There are two ways to wire components together, and they behave like opposites. Line them up one after another and you have a series circuit. Give them separate branches and you have a parallel circuit. The rules for how current and voltage share out — and how the resistances add up — flip completely between the two. Get these rules straight and circuit questions become almost mechanical.
📘 What you need to know
Series: current is the same everywhere; voltage is shared between components
Parallel: current is shared between branches; voltage is the same across each branch
Adding resistors in series increases total resistance; in parallel it decreases it
Series circuits
In a series circuit, the components sit in a single line, one after the other — there’s only one path for the charge to follow. Two rules fall straight out of that:
The current is the same at every point. With one path, the charge that flows through the first component must flow through every other one too — it has nowhere else to go.
The voltage is shared between the components. The cell’s total push gets divided up, with each component taking a slice depending on its resistance.
One loop, one path. The same current passes through R₁ and R₂, while the cell’s voltage splits between them.
Adding resistors in series
Because the components sit end-to-end, the charge has to fight its way through all of them in turn. Each one adds its own resistance to the total, so you simply add them up:
Total resistance in seriesRtotal = R1 + R2 + R3 + …
So adding more resistors in series always makes the total resistance bigger — you’re making the charge’s obstacle course longer.
WE 1
Three resistors of 10 Ω, 20 Ω and 30 Ω are connected in series. Calculate the total resistance.
Step 1 — series resistors just addRtotal = R1 + R2 + R3Step 2 — substituteR = 10 + 20 + 30R = 60 ΩThe total is bigger than any single resistor — that’s always true for series.
WE 2
A 12 V cell is connected in series with a 4.0 Ω and an 8.0 Ω resistor. Find the current in the circuit and the voltage across each resistor.
Step 1 — total resistanceR = 4.0 + 8.0 = 12 ΩStep 2 — current (same everywhere in series)I = V/R = 12 ÷ 12 = 1.0 AStep 3 — voltage across each (V = IR)V₁ = 1.0 × 4.0 = 4.0 V ; V₂ = 1.0 × 8.0 = 8.0 VI = 1.0 A, V₁ = 4.0 V, V₂ = 8.0 VCheck: 4.0 + 8.0 = 12 V, the full cell voltage. The bigger resistor takes the bigger share.
Here’s the intuition for why series voltage splits by resistance: the harder a component is to push through, the more of the cell’s “effort” gets used up crossing it. A big resistor is a steep hill — it eats a big chunk of voltage. A small one is a gentle slope and takes only a little. Add all the slices and you always get back the full cell voltage.
Parallel circuits
In a parallel circuit, each component gets its own branch — the charge reaches a junction and chooses a path. This flips both rules around:
The current is shared between the branches. It splits at the junction and recombines afterwards, so the total current equals the sum of the branch currents.
The voltage is the same across every branch. Each branch connects to the same two points, so each feels the full cell voltage.
Two branches, two paths. The current divides between R₁ and R₂, but both branches share the same voltage.
Adding resistors in parallel
Parallel is the tricky one, because you add the reciprocals (the “one-over” values), not the resistances themselves:
Total resistance in parallel
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
The surprising result: adding more branches in parallel lowers the total resistance. It makes sense once you see it — every new branch is another path for the charge, so overall it’s easier for current to flow. The combined resistance always ends up smaller than the smallest branch.
WE 3
A 6.0 Ω resistor and a 3.0 Ω resistor are connected in parallel. Calculate the total resistance.
Step 1 — add the reciprocals
1/R = 1/6.0 + 1/3.0
1/R = 0.1667 + 0.3333 = 0.5Step 2 — flip to get R (don’t forget this!)R = 1 ÷ 0.5R = 2.0 Ω2.0 Ω is smaller than either the 3.0 or the 6.0 — always true in parallel. And never forget to flip at the end!
WE 4
In a parallel circuit, the total current leaving the cell is 0.90 A. It splits between two branches. If one branch carries 0.30 A, what is the current in the other branch?
Step 1 — total current = sum of branch currentsItotal = I1 + I2Step 2 — rearrange for the missing branchI₂ = 0.90 − 0.30I₂ = 0.60 AThe two branches must add back up to the total. Whatever doesn’t go one way goes the other.
Why do parallel branches always share the same voltage? Because each branch is joined to the exact same two points — the two ends of the cell. It’s like several water slides all starting from the same high platform and ending in the same pool: every slide has the same drop, no matter how steep or gentle. Same two points, same voltage.
The two sets of rules, side by side
This little table is the heart of the whole topic. If you memorise one thing, memorise this:
Quantity
Series
Parallel
Current
Same everywhere
Shared between branches
Voltage
Shared between components
Same across each branch
Total resistance
R₁ + R₂ + … (increases)
1/R₁ + 1/R₂ + … (decreases)
Notice the neat symmetry: current and voltage simply swap roles. What’s “the same” in series is “shared” in parallel, and vice versa.
Series same current
voltage shares out
Parallel same voltage
current shares out
💡 Top tips
Series: current same, voltage shares. Parallel: voltage same, current shares. They swap.
Series resistance adds up — total is bigger than any one resistor.
Parallel: add reciprocals, then flip. Forgetting to flip at the end is the classic error.
Parallel total is always smaller than the smallest branch — a great sanity check.
Two equal resistors in parallel give half the resistance — a handy shortcut.
⚠ Common mistakes
Forgetting to flip 1/R back to R at the end of a parallel calculation
Adding parallel resistors directly (like series) — you must use reciprocals
Thinking current is “used up” as it goes round — in series it’s the same everywhere
Mixing up the rules: current shares in parallel, voltage shares in series
Expecting parallel total resistance to be bigger — it’s always smaller
Quick recap: In series, current is the same and voltage shares out; resistances add (R = R1 + R2…), so total resistance rises. In parallel, voltage is the same and current shares out; resistances combine as reciprocals (1/R = 1/R1 + 1/R2…), so total resistance falls below the smallest branch.
You can now work out the current, voltage and resistance anywhere in a circuit. The natural next question is: how fast is that circuit turning electrical energy into light, heat or motion? That’s power — and in the next page, Electrical Power, we’ll meet P = IV and its two handy cousins, and see why doubling the current does far more than double the heat.
Circuits still tangling you up?
Book a free meeting and we’ll untangle series and parallel together, one clear step at a time.
