When preparing for the British Physics Olympiad, knowing a circuit formula is only the first step. You also need to decide which voltage and current belong to each component. A useful starting point is to compare the same resistors in two arrangements while keeping the supply conditions explicit.
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State the model before using the formulas
Consider an ideal 6 V battery and two identical 6 Ω resistors. Ignore wire resistance and assume each resistor remains at 6 Ω. The battery maintains a constant terminal voltage. These assumptions matter: a real battery with internal resistance can behave differently.
For each resistor, Ohm's law is V = IR. Its electrical power can be written as P = VI, I²R or V²/R when the relevant voltage and current refer to that resistor. This is an original learning example, not a BPhO paper question.
Two resistors in series
The total resistance is 6 + 6 = 12 Ω. The circuit current is 6/12 = 0.5 A. The same current passes through both resistors, so the voltage across each is 0.5 × 6 = 3 V.
Each resistor dissipates 3 × 0.5 = 1.5 W. Together they dissipate 3 W, matching the battery's output power of 6 × 0.5 = 3 W. This agreement checks that the component calculations and total calculation are consistent.
Two resistors in parallel
Each resistor is connected across the 6 V supply. Each branch current is 6/6 = 1 A, so the battery supplies 2 A in total. The equivalent resistance is 6/2 = 3 Ω.
Each resistor dissipates 6 × 1 = 6 W, giving 12 W in total. This also matches 6 V × 2 A. Under the stated model, the parallel arrangement draws four times the total power of the series arrangement.
Why “larger resistance means more power” can mislead
The formula P = I²R shows that power increases with resistance if the current is fixed. The formula P = V²/R shows that power decreases with resistance if the voltage is fixed. There is no contradiction; the quantity held constant is different.
In our comparison, the ideal battery voltage is fixed and the circuit current changes. You cannot treat the series current of 0.5 A as if it still flows through each parallel branch. Always establish the new circuit conditions before comparing power.
A short circuit review checklist
- Identify which components are genuinely in series or parallel.
- Calculate the equivalent resistance before the supply current.
- Find each component's voltage and current separately.
- Check that branch currents add correctly and voltage drops are consistent.
- Compare total component power with supply power under the model.
To extend the example, replace the ideal battery with a battery that has internal resistance. Predict whether the parallel circuit still receives the full 6 V before doing any calculation. This helps you notice where an assumption, rather than an algebraic step, controls the answer.
Use BPhO's official resources for the particular competition you are preparing for, and practise writing the physical reason alongside the equation. Do not infer a whole competition's difficulty from this introductory example.
New to the subject? Read our British Physics Olympiad Preparation: A Beginner's Guide to BPhO.
Official resources
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