Series Circuits
Three rules govern current, pd, and resistance. Memorise them and most series-circuit questions become routine.
SPEC 8463 • MODULE 2 • LESSON 2.05
What Is A Series Circuit?
The defining feature of a series circuit is simple: only one loop. Current has only one path round the circuit — through every component, in order, and back to the cell.
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A series circuit — single loop, single current path
Series Circuit
A circuit where components are connected end-to-end in a single loop, so the same current flows through each component.
Rule 1 — Current Is The Same Everywhere
The first rule follows directly from "one loop, one path".
RULE 1
The current is the same at every point in a series circuit.
Why? Charge Has Nowhere Else To Go
Current is the rate at which charge flows. In a series circuit, charge enters the loop, passes through every component in turn, and returns to the cell. There's no junction where charge can split. So whatever current flows through one component must flow through every other component — and through the cell — at the same rate.
Practical Consequence
It doesn't matter where you put the ammeter in a series circuit — before or after a resistor, near the cell or near the switch — the reading is the same. The ammeter measures the current of the loop, which is constant everywhere in that loop.
Rule 3 — Total Resistance Is The Sum
RULE 3 — RECALL EQUATION
The total resistance of components in series is the sum of the individual resistances.
R_total = R₁ + R₂
resistance, R, in ohms (Ω)
The spec gives this for two resistors. For three or more, just keep adding: R_total = R₁ + R₂ + R₃ + ... It's on the recall list.
Why? Each Resistor Adds More Opposition
Think of the resistors as obstacles in a single-lane corridor. The first slows the charge, then the second adds more opposition, then the third. There's no shortcut — every charge has to push through every resistor. So the total resistance is whatever the cell "sees" looking into the loop, which is the sum of all individual resistances.
Practical Consequence
Adding more resistors in series increases the total resistance. By V = I R applied to the whole circuit, this decreases the current. Same cell, more resistors → smaller current.
The Three Rules Together
This is what every series-circuit question tests. Memorise this trio.
RULE 1
Current is the same at every point.
I = I₁ = I₂ = ...
RULE 2
PD shares between components.
V_total = V₁ + V₂ + ...
RULE 3
Resistance adds up.
R_total = R₁ + R₂ + ...
The Standard Calculation Routine
Most series-circuit problems follow the same sequence:
1. Add resistances to get R_total.
2. Apply V = I R to the whole circuit to find the current.
3. Use V = I R for each individual resistor to find the pd across it (current is the same through all of them).
Worked Example — Finding The Current
"Three resistors of 5.0 Ω, 10 Ω and 15 Ω are connected in series with a 12 V battery. Calculate the current in the circuit."3 MARKS
E1
First equation: Total resistance — R_total = R₁ + R₂ + R₃
S1
Substitute: R_total = 5.0 + 10 + 15 = 30 Ω
E2
Second equation: V = I × R, rearranged → I = V / R_total
S2
Substitute: I = 12 / 30
U
Unit: amperes (A)
A
Answer: I = 0.40 A
⚠️
Common slip: jumping straight to I = V/R without summing first. Some students do "12 / 5.0 = 2.4 A" using just one resistor — wrong. Always sum the series resistances first.
Worked Example — Finding Each PD
Same circuit as Example 1 — same three resistors, same 12 V battery. Now: "Calculate the pd across each resistor."4 MARKS
Setup
Current is the same throughout: I = 0.40 A (from Example 1).
V₁
Across 5.0 Ω: V₁ = I × R₁ = 0.40 × 5.0 = 2.0 V
V₂
Across 10 Ω: V₂ = I × R₂ = 0.40 × 10 = 4.0 V
V₃
Across 15 Ω: V₃ = I × R₃ = 0.40 × 15 = 6.0 V
✓
Sanity check: V₁ + V₂ + V₃ = 2.0 + 4.0 + 6.0 = 12 V — matches the supply pd. ✓
Notice also: the bigger the resistance, the bigger the pd (15 Ω → 6 V is the largest share).
Cells in Series — Same Direction
Multiple cells in series follow the same pd-summing rule. When their + terminals all face the same way, their pds add up.
Two 1.5 V cells in series, same direction → 3.0 V total
Why It Works
Each cell adds its energy-per-coulomb contribution as the charge passes through. Two 1.5 V cells in the same direction give every coulomb of charge 1.5 J + 1.5 J = 3.0 J of energy as it goes through them — which is what 3.0 V means.
Cells In Series — Facing Each Other
If cells face opposite directions, their pds partially cancel. With equal cells facing each other, the net pd is zero.
Two 1.5 V cells facing opposite ways → 0 V net pd
Why It Cancels
Each cell tries to push current in its own direction. If they push against each other equally, neither wins — the net energy delivered to the circuit per coulomb is zero, so the net pd is zero, and no current flows.
Real-Life Consequence
This is exactly what happens when someone puts a battery in a torch the wrong way round — the cells fight each other and the bulb doesn't light. If the cells aren't equal, you get a partial cancellation: e.g. a 3.0 V cell opposed by a 1.5 V cell gives a net 1.5 V (in the direction of the bigger cell).
