Science
What is the difference between series and parallel circuits?
Quick answer
In a series circuit everything is on one loop, so the current is the same everywhere and the voltage is shared. In a parallel circuit each branch gets the full voltage and the currents add up.
In one sentence
A series circuit has all its components in one single loop, while a parallel circuit splits into branches so that each component has its own path back to the power supply.
Explained
Every electric circuit needs a complete loop of conductors. There are two basic ways to connect several components in it, and they behave very differently. Three quantities describe what happens:
- Current (I), measured in amperes (A): how much charge flows past a point each second. Measure it with an ammeter connected in series.
- Voltage or potential difference (V), measured in volts (V): the "push" given to the charge, or the energy it transfers. Measure it with a voltmeter connected in parallel across the component.
- Resistance (R), measured in ohms (Ω): how hard it is for current to flow through a component.
They are linked by Ohm's law: V = I × R (so I = V ÷ R and R = V ÷ I).
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In a series circuit there is only one path, so:
- the current is the same at every point: I = I₁ = I₂;
- the supply voltage is shared between the components: V = V₁ + V₂;
- the resistances add: R = R₁ + R₂ + …;
- if one bulb breaks, the loop is broken and everything goes off; adding more bulbs makes them all dimmer.
In a parallel circuit the current splits at a junction and joins up again, so:
- each branch gets the full supply voltage: V = V₁ = V₂;
- the branch currents add up to the total: I = I₁ + I₂;
- the total resistance is found from 1/R = 1/R₁ + 1/R₂ + … and is always smaller than the smallest branch resistance. For two resistors, R = (R₁ × R₂) ÷ (R₁ + R₂);
- if one bulb breaks, the others stay on, each at full brightness. The battery then supplies less current (with every bulb working, a parallel circuit draws more current than a series one, so its battery runs down faster).
Why does adding a branch lower the total resistance? Think of a supermarket: opening another checkout does not slow anyone down, it gives shoppers an extra way through. More branches mean more paths, so more total current flows from the same voltage.
The same rules apply to batteries and solar panels. Cells in series add their voltages: two 1.5 V cells give 3 V. Identical cells in parallel keep the same voltage but can supply current for longer. That is why devices that need more voltage hold their batteries end to end. This all comes from how electricity carries energy around a loop.
Examples
| Series | Parallel | |
|---|---|---|
| Paths for current | one | two or more branches |
| Current | same everywhere | splits; branch currents add |
| Voltage | shared; V = V₁ + V₂ | same across each branch |
| Total resistance | R = R₁ + R₂ | 1/R = 1/R₁ + 1/R₂ (smaller) |
| One bulb breaks | all go off | others stay on |
| Everyday use | simple fairy lights, a torch's cells | house wiring, car headlights |
Worked example (series): a 4 Ω and a 6 Ω resistor in series on a 12 V battery. R = 4 + 6 = 10 Ω, so I = 12 ÷ 10 = 1.2 A. The voltages are 1.2 × 4 = 4.8 V and 1.2 × 6 = 7.2 V, and 4.8 + 7.2 = 12 V.
Worked example (parallel): a 6 Ω and a 3 Ω resistor in parallel on a 6 V battery. Each gets 6 V, so the currents are 6 ÷ 6 = 1 A and 6 ÷ 3 = 2 A, total 3 A. Check: 1/R = 1/6 + 1/3 = 3/6, so R = 2 Ω, and 6 ÷ 2 = 3 A.
Common mistakes
- "Current gets used up by each bulb." The current is the same all the way round a series loop. What the bulbs transfer is energy, which is why the voltage is shared.
- "Parallel resistances add up." They do not. Use 1/R = 1/R₁ + 1/R₂, and remember the answer must be smaller than the smallest resistor.
- Forgetting to flip at the end. If 1/R = 1/2, then R = 2 Ω, not 0.5 Ω.
- Putting the meters the wrong way. Ammeters go in series in the loop; voltmeters go in parallel across a component.
Step by step
Step by step
- Identify the circuitTrace the wire from the battery. One path all the way round: series. A junction where the current can split: parallel.
- Find the total resistanceSeries: add them. Parallel: use 1/R = 1/R₁ + 1/R₂. Mixed: work out each parallel group first, then add the series parts.
- Find the total currentUse I = V ÷ R with the supply voltage and the total resistance.
- Share it outSeries: same current, find each voltage with V = I × R. Parallel: same voltage, find each branch current with I = V ÷ R.
- CheckSeries voltages should add to the supply; parallel branch currents should add to the total.
Practice questions
Series and parallel calculations
Try each one, then check your answer.
- What is the total resistance of 4 Ω and 6 Ω in series?
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4 + 6 = 10 Ω - Three 1.5 V cells are joined in series. What is the total voltage?
