LessonPower and energy · 15 min

Power: how fast energy is used

A phone charger is "10 W", a kettle "2000 W", a resistor "1/4 W". Power is the rate at which energy is delivered or turned into something else - light, heat, motion. It decides how hot parts get, how big the battery must be and what the electricity bill says.

P = V × I

P: the power, in watts (W); 1 W = 1 joule per second
V: the voltage across the part (V)
I: the current through it (A)

Why V × I? Voltage is the energy each coulomb carries (J/C) and current is how many coulombs pass each second (C/s). Multiply them and you get joules per second: watts.

Two more forms, from Ohm's law

For a resistance, put V = I × R or I = V / R into P = V × I:

P = I² × R P = V² / R

I² × R: use it when you know the current through the resistance
V² / R: use it when you know the voltage across the resistance

The lamp: 12 V across it and 0.417 A through it, so P = 12 × 0.417 = 5 W.

Worked example: a 12 V 5 W lamp

A lamp is marked 12 V 5 W. What current does it take, and what is its (hot) resistance?

I = P / V = 5 / 12 = 0.417 A.
R = V² / P = 144 / 5 = 28.8 Ω.
Check: P = I² R = 0.417² × 28.8 = 5.0 W.

Answer: 0.417 A and 28.8 Ω.

Worked example: a small resistor

How much power does a 1 kΩ resistor take across 9 V?

P = V² / R = 81 / 1000.
P = 0.081 W = 81 mW.

Answer: 81 mW - easily handled by a normal 1/4 W (250 mW) resistor.

Power in a resistor: on a fixed 12 V, and with a fixed 0.2 A

fixed 12 V: P = V² / Rfixed 0.2 A: P = I² R

Which makes more heat: a bigger or a smaller resistance? It depends what is fixed. On a fixed voltage (a battery, the mains), a smaller R takes more current and more power - a kettle element is only 26 Ω. With a fixed current (a series circuit), the bigger R takes more power - the poor connection in a cable gets hot.

InteractiveTry it: power in a resistor

VoltageVResistanceΩ

Current-A

Power-W

Double the voltage: four times the power (V² / R).

Circuit for: Try it: power in a resistor — The circuit at the starting values

Typical power ratings.
Device	Power
Phone charger	10 - 25 W (fast chargers 65 W+)
LED bulb	5 - 12 W
Ceiling fan	50 - 75 W
LED TV (40 inch)	50 - 100 W
Fridge (while its compressor runs)	100 - 200 W
Electric iron	1000 W
Electric kettle	2000 W

Where you meet it

Power ratings on labels

"5 V 2 A" on a charger means up to 10 W.

The national grid

P = I² R in the lines is wasted. Sending the same power at a higher voltage needs less current, so far less loss - which is why Ghana's grid carries power at 161 000 V and 330 000 V and steps it down near you.

Heaters

Kettles, irons and water heaters are resistances chosen to turn electrical power into heat.

Practice 1A phone charger supplies 5 V at 2 A. What is its power?

Hint

P = V × I.

Show the answer

Answer: 10 W

P = 5 × 2 = 10 W.

Practice 2What current does a 60 W appliance take from 230 V?

Hint

I = P / V.

Show the answer

Answer: 0.261 A

I = 60 / 230 = 0.261 A.

Practice 320 mA flows through 220 Ω. How much power does the resistor take?

Hint

P = I² R with I in amps.

Show the answer

Answer: 0.088 W

P = 0.02² × 220 = 0.0004 × 220 = 0.088 W (88 mW).

Challenge 4A 230 V 1000 W iron is run on a 115 V supply. Assuming its resistance stays the same, what power does it give?

Hint

First its resistance: R = V² / P at 230 V. Then P at 115 V.

Show the answer

Answer: 250 W

R = 230² / 1000 = 52.9 Ω. At 115 V: P = 115² / 52.9 = 250 W. Half the voltage gives a quarter of the power (P = V² / R).