The Slip That Loses Marks
The single most common error in series-circuit calculations: forgetting to sum the resistances first.
✗ Loses 3 marks
Three resistors 5.0 Ω, 10 Ω, 15 Ω with 12 V cell. Find I.
I = V / R
I = 12 / 5.0
I = 2.4 A
Substituted just one resistor's R instead of the total. Answer wrong by a factor of 6.
✓ Full marks
Same circuit.
R_total = 5.0 + 10 + 15 = 30 Ω
I = V / R_total
I = 12 / 30
I = 0.40 A
Total resistance line first, then V = IR with the right R.
The Habit That Saves The Mark
For any series-circuit calculation, write "R_total = ..." as the first line of working. Even if the calculation has only two resistors and looks "obvious", the explicit total-resistance line shows the examiner you've applied Rule 3 — and protects against substituting the wrong R later.
Common Errors
Students often writeCorrect versionWhy it matters
"Current divides between resistors"Current is the same at every point in seriesConfuses with parallel
"PD stays the same across each resistor"PD shares in proportion to resistanceWrong rule — that's parallel
I = V / R using only one resistor's RSum series resistances first → R_total → then I = V / R_totalWrong total current
"R_total is some kind of average"R_total is the sum of all series resistancesSpec recall is "sum"
Adding pds across resistors that aren't all the resistors in the loopV_total covers every component in the loopDrops marks for incomplete answers
Treating cells facing each other as if they addOpposed cells (partially) cancel; same-direction cells addStandard cell-arithmetic error
Practice Question
Two resistors, 3.0 Ω and 6.0 Ω, are connected in series with a 9.0 V battery.
(a) Calculate the current in the circuit.
(b) Calculate the potential difference across each resistor. 4 MARKS
a-1
R_total: R_total = R₁ + R₂ = 3.0 + 6.0 = 9.0 Ω
a-2
Current: I = V / R_total = 9.0 / 9.0 = 1.0 A
b-1
Across 3.0 Ω: V₁ = I × R₁ = 1.0 × 3.0 = 3.0 V
b-2
Across 6.0 Ω: V₂ = I × R₂ = 1.0 × 6.0 = 6.0 V
✓
Check: V₁ + V₂ = 3.0 + 6.0 = 9.0 V — equals the supply pd, as Rule 2 requires. ✓
Notice the bigger resistor (6.0 Ω) gets the bigger share of the pd (6.0 V) — twice the resistance, twice the pd, exactly as expected.
Three Things to Remember
1. The Three Rules — Memorise Them
Rule 1: Current is the same at every point in series. Rule 2: PDs add up to give the supply pd. Rule 3: Resistances add up. These three are the spec wording — match them word-for-word in recall questions.
2. Always Sum The Resistances First
The single biggest slip in series-circuit calculations is using V = I R with one resistor's R instead of the total. Write "R_total = R₁ + R₂ + ..." as line 1 of every series-circuit calculation, before applying V = IR.
3. PDs Always Add Up To The Supply PD
Every series-circuit answer has a built-in sanity check: add up all the individual pds. The total should equal the supply pd. If it doesn't, somewhere your calculation has gone wrong.
Summary
The Three Series Rules (Spec 4.2.2)
Current is the same through every component · I = I₁ = I₂ = ...
Total pd of supply is shared between components · V_total = V₁ + V₂ + ...
Total resistance = sum of individual resistances · R_total = R₁ + R₂ + ... (recall equation)
The Standard Calculation Routine
Sum resistances → R_total
Apply V = I R_total → I (the same current everywhere)
Use V = I × Rᵢ for each component → pd across each
Sanity check: pds should add to supply pd ✓
Cells In Series
Same direction → pds add: 1.5 V + 1.5 V = 3.0 V
Opposed → pds (partially) cancel: equal cells facing each other → 0 V net
Worked Example Headlines
5.0 Ω + 10 Ω + 15 Ω in series with 12 V → R_total = 30 Ω, I = 0.40 A
PDs across each: 2.0 V, 4.0 V, 6.0 V (sum = 12 V ✓)
Checkpoint
You should now be able to:
✅ State the three series rules — same current, pds add up, resistances add up — using the spec's exact wording.
✅ Calculate the total resistance of any number of resistors in series, using R_total = R₁ + R₂ + ...
✅ Find the current in a series circuit using V = I R_total, and the pd across each component using V = I × R individual.
✅ Combine cells in series — adding pds for same-direction cells, recognising partial or full cancellation for opposed cells.
✅ Avoid the classic slip — always sum the resistances before applying V = I R.
Next Lesson
2.06 — Parallel circuits. Three different rules — almost the opposite of series in some ways. Pd is the same across each branch (not divided); currents add up (instead of being the same); and total resistance is less than the smallest individual resistor (instead of being the sum). Confusing series with parallel is one of the most common errors in this topic — we'll cover the contrasts directly.
Next: What Is A Series Circuit?