Series and Parallel Circuits
How components combine in series vs parallel, and how voltage, current, and resistance behave differently in each.
Series Circuits
Components are connected end-to-end, forming a single path for current.
(+) ── R1 ── R2 ── R3 ── (−)
Rules:
- Current is the same through every component (there’s only one path)
- Voltage divides across components (each gets a share)
- Total resistance adds: R_total = R1 + R2 + R3
Voltage divider formula:
V_R1 = Vsupply × (R1 / R_total)
If R1 = 100Ω and R2 = 300Ω on a 12V supply:
- R_total = 400Ω
- V_R1 = 12 × (100/400) = 3V
- V_R2 = 12 × (300/400) = 9V
This is the voltage divider — one of the most useful basic circuits. Used everywhere to scale voltages down for sensors or ADC inputs.
Break a series circuit anywhere: current stops everywhere. Christmas lights used to be wired this way. One bulb out = whole string dark.
Parallel Circuits
Components share the same two nodes — they’re all connected directly between the same + and − points.
(+) ──┬── R1 ──┬── (−)
├── R2 ──┤
└── R3 ──┘
Rules:
- Voltage is the same across every component (they share the same nodes)
- Current divides between branches (each branch draws independently)
- Total resistance decreases: 1/R_total = 1/R1 + 1/R2 + 1/R3
For two resistors in parallel:
R_total = (R1 × R2) / (R1 + R2)
Two 100Ω resistors in parallel = 50Ω. Adding parallel paths always reduces total resistance.
The intuition: more paths → easier for current to flow → lower total resistance.
Break one branch: the others keep working. Household wiring is parallel. One lamp off doesn’t kill the rest.
Measured vs Calculated
I built both circuits, calculated expected values, then measured with the multimeter. Results matched within a few percent. The act of predicting before measuring makes the measurement meaningful — it tells you whether your model of the circuit is correct.
Real-World Mix: Series-Parallel
Most real circuits mix both. A battery powers multiple branches in parallel, but each branch may have series components (a resistor + LED in series, for example). You analyze by breaking it into series and parallel sections.
Equivalent Resistance Mental Model
| Configuration | Effect |
|---|---|
| Add a resistor in series | Total resistance goes up |
| Add a resistor in parallel | Total resistance goes down |
| Short circuit (R = 0) in series | Whole circuit goes to 0Ω — dangerous |
| Open circuit (R = ∞) in series | No current anywhere |
| Open circuit in parallel | Other branches unaffected |
Current in Parallel Branches
Each branch draws current independently based on its own resistance:
I_branch = Vsupply / R_branch
The supply must provide the sum of all branch currents. This is why more parallel devices drain a battery faster — total current demand adds up.