Lessons · Engineering · electrical power
Electrical power: how fast the circuit turns energy into heat or work
Power is volts times amps, P = V × I, in watts. With Ohm's law it is also I² R and V² / R.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A quarter-watt resistor on a prototype went brown and the smell reached the review meeting. Nobody had multiplied the current by itself and by the resistance. Power is where components die, and it is one line.
How to think about it
Use the form that has the two things you know. If you know current and resistance, I² R; voltage and resistance, V² / R. Current in amps before it is squared. Energy is power times time.
Worked example
P = V × I; with Ohm's law also P = I² R = V² / RThree forms of one idea. Pick the one with your two knowns.
A 12 V motor drawing 3 A: P = 12 × 3 = 36 WVolts times amps.
A 100 Ω resistor with 0.1 A through it: P = 0.1² × 100 = 1 WA quarter-watt part in that spot would cook.
Energy: 36 W for 2 h = 72 WhPower over time is energy, which is what the meter bills.
Your turn
A 220 Ω resistor carrying 50 mA. Write the power.
P = 0.05² × = 0.55 W
Solve one, graded on the server
The trap
Squaring the current in milliamps. 50² × 220 is 550,000; in amps it is 0.55 W. The current has to be in amps before it is squared, and the mistake is a factor of a million.