Section Overview
Voltage, current, and resistance describe what a circuit is doing. Power describes how hard it is working — the rate at which it turns electrical energy into light, motion, or heat. This section introduces power and its unit, the watt; shows how power combines with Ohm's law into three interchangeable forms; separates power from energy (the thing you actually pay for); and explains the single most practical consequence of all of it — why every part you'll ever handle carries a rating, and what happens when that rating is crossed.
Why This Matters
Almost every rating printed on almost every device is a power or current limit, and almost every dramatic failure in electronics — the scorched resistor, the melted connector, the swollen adapter — is that limit being exceeded. Ohm's law told you how much current flows; power tells you how much heat that flow produces, and heat is what destroys things. A technician who can look at a burned component and calculate the power it was dissipating knows whether the part simply failed or whether something upstream is forcing too much through it. That distinction is the difference between a parts-swap and a real repair.
Required Prerequisites
- What Is Electricity? — charge and energy, the raw ideas power is a rate of.
- Voltage — The Pressure of Electrons — the V in P = V × I: the pressure whose product with current is power.
- Current — The Flow of Electrons — the I in P = V × I.
- Resistance — Opposition to Flow — where "opposition becomes heat" was promised a number; this section delivers it.
- Ohm's Law — The Foundation of Circuit Analysis — the relationship that lets power be written three equivalent ways. This section assumes you can rearrange V = I × R fluently.
Recommended Consumables
No consumables required. The exercises are pen-and-paper arithmetic plus reading the wattage and current labels already on devices you own — nothing is used up.
Recommended Practice Hardware
- Several devices with a power or current rating on the label — a light bulb (look for "W"), a phone charger ("5V 2A"), a laptop adapter ("65W"), a microwave or kettle ("1200W")
- Any battery with a capacity marking — a phone battery ("3000mAh"), a power bank ("10000mAh 37Wh"), or an AA cell's datasheet value
- Pen and paper or a basic calculator
No live measurement is needed. Every rating this section asks you to read is printed on the outside of the device.
Real-World Applications
Power reasoning is everywhere on a bench: the wattage rating that tells you whether a replacement resistor will survive, the current rating that sizes a fuse or a wire, the "65W" on a laptop charger that must at least match the laptop's appetite, and the milliamp-hour number that decides how long a battery lasts. It is also the quantity behind your electricity bill — utilities charge for energy in kilowatt-hours, and every "is it worth leaving this on?" question is really a power-times-time calculation. Learn to think in watts and a device's label stops being decoration and becomes a specification you can reason about.
Common Challenges
- Power and energy get used as synonyms. They aren't. Power is a rate (how fast energy is used, right now); energy is the total (power accumulated over time). A 100-watt bulb has a power of 100 watts whether it's on for a second or a day — but the energy it uses, and the cost, grows with time.
- The three power formulas look like three things to memorize. They're one idea (P = V × I) with Ohm's law substituted in twice. Understand the substitution and you never have to memorize the other two.
- Wattage ratings feel like arbitrary numbers. A power rating is a promise about heat: it's the most power a part can turn into heat without damaging itself. Cross it and the part overheats — exactly the resistance-becomes-heat mechanism from Section 1.4, now with a limit attached.
Safety Notes
Risk Level: Low. This section is conceptual and arithmetic; no exercise requires opening a device, probing a live circuit, or touching anything beyond a device's printed label.
Professional Tips Before Starting
- Get fluent estimating power in your head: "12 volts, a couple of amps — that's around 25 watts." The rough number is usually all a diagnosis needs.
- When something runs hot, reach for the power forms, not just Ohm's law. Heat is a power question, and P = I² × R often tells the story faster than the current alone.
- Read the rating and the actual together. A part's rating tells you what it can survive; a quick power calculation tells you what it's being asked to survive. The gap between those two numbers is where failures live.
