Power: where push meets flow
In the last guide, voltage was the push (like the pressure in a water pipe) and current was the flow (how much charge moves past each second). But neither one alone tells you how much actual work is being done. Multiply them together and you get power: P = V times I. Power measures the rate at which energy is being delivered.
What about units? One watt (W) is one volt times one amp, which is also one joule per second. Concretely: a small LED running at 2 V and 10 mA burns 2 times 0.01 = 0.02 W = 20 mW, just a faint glow; an electric kettle is roughly 230 V times 9 A ≈ 2000 W. Same formula, yet the two are five orders of magnitude apart.
The water-pipe picture, all the way to power
Deepen the analogy: pressure times flow rate equals the power the water carries. A thin trickle at huge pressure and a flood at tiny pressure can deliver exactly the same power. So 12 V times 1 A and 120 V times 0.1 A both deliver 12 W. This is precisely why the grid transmits at high voltage and low current — for the same power, smaller current means smaller losses in the wires.
Energy is power accumulated over time. Power is the rate (how much work per second); energy is the total (how much was delivered in all). E = P times time. Picture a water wheel: more power makes it spin faster, but how much grain it grinds depends on how long it runs.
Every analogy has cracks. Water can leak out of a pipe and be lost; the charge in a wire is conserved and returns to the source after going around — what actually gets spent is the energy the charge carried along the way (turned into light, heat, motion). Keep the picture when you want intuition; drop it the moment it would mislead.
Energy, joules, and the electric bill
The joule (J) is the unit of energy, and a watt is simply one joule per second. Run a 1 W device for 1 second and you have spent 1 joule. The bill uses kilowatt-hours (kWh): a 1000 W heater for 1 hour = 1 kWh, which in Taiwan is called 一度電. Work one out: a 60 W bulb left on for 2 hours = 120 Wh = 0.12 kWh.
Use a battery to tie charge and energy together. A 9 V battery rated at about 500 mAh stores roughly 9 times 0.5 = 4.5 Wh ≈ 16,000 joules. If your circuit draws 45 mA, it lasts about 500 mAh / 45 mA ≈ 11 hours. Note the units: mAh measures charge (how much flowed over a stretch of time); multiply by voltage to turn it into energy.
Where the power goes: heat and the power rating
Every resistor turns the power it drops into heat — this is power dissipation. Because a resistor obeys Ohm's law, the same power has three equivalent forms: P = V times I = I^2 times R = V^2 / R. Use whichever one matches the numbers you already have.
Quantity Symbol Unit Water-pipe picture ---------------------------------------------------- voltage V volt (V) pressure across the pipe current I amp (A) flow rate through the pipe power P watt (W) pressure x flow = delivery rate energy E joule (J) total water delivered, over time Same power, three ways (a resistor obeys Ohm's law): P = V x I push times flow P = I^2 x R flow squared, times resistance P = V^2 / R push squared, over resistance
This heat is exactly why parts carry a power rating. A 1/4 W resistor asked to dissipate 1/2 W will cook. And the rating assumes a cool ambient and moving air; stuffed inside a hot enclosure you must derate it. The water-pipe picture can barely show heat at all — that is one place it quietly fails.
A worked example: sizing an LED resistor and checking its power
Put it all together. An LED fed from a 5 V supply needs a series current-limiting resistor — without it the current runs away and burns the LED out. We size it step by step, then circle back to check how much heat that resistor makes.
- Fix the LED's working point: from the datasheet, about 2 V across it and about 10 mA through it.
- Find the voltage the resistor must drop: 5 - 2 = 3 V.
- Size it with Ohm's law: R = 3 / 0.01 = 300 ohm.
- Check the resistor's power: P = 3 times 0.01 = 0.03 W = 30 mW.
- Choose a part with margin: a common 1/4 W (250 mW) resistor is plenty — about 8x headroom, and it runs cool.
The whole branch draws 10 mA from 5 V, so 5 times 0.01 = 50 mW total: the LED takes 20 mW to make light, and the resistor "wastes" 30 mW as heat. The goal here was never efficiency — it was limiting the current. Choosing 1/4 W instead of the bare-minimum part is your design margin, keeping the resistor safe through surprises, heat, and ageing.