Series vs parallel circuits: rules and calculations
By Engr. Mehmood Kakar · Updated
Quick answer
In series, the current is the same everywhere and the potential difference is shared; in parallel, the potential difference is the same across each branch and the current is shared. Series resistances add up (R = R₁ + R₂). Adding a resistor in parallel always makes the total resistance smaller than the smallest single resistor.
The rules side by side
| Series | Parallel | |
|---|---|---|
| Current | Same at every point: I = I₁ = I₂ | Splits between branches: I = I₁ + I₂ |
| Potential difference | Shared: V = V₁ + V₂ | Same across each branch: V = V₁ = V₂ |
| Total resistance | Adds up: R = R₁ + R₂ | Less than the smallest single resistor |
| One lamp breaks | All go off | The others stay on |
Every calculation below uses these rules plus V = I × R, applied either to the whole circuit or to one component at a time.
Series circuits
In series, find the total resistance first, then the current, then the pd across each resistor.
A 4 Ω resistor and an 8 Ω resistor are in series with a 6.0 V battery. Find the current and the pd across each resistor.
- Total resistance: R = 4 + 8 = 12 Ω
- Current: I = V ÷ R = 6.0 ÷ 12 = 0.50 A (the same through both)
- pd across 4 Ω: V₁ = I × R₁ = 0.50 × 4 = 2.0 V
- pd across 8 Ω: V₂ = I × R₂ = 0.50 × 8 = 4.0 V
- I = 0.50 A; V₁ = 2.0 V, V₂ = 4.0 V (check: 2.0 + 4.0 = 6.0 V)
The bigger resistor gets the bigger share of the pd. That check, adding the pds back up to the supply, catches most slips.
Parallel circuits
In parallel, each branch has the full supply pd, so work out each branch on its own and then add the currents.
A 4 Ω resistor and a 12 Ω resistor are in parallel with a 6.0 V battery. Find each branch current, the total current and the total resistance.
- Branch 1: I₁ = V ÷ R₁ = 6.0 ÷ 4 = 1.5 A
- Branch 2: I₂ = V ÷ R₂ = 6.0 ÷ 12 = 0.50 A
- Total current: I = 1.5 + 0.50 = 2.0 A
- Total resistance: R = V ÷ I = 6.0 ÷ 2.0
- R = 3.0 Ω, which is less than 4 Ω, the smallest resistor
Courses that use the reciprocal equation give the same answer: 1/R = 1/4 + 1/12 = 4/12, so R = 3 Ω. The parallel resistance calculator shows that working step by step.
Why parallel lowers resistance
Adding a branch gives the charge another path. The pd across the old branches doesn’t change, so they carry the same current as before, and the new branch carries extra current on top. More total current from the same pd means a smaller total resistance (R = V ÷ I). In an exam, say both parts: another path for the current, and the total current increases for the same pd.
Why homes are wired in parallel
- Every appliance gets the full mains pd of 230 V.
- Each one can be switched on and off on its own.
- If one appliance fails, the others keep working.
Common mistakes
- Sharing the pd in parallel. Each branch gets the whole supply pd, not a share of it.
- Adding parallel resistances. 4 Ω and 12 Ω in parallel is 3 Ω, not 16 Ω.
- Using the total pd for one series resistor. In series, use that resistor’s own pd with V = IR, or the total pd with the total resistance.
- Forgetting units. Convert mA to A and kΩ to Ω before using V = IR.
Practice
1. Three resistors of 2 Ω, 3 Ω and 5 Ω are in series with a 12 V supply. Find the current.
R = 2 + 3 + 5 = 10 Ω → I = V ÷ R = 12 ÷ 10 → I = 1.2 A
2. Two lamps are in parallel with a 9.0 V battery. One takes 0.30 A and the other 0.45 A. What is the current from the battery, and the pd across each lamp?
I = 0.30 + 0.45 = 0.75 A; each lamp has the full 9.0 V across it.
3. A 10 Ω and a 15 Ω resistor are in series with a 5.0 V supply. Find the pd across the 15 Ω resistor.
R = 25 Ω → I = 5.0 ÷ 25 = 0.20 A → V = I × R = 0.20 × 15 → V = 3.0 V
4. A third resistor is added in parallel to a circuit. What happens to the total resistance and the total current?
The total resistance decreases and the total current from the supply increases, because there is another path for the current and the pd across each branch is unchanged.
Frequently asked questions
What is the difference between series and parallel circuits?
A series circuit has one loop, so the same current passes through every component and the potential difference of the supply is shared between them. A parallel circuit has two or more branches; each branch gets the full potential difference and the current splits between the branches.
Is current the same in a parallel circuit?
No. The current splits at a junction and the branch currents add up to the total current. The branch with the lower resistance takes the larger current.
Do I need 1/R = 1/R₁ + 1/R₂ for AQA GCSE?
No. AQA GCSE Physics asks you to explain why adding resistors in parallel lowers the total resistance, not to calculate it with that equation. You can still find the total resistance of a parallel circuit from the supply pd and total current using R = V ÷ I. The reciprocal equation is used in A-level and some other courses.
Why does adding resistors in series increase resistance?
The charge has to pass through every resistor one after another, so each one adds its resistance to the total: R = R₁ + R₂ + R₃.
Written by Engr. Mehmood Kakar
Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)
Checked against the AQA GCSE Physics (8463) specification on 15 November 2026.