Resistors in series and parallel

Series vs parallel: the rules

These are the rules in AQA's GCSE Physics specification. In AQA's words, a series circuit has the same current through each component, while in a parallel circuit the branch currents add up to give the total.

Resistors in series

In series, the current has to pass through every resistor in turn, so their resistances simply add:

Why adding resistors in series increases resistance: the charge has to get through more obstacles one after another, so for the same supply pd, less current flows.

Example 1: a series circuit

A 4 Ω and a 6 Ω resistor are in series with a 12 V supply.

1. Total resistance: 4 + 6 = 10 Ω.
2. Current, the same everywhere: I = V ÷ R = 12 ÷ 10 = 1.2 A.
3. Pd across each: 1.2 × 4 = 4.8 V and 1.2 × 6 = 7.2 V. Check: 4.8 + 7.2 = 12 V, the supply.

The bigger resistor takes the bigger share of the pd, in proportion to its resistance.

Resistors in parallel

In parallel, each resistor gives the current another route, so the circuit lets more current through overall.

Why adding resistors in parallel decreases resistance: each extra branch is an extra path for charge, so more current flows from the same supply pd. That is why the total resistance of two resistors in parallel is less than the resistance of the smaller one.

How to calculate resistance in parallel

For exactly two resistors, this rearranges to a shortcut, product over sum:

At GCSE, AQA says you aren't required to calculate the total resistance of two resistors in parallel, but you need to know it is less than the smallest one and explain why. At A-level, the AQA specification includes the formula for resistors in parallel, so you do calculate it.

Example 2: two resistors in parallel

The same 4 Ω and 6 Ω resistors are now in parallel across 12 V.

1. Each branch gets the full 12 V.
2. Branch currents: 12 ÷ 4 = 3 A and 12 ÷ 6 = 2 A.
3. Total current: 3 + 2 = 5 A.
4. Total resistance: 12 ÷ 5 = 2.4 Ω. The formula agrees: 4 × 6 ÷ (4 + 6) = 24 ÷ 10 = 2.4 Ω, less than 4 Ω.

Compare the two examples: the same two resistors give 10 Ω in series but 2.4 Ω in parallel, and the supply delivers 1.2 A or 5 A.

Quick rules for parallel resistors

• Two equal resistors in parallel give half the resistance of one: two 10 Ω resistors make 5 Ω.
• n equal resistors in parallel give R ÷ n.
• Three or more: add the reciprocals. For 2 Ω, 3 Ω and 6 Ω: 1/2 + 1/3 + 1/6 = 1, so the total is 1 Ω.
• Check your answer is smaller than the smallest resistor. If it isn't, something has gone wrong.

Try calculating a total resistance yourself, then press Mark to check it in our Circuits course.

Circuits with series and parallel parts

Work from the inside out: replace each parallel group with its total, then add the series parts.

Example 3: a combined circuit (A-level)

A 2 Ω resistor is in series with a parallel pair of 6 Ω and 3 Ω, across a 9 V supply. Find the current from the supply.

1. Parallel pair: 6 × 3 ÷ (6 + 3) = 18 ÷ 9 = 2 Ω.
2. Total resistance: 2 + 2 = 4 Ω.
3. Supply current: 9 ÷ 4 = 2.25 A.
4. The 2 Ω resistor and the parallel pair (2 Ω in total) share the 9 V equally, so the pair has 4.5 V across it: 0.75 A through the 6 Ω and 1.5 A through the 3 Ω.

Why homes are wired in parallel

Every socket and light in a house is connected in parallel. Each appliance gets the full mains pd, about 230 V in the UK, and each can be switched on or off without affecting the others. If homes were wired in series, every appliance would share the pd, and turning one off would turn them all off, like an old string of fairy lights where one dead bulb blacks out the lot.

Measuring current and pd

• Ammeter: connect in series, in the branch you want to measure.
• Voltmeter: connect in parallel, across the component.

In AQA's resistance required practical, you investigate how the total resistance changes when resistors are combined in series and in parallel. You can build these circuits and watch the meters in the Circuit Builder. Our guides to potential difference and variable resistors go further.

Common mistakes

• Adding resistances in parallel. That's the series rule. In parallel the total is smaller than any one resistor.
• Forgetting the final step of 1/R: after adding the reciprocals, flip the answer.
• Thinking current is used up along a series circuit. It is the same all the way round. Energy is transferred, not current.
• Thinking pd is shared in parallel. Each branch has the full supply pd. Current is what splits.
• Using the product-over-sum shortcut for three resistors. It only works for two at a time.

Read next

Physics · Electricity and magnetismParallel resistor calculator: total resistance and currentFind the total resistance of resistors in parallel, the current in each branch and the supply current, with the formula and examples to check.