From Volts and Amps to Watts
P = V × I — Power Is Pressure Times Flow
Power is the rate at which a circuit uses energy, and for a DC circuit it's simply the voltage across a device multiplied by the current through it:
P = V × I
The unit is the watt (W): one watt is one volt driving one amp. The intuition follows everything you've built so far — voltage is the pressure, current is the flow, and power is how much work that pressure-driven flow accomplishes per second. A device with 12 volts across it drawing 2 amps uses:
P = V × I = 12 × 2 = 24 watts
That single multiplication is the whole foundation. A 5-volt phone charger delivering 2 amps is doing 10 watts of work; a laptop adapter at 19 volts and 3.4 amps is doing about 65 watts — which is exactly why its label says "65W."
P = I² × R and P = V² ÷ R — Power Through the Lens of Resistance
Often you don't know both the voltage and the current directly — you know a resistance and one of the two. Because Ohm's law relates all three, you can substitute it into P = V × I and get power from whatever pair you have.
Substitute V = I × R:
P = I² × R
Substitute I = V ÷ R:
P = V² ÷ R
These aren't new laws — they're P = V × I wearing Ohm's law. Two quick examples:
- A resistor carrying 0.5 amps with 100 ohms of resistance dissipates P = I² × R = 0.5² × 100 = 0.25 × 100 = 25 watts.
- A 10-volt supply across a 50-ohm resistor delivers P = V² ÷ R = 10² ÷ 50 = 100 ÷ 50 = 2 watts.
Notice the squares. Power depends on the square of current or voltage, which is why heat problems escalate so fast: double the current through a fixed resistance and the power — the heat — goes up not twice but four times. That single fact is behind an enormous share of overheating failures.
Power Versus Energy — The Thing You Pay For
Power is a rate; energy is power accumulated over time:
E = P × t
Run a 100-watt device for one hour and it uses 100 watt-hours of energy; run it for ten hours and it uses 1,000 watt-hours, or 1 kilowatt-hour — the unit your electricity provider bills. Power hasn't changed; energy has, because time has. The formal SI unit of energy is the joule (one watt for one second), but for anything lasting minutes or hours the watt-hour is the practical unit, and the kilowatt-hour is what shows up on a bill.
This is also how batteries are honestly rated. A power bank marked "37 Wh" stores 37 watt-hours of energy — enough to run a 37-watt load for one hour, or a 3.7-watt load for ten. The "milliamp-hour" number you see more often (say, "10000 mAh") is a charge-capacity shorthand that only becomes energy once you multiply by the battery's voltage — which is exactly why two "10000 mAh" packs at different voltages don't store the same energy. Keep power, energy, and charge-capacity separate and battery labels stop being confusing.
Ratings — A Promise About Heat
Every power rating is a limit on heat. A resistor marked "1/4 watt" can turn up to a quarter-watt into heat and shed it safely; ask it to dissipate half a watt and it runs hot, discolors, and eventually fails — the burned resistor from Section 1.4, now explained by a number. A wire's current rating is the same idea: push more current than rated and the wire's own small resistance (P = I² × R) makes more heat than the wire can shed. A charger's wattage rating is its promise about how much power it can deliver continuously without overheating.
This is why, at the bench, a replacement's rating matters as much as its value. The right ohms at the wrong wattage is a slow failure waiting to happen. And a component that runs hotter than it should is telling you, in the language of power, that either it's under-rated for its job or something upstream is forcing more through it than the design intended — the beginning of a real diagnosis rather than a guess.
Common Mistakes
- Confusing power with energy. "This device uses a lot of power" and "this device uses a lot of energy" are different claims — a high-power device used briefly can cost less than a low-power device left on for days.
- Forgetting the squares. Treating power as proportional to current or voltage (rather than their square) badly underestimates how fast heat rises. Doubling current quadruples heating.
- Matching value but not rating. Replacing a part by its ohms or amps while ignoring its wattage or current rating is one of the most common ways a "repaired" device fails again — sometimes dangerously.
- Mixing units. Watts, watt-hours, and milliamp-hours describe different quantities; comparing a "10000 mAh" battery to a "37 Wh" one without accounting for voltage compares apples to oranges.
Troubleshooting Guidance
Power turns "this part is hot" into a measurement you can reason about. When a component runs hot, estimate the power it's dissipating from whatever two quantities you can find — P = V × I, P = I² × R, or P = V² ÷ R — and compare that to its rating. If the dissipation is near or above the rating, the part is being overworked, and the real question is why: is it simply under-rated for the job, or is a fault upstream (a partial short, a wrong supply voltage) forcing more power through it than the design intended? A resistor dissipating far more than its rating rarely fails on its own — something made it. Chasing the cause of excess power, not just replacing the casualty, is what separates a lasting repair from a repeat visit.
