Series and parallel circuits are the two basic ways to connect components in an electrical circuit. In a series circuit, components sit on a single current path, so the same current flows through each one and their voltages add up. In a parallel circuit, components share the same voltage across separate branches, and their currents add up.
Flip one switch in your house and the other lights stay on. Pull a single bulb from an old string of fairy lights and the whole strand goes dark. Same electricity, completely different behaviour — and the only thing that changed is how the parts are wired together.
That wiring choice sits at the heart of every circuit you will ever build or fix. Get it right and you can share a voltage, limit a current, or keep devices independent. Get it wrong and nothing lights up. This guide shows exactly how each arrangement behaves, with original diagrams, formulas, and eight worked examples.
What Are Series and Parallel Circuits?
Picture a single-lane road next to a motorway with several lanes. On the single lane, every car follows the one in front — that is a series circuit. On the motorway, traffic spreads across lanes and travels side by side — that is a parallel circuit.
More precisely, a series circuit connects components end to end in one continuous loop, leaving a single path for current. A parallel circuit connects components across the same two points, giving the current two or more separate branches to flow through.
This one structural choice decides three things at once: how the current splits, how the voltage divides, and what happens when a component fails. Everything else below follows from those three rules.
Figure 1: The same three resistors wired in series (one loop) and in parallel (three branches).
The single rule that defines each
In a series circuit there is only one path, so the current has nowhere else to go — it is identical through every component. In a parallel circuit every branch connects to the same two nodes, so each branch feels the same voltage.
Hold onto one line and the rest is bookkeeping: series shares current, parallel shares voltage. The two cases are mirror images — voltage and current simply swap roles between them.
The Series and Parallel Circuit Formulas
All of the maths rests on a single relationship — Ohm’s law — which ties voltage, current, and resistance together.
- V — voltage (potential difference), measured in volts (V)
- I — current, measured in amperes (A)
- R — resistance, measured in ohms (Ω)
From here, the two circuit types differ only in how you combine the resistances.
Total resistance in series
Resistors in series simply add. Each one blocks the current one after another, so the obstacles stack up.
Adding any resistor in series always increases the total resistance.
Total resistance in parallel
Resistors in parallel combine through their reciprocals, because each extra branch gives current a new route — making it easier, not harder, for charge to flow.
For two resistors, a shortcut avoids the fractions entirely:
The answer is always smaller than the smallest resistor in the group. That is a fast sanity check — if your parallel total comes out bigger than a branch, you have slipped somewhere.
Power in any circuit
However the parts are wired, the power each component dissipates comes from the same trio of equations:
- P — power, measured in watts (W)
In practice this hides a neat twist. In series the largest resistor turns the most energy to heat, because the current is shared and P = I²R favours big R. In parallel the smallest resistor dissipates the most, because the voltage is shared and P = V²/R favours small R.
Need a number fast? Drop your values into our Resistor Calculator to get the total series or parallel resistance instantly, then check it against the worked examples below.
How Series and Parallel Circuits Work
Start with series. The battery pushes charge around a single loop, so whatever current leaves the battery must pass through every component and return unchanged. There is no junction for it to split at.
Because each component resists that shared current, each one claims a slice of the battery’s voltage. Add the slices and you recover the full supply voltage — Kirchhoff’s voltage law, stated in plain English.
So in series the current is shared and the voltage is divided. The bigger a resistor, the bigger its share of that voltage.
Why parallel behaves the opposite way
In parallel, every branch is wired straight across the battery’s two terminals. Each branch therefore sees the full supply voltage, exactly as if the others were not there.
The current is what splits. Each branch draws its own current set by its resistance, and those branch currents add up to the total leaving the battery.
A low-resistance branch is a wide-open door and grabs a large current; a high-resistance branch barely sips. That is why parallel current divides inversely with resistance.
Combination circuits
Real circuits usually mix both arrangements. The trick is to reduce them in stages: collapse each parallel group into one equivalent resistor, then add up everything that is now in series.
