Edexcel IGCSE Physics · Spec 2.8, 2.19
Complete Series-Circuit Calculations
Covers predict how current changes, Combine series resistances and Calculate current and component voltages.
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Complete Series-Circuit Calculations
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Explained
Working through a series circuit in the right order
A series circuit has one path, so the same current passes through every component. That single fact makes these calculations mechanical once you do the steps in the right order.
The order
- Add the resistances to find the total. In series, R total equals R1 plus R2.
- Find the current using the supply voltage and the total resistance: I equals V supply divided by R total.
- Find each component's potential difference using that same current: V equals I times R for each one.
- Check that the component voltages add up to the supply voltage.
Step two is the one people skip. You cannot find one component's voltage without knowing the current, and you cannot find the current without the total resistance, so the order is forced.
A worked example
A 12 V supply with a 4 ohm and an 8 ohm resistor in series.
Total resistance is 4 plus 8, which is 12 ohms. Current is 12 divided by 12, which is 1 A, and that same 1 A flows through both resistors.
Across the 4 ohm resistor: 1 times 4 gives 4 V. Across the 8 ohm resistor: 1 times 8 gives 8 V.
Check: 4 plus 8 is 12, which is the supply. The larger resistance takes the larger share of the voltage, which is the sense check to apply to every answer of this kind.
Predicting changes without calculating
Questions often ask what happens rather than how much.
Adding another component in series increases the total resistance, so at a fixed supply voltage the current falls, and every component's voltage share changes.
Increasing the supply voltage with the same resistance increases the current in proportion.
Replacing a resistor with a larger one raises the total resistance, lowers the current, and gives that resistor a larger share of the voltage while the others get less.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme asks why two components have particular voltages and credits two things: that the components are connected in series, and that the voltages must add up to the battery voltage. It accepts the arithmetic shown directly, in that case 6.0 minus 3.9 equals 2.1, and instructs the examiner to ignore the observation that the voltmeter is in parallel.
That last note is worth understanding rather than resenting. The voltmeter being in parallel is true and is the right answer to a different question. Here it explains nothing about why the voltages share.
On the calculations that follow, the mark scheme splits each into substitution, rearrangement and evaluation, and allows an error carried forward from an incorrect voltage at every stage. On one part it even allows a dimensionally correct rearrangement using the wrong voltage.
So a mistake early in a multi step question does not have to cost the later marks, provided every step is written down. The examiners are marking the method separately from the arithmetic, which is the strongest argument there is for showing the whole chain.
One further part simply says: same answer as the previous one. Recognising that a quantity has not changed is sometimes the entire mark.
Why the voltage divides the way it does
Voltage is energy transferred per unit of charge. The same charge passes through both resistors, and it gives up more of its energy in the one that opposes it more.
So the ratio of the voltages is the ratio of the resistances. Two equal resistors split the supply equally; a resistor with three times the resistance of its partner takes three quarters of the supply voltage. Spotting that can sometimes answer a question without any calculation at all.
Spec 2.8, 2.19
What you need to know
- Predict how current changes
- Combine series resistances
- Calculate current and component voltages
Active recall
Quick check
Answer each question before opening the answer.
What happens to current when series resistance increases?
It decreases for a fixed supply voltage
How are series resistances combined?
They are added
What is the current through each resistor in the example?
0.50 A
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