Verification & Testing Methods
Check your understanding before moving on:
- [ ] State what power is and give its unit, without looking at the formula.
- [ ] Given any two of voltage, current, and resistance, calculate the power for a simple case.
- [ ] Explain the difference between power and energy, and which one an electricity bill charges for.
- [ ] Explain, in terms of power, why a component overheats when its rating is exceeded.
Then try the practice exercises below — all reading labels and arithmetic, no probing.
Practice Exercises
- Power from volts and amps (5 minutes, pen and paper). Calculate the power for each: (a) 5 V at 0.4 A; (b) 19 V at 3.4 A; (c) 3.7 V at 1.5 A. For each, write one everyday device that roughly matches that wattage.
- The other two forms (10 minutes, pen and paper). Find the power dissipated for: (a) 2 A flowing through a 3 Ω resistor (use P = I² × R); (b) 12 V across a 6 Ω resistor (use P = V² ÷ R). Then confirm case (b) a second way by first finding the current with Ohm's law and using P = V × I — the two answers must match.
- Will the resistor survive? (5 minutes, pen and paper). A 100 Ω resistor rated for 1/4 watt has 8 V across it. Calculate the power it must dissipate (P = V² ÷ R) and decide whether it's within its rating. If not, state what you'd change — a higher-wattage resistor, or fixing whatever put 8 V across it.
- Energy and the bill (5 minutes, pen and paper). A 60 W bulb runs 5 hours a day. Find the energy it uses per day in watt-hours, then per 30-day month in kilowatt-hours. If energy costs $0.15 per kilowatt-hour, estimate the monthly cost.
- Read a battery honestly (5 minutes, using a device). Find a battery or power bank with both a voltage and a capacity marking. If it lists watt-hours, state how long it could run a 5 W load. If it lists only milliamp-hours, note that you'd need the voltage to convert it to energy — and find that voltage on the label if it's there.
These core ideas — power as V × I, its three forms, power versus energy, and ratings as heat limits — are tested in the Chapter Quiz at the end of this chapter, where a score of 80% is required to continue.
Key Takeaways
- Power is the rate a circuit uses energy; for DC it is voltage times current, P = V × I, measured in watts.
- Substituting Ohm's law gives the same power two other ways: P = I² × R and P = V² ÷ R — one idea, three forms.
- Power depends on the square of current or voltage, so heating escalates fast: double the current, quadruple the heat.
- Energy is power over time, E = P × t, measured in watt-hours (or joules); it is what a utility bills and what a battery stores.
- Watts (power), watt-hours (energy), and milliamp-hours (charge capacity) are different quantities — don't interchange them.
- Every power or current rating is a limit on heat; exceeding it is what makes parts overheat and fail, and a replacement's rating matters as much as its value.
Skills Learned
- You can now calculate the power a simple DC device uses from any two of voltage, current, and resistance.
- You can now read a wattage or current rating and explain what it promises and what it limits.
- You can now explain, with a number, why a component overheats — the power it dissipates versus the power it can survive.
- You can now tell power and energy apart and estimate a device's energy use and cost over time.
- You can now reason about battery capacity without confusing watt-hours and milliamp-hours.
Glossary Additions
- power — the rate at which a circuit uses or delivers energy; for a DC circuit, voltage times current (P = V × I), measured in watts.
- watt — the unit of power; one watt is one volt driving one amp, equivalent to one joule of energy per second.
- energy — the total amount of work done or heat produced, equal to power multiplied by time (E = P × t); measured in joules or, practically, watt-hours and kilowatt-hours.
Suggested Next Sections
Must read next:
- Practical Measurement: Reading Voltage and Current — the hands-on close of Chapter 1, where the meter finally comes out and everything from voltage to power becomes something you measure, not just calculate.
Recommended:
- Ohm's Law — The Foundation of Circuit Analysis — worth revisiting now that its three quantities carry a fourth, power, on their backs; the two sections together are the whole toolkit of basic DC analysis.