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1.5 + 1.5 + 1.5 = 4.5 V - In a series circuit the ammeter next to the battery reads 0.5 A. What does an ammeter between the two bulbs read?
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The current is the same everywhere in series: 0.5 A - Two parallel branches carry 0.2 A and 0.3 A. What current leaves the battery?
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0.2 + 0.3 = 0.5 A - A 9 V battery powers two bulbs in series. One bulb has 3 V across it. What is the voltage across the other?
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9 − 3 = 6 V - A 6 V battery powers three bulbs in parallel. What is the voltage across each bulb?
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Each branch gets the full supply: 6 V - A 12 V battery is connected to 2 Ω and 4 Ω in series. Find the current.
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R = 6 Ω, I = 12 ÷ 6 = 2 A - In question 7, what is the voltage across the 4 Ω resistor?
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V = 2 × 4 = 8 V - What is the total resistance of two 10 Ω resistors in parallel?
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(10 × 10) ÷ (10 + 10) = 100 ÷ 20 = 5 Ω - What is the total resistance of 6 Ω and 3 Ω in parallel?
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1/R = 1/6 + 2/6 = 3/6, so R = 2 Ω - What is the total resistance of 2 Ω, 3 Ω and 6 Ω in parallel?
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1/R = 3/6 + 2/6 + 1/6 = 6/6 = 1, so R = 1 Ω - Is the total resistance of 5 Ω and 20 Ω in parallel more or less than 5 Ω? Find it.
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1/R = 4/20 + 1/20 = 5/20, so R = 4 Ω, less than 5 Ω. - A 12 V supply drives 0.4 A through 10 Ω and an unknown resistor in series. Find the unknown resistor.
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Total R = 12 ÷ 0.4 = 30 Ω, so R₂ = 30 − 10 = 20 Ω - A 6 Ω and a 12 Ω resistor in parallel are joined in series with a 4 Ω resistor on a 24 V supply. Find the total resistance and the total current.
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Parallel pair: (6 × 12) ÷ 18 = 4 Ω; total 4 + 4 = 8 Ω; I = 24 ÷ 8 = 3 A - In question 14, find the current in the 6 Ω and the 12 Ω branches.
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The 4 Ω resistor takes 3 × 4 = 12 V, leaving 12 V across the pair: 12 ÷ 6 = 2 A and 12 ÷ 12 = 1 A (2 + 1 = 3 A ✓) - Where do you connect an ammeter and a voltmeter to measure a bulb?
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Ammeter in series with the bulb; voltmeter in parallel across it.
Word problems
Circuits in real life
Try each one, then check your answer.
- A torch holds two 1.5 V cells end to end and the bulb has a resistance of 6 Ω. What current flows?
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The cells are in series: 3 V. I = 3 ÷ 6 = 0.5 A - A string of 10 identical bulbs is wired in series on a 12 V supply. What is the voltage across each bulb, and what happens if one fails?
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12 ÷ 10 = 1.2 V each; if one fails the loop breaks and all go out. - On a kitchen circuit a kettle draws 8 A and a toaster draws 4 A at the same time. What total current flows in the supply cable?
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The appliances are in parallel, so the currents add: 8 + 4 = 12 A - Why are a car's two headlights wired in parallel?
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Each gets the full battery voltage, and if one bulb fails the other still works. - Two solar panels each give 20 V and 5 A. What do you get if you connect them in series, and in parallel?
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Series: 40 V at 5 A. Parallel: 20 V at 10 A. - A phone charger supplies 5 V and 2 A. What power does it deliver? (P = V × I)
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P = 5 × 2 = 10 W
Questions people ask
What are the formulas for series and parallel circuits?
Series: I is the same, V = V₁ + V₂, R = R₁ + R₂. Parallel: V is the same, I = I₁ + I₂, 1/R = 1/R₁ + 1/R₂. In both, V = I × R for each component.
How do you identify a series or parallel circuit?
Trace the current with your finger from the battery. If it can only go one way round, it is series. If it reaches a junction and can split into branches that rejoin, those branches are in parallel.
Which is better, series or parallel?
It depends on the job. Parallel is used in homes because each appliance gets the full voltage and works on its own. Series is used where the same current must pass through everything, such as a switch or fuse controlling a device, or cells stacked to give a bigger voltage.
Why does adding resistors in parallel decrease the resistance?
Each new branch is another path for the current. With more paths, more current flows from the same voltage, which means the total resistance is lower.
What are series and parallel connections in batteries?
In series, the voltages add (four 1.5 V cells give 6 V). In parallel, identical batteries give the same voltage but last longer because they share the current.
Are bulbs brighter in series or in parallel?
In parallel. Each bulb gets the full supply voltage, whereas in series the voltage is shared, so each bulb is dimmer.
Quick quiz
Series and parallel circuits
Check what you know with 5 quick questions.
Question 1 of 5
In a series circuit, how does the current compare at different points?
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