Power

This lesson covers power and how to calculate it using $P = \frac{E}{t}$P=tE​ and $P = \frac{W}{t}$P=tW​, as required by the Edexcel GCSE Combined Science specification (1SC0). Understanding power allows you to compare how quickly different devices transfer energy.

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What Is Power?

Power is the rate at which energy is transferred or the rate at which work is done.

• A powerful device transfers energy quickly.
• A less powerful device transfers the same amount of energy, but more slowly.

The unit of power is the watt (W).

$1 \text{ W} = 1 \text{ J/s}$1 W=1 J/s

One watt means one joule of energy is transferred per second.

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The Power Equations

There are two versions of the power equation:

$P = \frac{E}{t} \qquad \text{and} \qquad P = \frac{W}{t}$P=tE​andP=tW​

where:

• P = power in watts (W)
• E = energy transferred in joules (J)
• W = work done in joules (J)
• t = time in seconds (s)

Both equations say the same thing — power is energy (or work done) divided by time.

Quantity	Unit	Symbol
Power	watt	W
Energy transferred	joule	J
Work done	joule	J
Time	second	s

Exam Tip: Be careful not to confuse the symbol for power (P) with the symbol for pressure (p), or the unit watt (W) with the variable for work done (W). Context will always make it clear.

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Worked Examples

Worked Example 1

A motor transfers 6000 J of energy in 30 s. Calculate the power of the motor.

1. Write the equation: $P = \frac{E}{t}$P=tE​
2. Substitute: $P = \frac{6000}{30}$P=306000​
3. $P = 200 \text{ W}$P=200 W
4. Answer: P = 200 W

Worked Example 2

A 2000 W kettle is switched on for 3 minutes. How much energy is transferred?

1. Convert time: 3 minutes = 3 × 60 = 180 s
2. Rearrange: $E = P \times t$E=P×t
3. $E = 2000 \times 180 = 360\,000 \text{ J}$E=2000×180=360000 J
4. Answer: E = 360 000 J (360 kJ)

Worked Example 3

A crane does 50 000 J of work lifting a load in 25 s. What is the power output?

1. $P = \frac{W}{t} = \frac{50\,000}{25} = 2000 \text{ W}$P=tW​=2550000​=2000 W
2. Answer: P = 2000 W (or 2 kW)

Exam Tip: Always convert minutes to seconds before substituting into the equation. Forgetting to do this is one of the most common errors.

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Comparing Devices

Power tells you how quickly a device does its job. Let us compare two lifts that both raise a 500 kg load by 10 m (g = 10 N/kg):

Quantity	Lift A	Lift B
Work done (J)	50 000	50 000
Time (s)	10	25
Power (W)	5000	2000

Both lifts do the same amount of work, but Lift A is more powerful because it does the work in a shorter time.

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Larger Units of Power

Unit	Symbol	Equivalent
watt	W	1 W
kilowatt	kW	1 kW = 1000 W
megawatt	MW	1 MW = 1 000 000 W
gigawatt	GW	1 GW = 1 × 10⁹ W

Worked Example 4

A wind turbine generates 1.5 MW of power. Express this in watts.

$1.5 \text{ MW} = 1.5 \times 10^6 \text{ W} = 1\,500\,000 \text{ W}$1.5 MW=1.5×106 W=1500000 W

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Linking Power, Force and Speed

By combining $P = \frac{W}{t}$P=tW​ and $W = Fd$W=Fd:

$P = \frac{Fd}{t} = F \times \frac{d}{t} = Fv$P=tFd​=F×td​=Fv

where v is the speed. This is not on the equation sheet but can be useful.

Worked Example 5

A car engine produces a driving force of 800 N while travelling at a constant speed of 25 m/s. What is the power output?

1. $P = Fv = 800 \times 25 = 20\,000 \text{ W}$P=Fv=800×25=20000 W
2. Answer: P = 20 000 W (20 kW)

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Power and Human Activity

Activity	Approximate power output
Resting	80 W
Walking	200–300 W
Cycling	400–500 W
Sprinting	700–2000 W

Worked Example 6

A student of mass 50 kg runs up a flight of stairs (vertical height 4 m) in 5 s. Calculate their power output. (g = 10 N/kg)

1. Work done = GPE gained: $W = mgh = 50 \times 10 \times 4 = 2000 \text{ J}$W=mgh=50×10×4=2000 J
2. $P = \frac{W}{t} = \frac{2000}{5} = 400 \text{ W}$P=tW​=52000​=400 W
3. Answer: P = 400 W

Exam Tip: Questions about running up stairs or cycling uphill combine power with GPE. Always calculate the work done (or energy transferred) first, then divide by time.

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Rearranging the Equations

To find	Rearranged equation
P	$P = \frac{E}{t}$P=tE​
E	$E = P \times t$E=P×t
t	$t = \frac{E}{P}$t=PE​

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Summary

• Power is the rate of energy transfer: $P = \frac{E}{t}$P=tE​ or $P = \frac{W}{t}$P=tW​.
• The unit of power is the watt (W), where 1 W = 1 J/s.
• A more powerful device transfers energy faster.
• Larger units: kilowatt (kW), megawatt (MW), gigawatt (GW).
• Power can also be calculated as $P = Fv$P=Fv (force × speed).
• Always convert time to seconds before using the equation.

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Extended Worked Examples

Worked Example 7 — Electric Shower

An electric shower is rated 9 kW and is used for 6 minutes. How much energy is transferred?

1. Convert: $P = 9000 \text{ W}, \quad t = 6 \times 60 = 360 \text{ s}$P=9000 W,t=6×60=360 s
2. $E = Pt = 9000 \times 360 = 3\,240\,000 \text{ J} = 3.24 \text{ MJ}$E=Pt=9000×360=3240000 J=3.24 MJ
3. If 90% becomes useful heating of the water, the useful output is 2.92 MJ; the rest is transferred to the pipes and surroundings (wasted thermal store).

Worked Example 8 — Linking Power and Specific Heat Capacity