Power
Two equations, one definition, one unit. Examined every series. The marks live in the unit conversions — minutes to seconds, milliwatts to watts. Get those right and this is one of the cleanest topics in Paper 1.
SPEC 4.1.1.4 • ENERGY — POWER
Two Equations, One Habit
Power is one of the most reliably-examined topics in Paper 1. The physics is short — the marks come from unit discipline: convert minutes to seconds, convert mW or kW to W, then substitute. Get the units right and the calc is almost always a one-line answer.
2
Equations
1
Unit (the watt)
⭐
High-Priority Topic
By the end of this lesson
You'll define power, apply P = E/t and P = W/t, convert between mW, W, kW, MW and GW with confidence, chain a work-against-gravity calc into a power calc, and avoid the mW-conversion trap that examiners flagged as the #1 mistake on Jun 2024 Q5.2.
What Is Power?
Power isn't how much energy moves — it's how fast it moves. A 60 W bulb and a 60 J battery sound similar but mean very different things: the battery stores 60 J; the bulb transfers 60 J every second.
Power
Power is defined as the rate at which energy is transferred — or equivalently, the rate at which work is done.
Both definitions describe the same thing: how fast energy is moving between stores.
Energy vs work
"Energy transferred" and "work done" describe the same physics — energy moving from one store to another. Engineers usually say "work" for mechanical situations (lifting, pushing); we usually say "energy" for electrical and thermal situations. AQA uses both, and the equation works the same either way.
Spec example — two motors
Two electric motors lift the same weight through the same height. Motor A takes 5 seconds; Motor B takes 10 seconds. They've transferred the same amount of energy, but Motor A has twice the power because it did the work in half the time. This is the AQA-recommended example for illustrating the definition of power.
Two Equations
Two formulas — same physics, different symbols. Use whichever symbol the question uses (E for energy, W for work).
P = E / t
Energy form
P = W / t
Work form
Units (same for both)
P = power in watts (W)
E = energy transferred in joules (J)
W = work done in joules (J)
t = time in seconds (s)
Equation sheet
Both equations are on the AQA equation sheet (provided in the exam since June 2022). You still need to recognise them, choose between them, and apply them with correct units.
Rearranging
The same equation can be rearranged depending on what you're given:
Find power from energy and time: P = E / t
Find energy from power and time: E = P × t (this form is also on the equation sheet, formally as E = P t in Lesson 2.09)
Find time from energy and power: t = E / P
The Watt
The unit of power. Named after James Watt, who improved the steam engine. The definition is simple — and worth memorising in this exact form:
Definition
1 W = 1 J/s
"One watt equals one joule per second."
What this means
A 60 W bulb transfers 60 joules every second.
A 2 kW (2000 W) kettle transfers 2000 joules every second.
A 1 GW power station transfers 10⁹ joules every second.
Sanity check
Whenever you finish a power calculation, ask: "is this number plausible?" A typical bulb is around 10–60 W. A typical kettle is around 2 kW. A car engine at full throttle is around 100 kW. If your answer is 0.000003 W or 5 GW, recheck the unit conversions.
Power Prefixes
Power values span a huge range — from microwatts (a wristwatch) to gigawatts (a power station). Always convert to watts (W) before substituting into either equation.
PrefixSymbolConversion to WExample
milli-mW÷ 1000 (or × 10⁻³)LED indicator: 0.5 mW = 0.0005 W
(none)WSI unit (no conversion)Light bulb: 60 W
kilo-kW× 1000 (or × 10³)Electric kettle: 2.5 kW = 2500 W
mega-MW× 10⁶ (× 1 000 000)Wind turbine: 3 MW = 3 000 000 W
giga-GW× 10⁹Power station: 2 GW = 2 × 10⁹ W
The rule
Each step up the ladder is ×1000. Each step down is ÷1000. Convert before substituting into the equation, never after.
Power at a Glance
The same scale shown visually. Use this to sanity-check any calculation you do.
Which Equation Do I Use?
Both equations are mathematically identical (energy and work are both measured in joules). The choice is just about matching the symbols the question uses.
Use P = E / t when
The question mentions energy transferred, or "energy used", or gives a value in joules (J) or kilojoules (kJ).
Examples: heating, electrical appliances, energy from a battery.
Use P = W / t when
The question mentions work done — typically a force moving an object (a motor lifting a load, a person pushing a trolley).
Examples: motors, cranes, escalators.
When you need work done from gravity
If the question describes lifting an object against gravity, the work done by the lifter equals the GPE gained by the object. Both equal m × g × h. So you can use the GPE equation from Lesson 1.02 to find the work, then divide by t to get power. This is the most common chained calculation in this topic.
Worked Example — Simple Power
A microwave oven transfers 240 000 J of energy in 4.0 minutes. Calculate its power. 3 marks
EEquation:P = E / t
SSubstitute:Convert t = 4.0 min = 4.0 × 60 = 240 s. P = 240 000 / 240
UUnit: watts (W)
AAnswer:P = 1000 W = 1.0 kW
The conversion line earns marks
Writing "t = 4.0 min = 240 s" on its own line is the habit that defends against the time-conversion trap. Mark schemes typically award one of three marks for showing this conversion explicitly.
