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Power in watts

Electricity and magnetism · level 4, lesson 3 of 6

A question to start

A kettle and an LED bulb both run from the wall socket at 120 V. One boils water in minutes, the other barely gets warm. What is different?

The idea

Power is how fast energy is delivered, in watts (W): 1 W is 1 joule each second.

Voltage is the energy per coulomb, and current is the coulombs per second. Multiply them and you get the joules per second:

\[P = VI.\]
Device Voltage Current Power
Kettle 120 V 12.5 A 1,500 W
LED bulb 120 V 0.075 A 9 W
Phone charging 5 V 2 A 10 W
Small LED 3 V 0.02 A 0.06 W

Same voltage, very different current, very different power.

Energy is then power times time: \(E = Pt\), in joules if \(t\) is in seconds, or in watt-hours (Wh) if \(t\) is in hours.

V = 120 VI = 12.5 AP = VI = 1,500 W

Worked examples

1. The kettle. \(P = 120 \times 12.5 = 1{,}500\) W.

2. Finding the current. A 60 W lamp on 120 V: \(I = P/V = 60/120 = 0.5\) A.

3. Energy. The kettle runs for 3 minutes: \(E = 1{,}500 \times 180 = 270{,}000\) J, or \(1{,}500 \times 0.05 = 75\) Wh.

Try it

  1. A heater draws 10 A from 120 V. Find its power.
  2. A 1,200 W hair dryer runs on 120 V. What current does it draw?
  3. A phone charger gives 9 V at 2 A. What is its power?
  4. A 9 W LED bulb is on for 5 hours. How many watt-hours does it use?
Answers
  1. \(120 \times 10 = 1{,}200\) W.
  2. \(1{,}200/120 = 10\) A.
  3. \(9 \times 2 = 18\) W.
  4. \(9 \times 5 = 45\) Wh.

Common mistake

"Higher voltage always means more power." Power needs both. A 120 V LED bulb uses far less power than a 12 V car starter motor, which draws hundreds of amps.

Where it leads