Series vs Parallel Circuits — Rules, Formulas and Examples

High School⏱ 10 min readElectricity & Magnetism

Series and parallel circuits: how current and voltage split, equivalent resistance formulas, and worked examples with two bulbs.

Quick answer

Series: one path — same current everywhere, voltage divides. Parallel: multiple paths — same voltage across each branch, current divides. Your home is wired in parallel so each device gets full voltage.

Example: Two 10 Ω bulbs in series across 12 V: R_eq = 20 Ω, I = 0.6 A through both. In parallel: R_eq = 5 Ω, each bulb gets the full 12 V (1.2 A each).

What you will learn

State the current/voltage rules for series and parallel
Compute equivalent resistance in both configurations
Predict what happens when a component fails
Identify series vs parallel in diagrams

One path vs many paths

Two ways to connect components:

Series: end to end, one single path for current — like a one-lane road.
Parallel: side by side, multiple paths — like a multi-lane highway with exits.

Everything about circuit behavior flows from this geometric difference.

Series rules

In series, charge has nowhere else to go:

Current: identical through every component ( $I_1 = I_2 = …$ ).
Voltage: divides across components ( $V = V_1 + V_2 + …$ ) — bigger resistor drops more voltage.
Resistance: adds directly:

$R_{eq} = R_1 + R_2 + \dots$

Series is simple but fragile: one break anywhere stops everything, and each added resistor dims the rest.

Series: one loop, one current, voltages add up to the battery voltage.

Parallel rules

In parallel, each branch connects directly across the same two points:

Voltage: identical across every branch ( $V_1 = V_2 = … = V_{battery}$ ).
Current: divides among branches ( $I = I_1 + I_2 + …$ ) — easier paths take more.
Resistance: combines reciprocally:

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$

The equivalent is always less than the smallest branch — adding paths can only help current flow.

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

Parallel equivalent resistance

Which is which in your home?

Your home runs at full voltage on every outlet simultaneously because outlets are parallel: each appliance sees the full 120 V (or 230 V) independently. Unplug the toaster and the lamp never notices.

Wire them in series instead and every device would steal voltage from the others — plus one failed device would black out the house. That's why series survives only inside individual devices (like old flashlight bulbs), never between them.

Key idea

Series shares voltage; parallel shares current. Ask 'does each component get the full voltage?' — yes means parallel.

Worked mini-example: two bulbs, both ways

Two bulbs, $R_1 = 6\ \Omega$ and $R_2 = 12\ \Omega$ , across a $12\ \mathrm{V}$ battery.

Series: $R_{eq} = 18\ \Omega$ , $I = 12/18 = 0.67\ \mathrm{A}$ through both. Voltages: $V_1 = 4\ \mathrm{V}$ , $V_2 = 8\ \mathrm{V}$ (sum = 12 ✓).

Parallel: each gets $12\ \mathrm{V}$ . $I_1 = 2\ \mathrm{A}$ , $I_2 = 1\ \mathrm{A}$ , total $3\ \mathrm{A}$ . $R_{eq} = (1/6 + 1/12)^{-1} = 4\ \Omega$ — check: $12/4 = 3\ \mathrm{A}$ ✓. The parallel pair draws far more current — and glows far brighter.

Variables and units

Symbol	Name	Unit	Meaning
$R_eq$	Equivalent resistance	Ω	Single resistance equivalent to the whole network
$I$	Current	A	Current through a branch or the whole circuit
$V$	Voltage	V	Potential difference across a component

Common mistakes

✗ Adding resistors always increases total resistance.

Only in series. In parallel, adding a branch decreases total resistance — more paths make it easier for current to flow overall.

✗ Current splits equally in parallel branches.

It splits in inverse proportion to resistance (equal only for equal resistors). Voltage, not current, is what's equal across parallel branches.

✗ In series, the first bulb 'uses up' current so the second is dimmer.

Current is identical everywhere in series — charge is conserved. If bulbs are identical they glow equally; brightness differences come from different resistances.

Real-world applications

House wiring is parallel: every outlet gets the full 120/230 V, and one dead appliance doesn't kill the rest.
Old-style Christmas light strings were series — one burned bulb broke the whole string (modern ones add shunts).
Car electrical systems parallelize everything so headlights don't dim when you turn on the radio.

Frequently asked questions

What are the equivalent resistance formulas?

In series: R_eq = R₁ + R₂ + … In parallel: 1/R_eq = 1/R₁ + 1/R₂ + … Parallel equivalent resistance is always smaller than the smallest branch.

Why is house wiring parallel, not series?

Because every device needs full voltage to work properly, and parallel gives each branch the full voltage independently. Series would dim everything and let one failure kill all.

What happens when one bulb burns out in each type?

Series: the whole string goes dark (no complete path). Parallel: only that branch dies; the rest keep full voltage.

How do I tell series from parallel in a diagram?

Trace the current: if there's exactly one path from + back to −, it's series. If current can split into multiple paths that rejoin, those branches are parallel.