Worked Example — Chained Calc
An electric motor lifts a 200 kg load through 5.0 m in 8.0 s. Calculate the useful power output. Take g = 9.8 N/kg. 4 marks
E1Work done:W = m g h
S1Substitute:W = 200 × 9.8 × 5.0 = 9800 J
E2Power:P = W / t
S2Substitute:P = 9800 / 8.0
UUnit: watts (W)
AAnswer:P = 1225 W ≈ 1.2 kW (2 s.f.)
Why "useful" power
The motor itself uses more electrical energy than 9800 J because some is dissipated as heat. The 1225 W is the useful output — the rate at which work is done on the load. We'll meet efficiency formally in Lesson 1.06.
The Time Conversion Trap
Time must be in seconds for any power calculation. Minutes, hours, milliseconds — all need converting first. The mistake is to substitute the number directly without converting.
✗ Wrong substitution
"Motor lifts 200 kg through 5 m in 2 minutes."
P = 9800 / 2
= 4900 W
Used 2 (minutes) directly. Answer is 60× too big.
✓ Convert first
"Motor lifts 200 kg through 5 m in 2 minutes."
t = 2 min = 120 s
P = 9800 / 120
≈ 82 W
Conversion on its own line. Answer is realistic.
Quick-reference conversions
1 minute = 60 s · 1 hour = 3600 s · 1 millisecond (ms) = 0.001 s. Always do this conversion before dividing.
The Prefix Conversion Trap
The same trap, but for the power value itself. mW, kW, MW — none of these go straight into the equation. Convert to W first.
✗ Wrong substitution
"A 250 mW LED is on for 60 s. Energy?"
E = P × t
= 250 × 60
= 15 000 J
Used 250 (mW) directly. Answer is 1000× too big.
✓ Convert first
"A 250 mW LED is on for 60 s. Energy?"
P = 250 mW = 0.25 W
E = 0.25 × 60
= 15 J
Conversion on its own line. Realistic for a small LED.
The two-trap defence
Show both conversions on separate lines: "P = X mW = X/1000 W" and "t = X min = X×60 s". Two lines of working can earn two marks even before you've started dividing.
Examiner Alert
Jun 2024 P1H Q5.2 — milliwatt conversion
Q5.2 was a Grade 6–7 resistance calculation (using the electrical-power equations from Lesson 2.08), but the calc gave power in milliwatts. Many students substituted the mW value directly without converting and lost marks. The same unit-conversion habit applies to any power calculation — including the P = E/t and P = W/t equations in this lesson.
The conversion of milliwatts to watts proved a problem for the vast majority of students. 53% scored all 4 marks, while 36% scored 3 marks. — AQA P1H Jun 2024 Q5.2 examiner report
The three-topic pattern
Unit conversion failure is the most consistent error pattern in this whole module:
1.02 — cm → m for EPE (every series)
1.03 — kJ → J for SHC (Jun 2024 Q8.3)
1.04 — mW → W for power (Jun 2024 Q5.2)
One habit fixes all three: convert on a separate line, before substituting.
Common Errors That Cost Marks
Students often writeCorrect version
Time substituted in minutesConvert to seconds first: t (in min) × 60
Power substituted in mW or kWConvert to W first: mW ÷ 1000, kW × 1000
"Power = energy"Power = energy ÷ time — power is a rate, not an amount
P = m × g × h (skipping time)m × g × h gives energy in joules ; divide by t to get power
Using P = W/t when only E is givenUse P = E/t — same result, but matches the question's symbols
Final answer without unit (e.g. "1225")"P = 1225 W" or "1.2 kW" — number AND unit
Final answer to too many sig figsRound to the s.f. of the input data — usually 2 or 3 s.f.
Practice Question
An athlete of mass 60 kg climbs a flight of stairs that rises 3.0 m vertically in 2.0 s.
Calculate the useful power output. Take g = 9.8 N/kg. 4 marks
E1
Work done against gravity: W = m g h
S1
W = 60 × 9.8 × 3.0 = 1764 J
E2
Power: P = W / t
S2
P = 1764 / 2.0 = 882 W
A
P ≈ 880 W (to 2 s.f.) — about 0.88 kW
Checkpoint
✅ You can now
Define power as the rate at which energy is transferred or work is done.
State and apply P = E/t and P = W/t , choosing the right form from question wording.
Recall that 1 W = 1 J/s .
Convert between mW, W, kW, MW and GW using the ×1000 ladder.
Convert minutes / hours → seconds on a separate working line.
Chain a W = mgh calc with P = W/t for grade-7+ multi-step problems.
Avoid the mW-conversion trap documented in Jun 2024 Q5.2.
Coming Next
Lesson 1.05 — Energy transfers in a system & RP2. The conservation principle, the difference between useful and wasted (dissipated) energy transfers, and the second required practical: thermal insulation.
Summary
Power — One Concept, Two Equations
P = E / t or P = W / t
P in W · E or W in J · t in s
1 W = 1 J/s . The watt is the SI unit of power.
Both equations on the equation sheet (since June 2022).
Energy and work are interchangeable — same physics, different symbols.
Habits that earn marks
Time → seconds on a separate line
Power → watts on a separate line
Show the substitution clearly
Include the unit on the final answer
Sanity-check against the power scale
Errors that lose marks
Time in minutes substituted directly
Power in mW or kW substituted directly
Skipping ÷ time (using mgh as power)
Final answer without unit
Exam Tip
For chained calcs (W = mgh then P = W/t), show every line. The mark scheme awards each step separately, and an arithmetic slip in step 1 doesn't kill step 2 if your working is visible (error-carried-forward).
Next: Two Equations, One Habit