Electronics
Electrical power explained: P = V × I
Electrical power is how fast a circuit delivers or uses energy. Its unit is the watt (W), one joule per second, and you find it by multiplying voltage by current: P = V × I. In a resistor, all that power comes out as heat.
P = V × I
Voltage is energy per coulomb and current is coulombs per second. Multiply them and the coulombs cancel, leaving joules per second: watts.
Example: an LED circuit on 9 V drawing 20 mA uses 9 V × 0.02 A = 0.18 W.
Live experiment
Turn up the heat
A battery drives current through a 100 Ω resistor rated 0.25 W. Step the current from 10 mA to 90 mA and watch P = V × I worked out as an area, and the resistor glow past its rating. Then share the job between two 50 Ω resistors.
“Power and heat” is lesson 6 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Three ways to write it
Combine P = V × I with Ohm's law, V = I × R, and you get two more forms:
- P = V × I: when you know voltage and current
- P = I² × R: when you know current and resistance
- P = V² over R: when you know voltage and resistance
Example: 9 V across 100 Ω gives P = 81 over 100 = 0.81 W. The squared term matters: double the current through a resistor and it makes four times the heat.
Power ratings
Every resistor has a power rating, the most heat it can shed safely. Common small resistors are rated 0.25 W. Push one past that and it gets hot, discolours and can fail. A good rule is to keep parts at half their rating or less.
Check the example above: 0.81 W through a 0.25 W resistor is more than three times its rating, so it would cook. At 50 mA through 100 Ω it makes exactly 0.25 W, right at the limit.
Sharing the load
When one resistor can't take the heat, split the job. Two equal resistors, side by side or end to end, each handle half the power. Two 50 Ω resistors in series carry the same current as one 100 Ω, but each makes half the heat.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Power and heat” is lesson 6 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Or start from the very first lesson, no account neededWork it out
- Ohm's law calculatorAny two of V, I and R give the third, and the power.
- Electrical power calculatorWatts from any two of V, I and R, and the resistor rating that stays cool.
- Wire voltage drop calculatorVolts and watts lost in a cable, out and back, and the size that keeps it under 3%.
- Battery life calculatorHours from mAh and milliamps, for a steady load or a device that sleeps.
- Ohm's law practice problemsFind V, I or R, then the power, with the working for each.
- Electrical power practice problemsPower three ways, energy in kWh, battery life and running costs, all worked.
- Electronics formulas cheat sheetOhm's law to antenna length: every formula in the course, what it gives and where to learn it.
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: How fast energy is being used. Power is how fast energy is used or delivered. In a resistor, that energy turns into heat, so more power means hotter, faster.
- Why not “The colour of the glow”? The colour of a glow depends on what's glowing, not on power. Power is how many joules of energy are used each second.
- Why not “How much charge is stored”? Stored charge is what a capacitor holds, measured in coulombs. Power is a rate: joules of energy each second, in watts.
- Why not “How long a battery lasts”? How long a battery lasts depends on how much energy it holds as well as the power drawn. Power itself is how fast the energy goes.
Show the answer
Answer: 4. P = I² × R. Doubling I multiplies I² by 4.
- Why not “It doesn't change”? With the resistance fixed, any change in current changes the power. P = I² × R, so doubling I gives four times the power.
- Why not “½”? More current through the same resistor means more heat, not less. P = I² × R, so doubling I multiplies the power by 4.
- Why not “2”? Power goes with the square of the current, P = I² × R. Doubling I makes I² four times as big, not twice.
Show the answer
Answer: One joule of energy per coulomb of charge. Voltage is energy per unit of charge. Each coulomb that crosses 1 V gains or loses 1 joule.
- Why not “One ohm per amp”? From V = I × R, a volt is an amp times an ohm, not an ohm per amp. In energy terms it's one joule per coulomb.
- Why not “One coulomb per second”? One coulomb per second is one amp, the unit of current. A volt is energy per charge: one joule per coulomb.
- Why not “One watt per second”? A watt is already a rate, one joule per second, so a watt per second isn't a volt. A volt is one joule per coulomb.
“Power and heat” is lesson 6 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Questions people ask
What is the formula for electrical power?
P = V × I: power in watts equals voltage in volts times current in amps. Combined with Ohm's law it can also be written P = I² × R or P = V² ÷ R, depending on which two values you know.
What is a watt?
A watt is one joule of energy per second. A part using 1 W turns 1 joule of electrical energy into heat, light or motion every second.
What does a resistor's power rating mean?
It's the most power the resistor can turn into heat without overheating. Common small resistors are rated 0.25 W. Designers usually keep a part at half its rating or less so it runs cool and lasts.
Why does doubling the current give four times the heat?
In a resistor, doubling the current also doubles the voltage across it (V = I × R). Power is voltage times current, so it goes up by 2 × 2 = 4. That's the I² in P = I² × R.
Related topics
- Ohm's law explainedV = I × R: set any two of voltage, current and resistance and the third follows.
- What is resistance?The squeeze on the flow, in ohms: how resistors set the current and protect an LED.
- AC voltage and RMS explainedPeak, period, frequency and RMS: the numbers that describe an AC sine wave.