until you see it as opening another lane for current. More parallel branches always mean more total current from the same voltage.