Work from the inside out, one block at a time, until a single resistance remains. For longer multi-step examples, the open-access University Physics chapter on resistors in series and parallel is a thorough reference. The diagram below shows the idea on a simple three-resistor network.
Figure 2: Reduce the parallel pair first, then add the series resistor — a single 6 Ω equivalent remains.
Series vs Parallel Circuits: 7 Key Differences
The table below sums up everything that changes when you switch a circuit from series to parallel. Master these seven contrasts and you can predict how almost any simple circuit will behave.
| Feature | Series circuit | Parallel circuit |
|---|---|---|
| Current paths | One single loop | Two or more branches |
| Current | Same through every component | Splits between branches (I = I₁ + I₂ + …) |
| Voltage | Divides across components (V = V₁ + V₂ + …) | Same full voltage across each branch |
| Total resistance | Adds up: R₁ + R₂ + … | Reciprocal sum; less than the smallest resistor |
| Adding a resistor | Total resistance rises | Total resistance falls |
| If one component fails (open) | Whole circuit stops | Other branches keep working |
| Common uses | Voltage dividers, current-limiting, older fairy lights | Mains/house wiring, appliances, car electrics |
Real-World Examples of Series and Parallel Circuits
These arrangements are not textbook abstractions — you are surrounded by both right now. Here are five places the choice shows up.
1. Household wiring (parallel)
Every socket and light in your home sits in parallel across the mains. That is why each one gets the same voltage — about 230 V in the UK and Europe, 120 V in North America — and why switching off the kettle never dims the lamps.
2. Fairy lights and the classic “one out, all out” (series)
Older string lights wired their bulbs in series. Lovely when they worked, maddening when they did not — a single broken filament opened the loop and killed the whole strand.
Modern LED strings dodge this with tiny shunts or parallel sections, so one dead lamp no longer drags the rest down with it.
3. Car headlights and electronics (parallel)
A car wires its lamps and modules in parallel, so one can fail without blacking out the others and each still receives the full 12 V from the battery.
4. Battery packs (series and parallel)
Stack cells in series and their voltages add — four 1.5 V AA cells in a row give 6 V. Wire identical cells in parallel instead and the voltage stays put while the pack delivers more current for longer.
5. Voltage dividers (series)
Two resistors in series split a voltage in a fixed ratio. This humble series trick sets reference voltages, scales sensor signals, and sits inside countless volume knobs and dimmers.
Common Misconceptions About Series and Parallel Circuits
A few sticky beliefs trip up almost everyone learning this topic. Clear these and the rest clicks into place.
“Current gets used up as it flows”
It does not. Charge is conserved — the current returning to the battery equals the current that left it. What the components consume is energy, not current. In series, the same amperage flows at every point in the loop.
“Adding resistors always increases resistance”
True for series, false for parallel. Each parallel resistor opens a fresh path, so the total resistance drops below the smallest branch. More routes mean less overall opposition.
“Every branch in a parallel circuit carries the same current”
It is the voltage that is shared in parallel, not the current. Branch currents depend on resistance — the smaller the resistance, the larger its share.
“A bigger resistor always means a bigger voltage drop”
Only when components share the same current, which is the series case. In parallel, every branch already sits at the same voltage, so a bigger resistor just means a smaller current, not a bigger drop.
How Series and Parallel Circuits Relate to Charge and Energy
Every result on this page is Ohm’s law wearing different clothes. Get fluent with that one relationship and the series and parallel rules stop being something to memorise — you can derive them on the spot.
Underneath the current, what actually moves is electric charge. The same electrostatic forces captured by Coulomb’s law are what nudge electrons through each resistor, whichever way the circuit is wired.
Resistors destroy nothing — they convert electrical energy into heat and light. The rate of that conversion is power, which is simply the work done by the battery each second as it drives charge around the loop.
Worked Problems
Eight problems, building from a single addition to a reverse calculation. Try each before reading the solution — and watch the units the whole way through.
