The big idea: V = I × R and P = V × I.
Rearranged: I = V ÷ R, R = V ÷ I, V = P ÷ I, I = P ÷ V. Between them these cover almost every calculation in the topic — and every one of them needs the values in base units first.
The quantities, the two relationships and the multiplier ladder that unit errors come from.
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Four steps that stop the usual errors
Write the formula first
Before substituting anything. Quoting the formula is usually a mark, and it stops you dividing when you meant to multiply.
Convert to base units
Milliamps into amps, kilohms into ohms, microfarads into farads. This one step prevents almost every factor-of-a-thousand error.
Substitute and solve
Keep the units attached as you go, so an answer in the wrong unit shows itself.
Say what the number means
0.14 W means a quarter-watt resistor is comfortable. 20 mA means a chip pin can drive it. A number with no conclusion is half an answer.
A worked LED calculation: An LED needs 20 mA at 2 V from a 9 V supply.
Resistor voltage = 9 − 2 = 7 V. R = V ÷ I = 7 ÷ 0.020 = 350 Ω — note the current in AMPS. Power = V × I = 7 × 0.020 = 0.14 W, so a quarter-watt part is fine. Specify 390 Ω, the nearest standard value ABOVE, because rounding up protects the LED.
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| Calculation | The design decision it settles |
|---|---|
| Current through a load | Whether a chip pin can drive it directly, or whether it needs a transistor or a relay |
| Power in a component | The physical size of the resistor, whether a heatsink is needed, and how hot the product gets |
| Total current drawn | The rating of the power supply, the size of the battery, and how long it lasts |
| Voltage at a divider junction | Whether a sensor's signal reaches the threshold the next stage needs |
Battery life is a current calculation: A cell rated at 2,000 mAh supplies 2,000 mA for one hour, or 20 mA for 100 hours.
So a product drawing 20 mA continuously lasts about four days, and one that sleeps at 20 µA between events lasts years — which is the whole argument for a sleep mode, written as arithmetic.
How this is tested — calculating power, voltage, current and resistance by rearranging V = IR and P = VI. It comes up two ways:
Paper 1 — multiple choice
- Calculate a current, voltage, resistance or power.
- Convert a value between SI multipliers.
Paper 2 — analysing a product
- Specify a component from a calculation.
- Calculate a product's current draw and battery life.
The trap: Leaving the current in milliamps. Convert to amps before dividing, and the factor-of-a-thousand error disappears.
A battery product runs a 60 mA display for 2 hours a day and draws 150 µA the rest of the time. Apply the equations to find the daily charge used and the life of a 1,200 mAh cell.
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