Power

CIE A-Level Physics· Unit 5: Work, energy and power· 15 min read

1. Definition of Power★★☆☆☆⏱ 5 min

📘 Definition

Power

$P$

Power is defined as the rate of doing work or the rate of energy transfer. The SI unit of power is the watt ( $W$ ), where 1 watt = 1 joule per second.

Example:

A 60 W light bulb transfers 60 J of electrical energy to heat and light every second.

Average power over a time interval $Δ t$ is calculated as:

P_{average} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}

📐 Worked Example

A weightlifter lifts a 100 kg barbell 2 m above the ground in 2.5 seconds. What is their average power output?

1
First calculate work done to lift the barbell: $W = m g h = 100 \times 9.81 \times 2 = 1962 J$
2
Substitute into average power formula:
3
$P = \frac{W}{\Delta t} = \frac{1962}{2.5} = 784.8 \approx 780 \text{ W}$

Exam tip:

Always check that your answer has the correct units: power is always in watts, not joules.

2. Mechanical Power for Moving Objects★★★☆☆⏱ 8 min

For a moving object with constant force applied, we can derive a simpler expression for power in terms of force and velocity.

🔬 Derivation

Goal:

Derive $P = F v$ for constant force parallel to motion

Starting from:

Starting from $P = \frac{W}{t}$ and $W = F d$

1
Substitute work into the power equation: $P = \frac{F d}{t}$
2
Since $\frac{d}{t} = v$ (constant speed), this simplifies to $P = F v$

Result:

This formula gives instantaneous power when $v$ is the instantaneous speed of the object.

📐 Worked Example

A cyclist travels at constant speed 8 m/s against a total resistive force of 30 N. What power must the cyclist produce to maintain this speed?

1
At constant speed, driving force equals resistive force, so $F = 30 N$
2
Use $P = F v$ :
3
$P = 30 \times 8 = 240 \text{ W}$

3. Electrical Power★★★☆☆⏱ 7 min

📘 Definition

Electrical Power

Rate of electrical energy transfer in a component, calculated from potential difference and current.

Base formula (always valid): $P = V I$
For ohmic components (constant $R$ ): $P = I^{2} R = \frac{V ^{2}}{R}$
Where $V$ = potential difference, $I$ = current, $R$ = resistance

📐 Worked Example

A 5 Ω resistor is connected to a 10 V battery. Calculate power dissipated in the resistor.

1
Use $P = \frac{V ^{2}}{R}$ :
2
$P = \frac{10^2}{5} = \frac{100}{5} = 20 \text{ W}$
3
Check with $P = V I$ : $I = V / R = 2 A$ , so $P = 10 \times 2 = 20 W$ , which matches.

4. Power and Efficiency★★★★☆⏱ 10 min

No real energy conversion process is 100% efficient. Some energy is always lost as heat to the surroundings, so useful output power is always less than total input power.

📘 Definition

Efficiency

$η$

Efficiency is the ratio of useful output power to total input power, expressed as a decimal or percentage.

\eta = \frac{P_{out}}{P_{in}} \times 100\%

📐 Worked Example

An electric motor has an input power of 2 kW. It lifts a 75 kg mass at a constant speed of 1.5 m/s. Calculate the efficiency of the motor.

1
Calculate useful output power: $F = m g = 75 \times 9.81 = 735.75 N$
2
Use $P_{o u t} = F v = 735.75 \times 1.5 = 1103.6 W$
3
Convert input power to watts: $P_{in} = 2 k W = 2000 W$
4
Calculate efficiency:
5
$\eta = \frac{1103.6}{2000} \times 100\% = 55.2\% \approx 55\%$

5. Common Pitfalls

Wrong move:

Confusing energy and power, using total energy instead of rate of energy transfer

Why:

Power is a rate, not a total quantity. Mixing them up leads to wrong units and wrong values.

Correct move:

Always check units first: power must be in watts (J/s), energy in joules. Divide total energy by time to get power.

Wrong move:

Forgetting to convert kW to W (or other unit prefixes) before calculation

Why:

CIE examiners regularly test unit conversion by giving power in kilowatts, leading to answers off by a factor of 1000.

Correct move:

Always convert all quantities to base SI units (watts, seconds, newtons) before starting any calculation.

Wrong move:

Using $P = F v$ when force and velocity are perpendicular

Why:

The formula $P = F v$ assumes force is parallel to motion. No work is done when force is perpendicular, so power is zero.

Correct move:

Use $P = F v cos θ$ , where $θ$ is the angle between force and velocity.

Wrong move:

Swapping input and output power in the efficiency formula

Why:

Misremembering the order of the ratio leads to efficiency greater than 100%, which is impossible.

Correct move:

Efficiency = useful output / total input, always. Output can never be larger than input.

Wrong move:

Using $P = \frac{V ^{2}}{R}$ for non-ohmic components like diodes

Why:

Resistance is not constant for non-ohmic components, so the derived formula does not hold.

Correct move:

Always use $P = V I$ for any electrical component, this formula is always valid.

6. Quick Reference Cheatsheet

Quantity	Formula	SI Units
Average Power	$P = \frac{W}{Δ t} = \frac{Δ E}{Δ t}$	watts (W = J/s)
Instantaneous Mechanical Power	$P = F v cos θ$	watts
General Electrical Power	$P = V I$	watts
Electrical Power (ohmic)	$P = I^{2} R = \frac{V ^{2}}{R}$	watts
Efficiency	$η = \frac{P _{o u t}}{P _{in}} \times 100%$	unitless / %

7. Frequently Asked

What is the difference between energy and power?

Energy is the total amount of work done/energy transferred, measured in joules. Power is the rate of energy transfer, measured in joules per second (watts). A 10 W process running for 100 seconds transfers more total energy than a 100 W process running for 5 seconds.

Can power be negative?

Yes, negative power indicates that energy is being absorbed by a system rather than output from it. For example, a resistive force doing negative work on a moving object has negative power.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
Power of moving car calculation
2021 · 2
Efficiency of water pump problem
2023 · 1
Compare power of two moving objects

Going deeper

syllabusCIE 9702 Official SyllabusCheck section 5 for full learning outcomes

What's Next

Power is a core concept that appears across multiple topics in CIE A-Level Physics. It is used to analyse the motion of vehicles, calculate energy losses in electrical circuits, and understand energy generation and conservation. Mastery of power calculations is essential for scoring full marks on both multiple choice and extended response questions, as it is often combined with other concepts like forces, energy conservation and Ohm's law. Building a strong understanding of power now will make more advanced topics easier to tackle later.