Power & Energy
How to calculate efficiency and find a circuit's losses
Efficiency is the share of the power going in that comes out where you want it: efficiency = Pout ÷ Pin. A charger taking 10 W and delivering 8 W is 80% efficient. The other 2 W doesn't vanish: every lost watt becomes heat in some part, a resistor, a diode, a regulator or a wire, and each has its own simple sum. Find the biggest loss and fix that first.
The sum for each part
- Resistor or wire: P = I² × R, or the volts across it times the current through it.
- Diode: P = VF × I. A silicon blocking diode dropping 0.8 V at 75 mA wastes 60 mW; a Schottky at about 0.3 V, well under half that.
- Linear regulator: P = (Vin − Vout) × I. From 12 V to 5 V it can never beat 5 ÷ 12 ≈ 42%.
- Switching converter: a few percent in its switch, diode and coil; 85 to 95% overall is typical.
Example: three LEDs on 12 V
Three white LEDs need 3.2 V each at 20 mA. Wired side by side, each with its own resistor, every resistor burns the other 8.8 V. The battery supplies 12 V × 60 mA = 0.72 W and only about 0.19 W reaches the LEDs: 27%.
Put them in a string instead: one current through all three, 9.6 V across the LEDs and one resistor for the last 2.4 V. Same light, a third of the current, 0.24 W in.
Live experiment
Silicon or Schottky?
The sun charges a cell through a blocking diode. Silicon drops 0.8 V, burns about 60 mW and lifts the panel past its knee, so the cell gets 0.28 W. Swap in a Schottky: it burns less than half as much, the cell gets 0.35 W, and it fills to full in under a second.
“Where the watts go” is lesson 6 of 6 in Solar Sound, Power & Energy World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.
Losses that multiply
A lossy part can also make the rest of the circuit worse. On a solar charger, a silicon blocking diode burns about 60 mW, but its drop also pushes the panel up its curve, past the knee, so the panel gives less too: the cell gets 0.28 W. Swap in a Schottky and the cell gets 0.35 W, a gain of twice what the diode alone saved. And stages in a chain multiply: two at 90% make 0.9 × 0.9 = 81%.
Where you'll meet it
A "10,000 mAh" power bank fills a 4000 mAh phone about twice, not two and a half times, because the boost to 5 V and the phone's own charger each lose about a tenth. Laptop and phone chargers switch rather than regulate linearly for the same reason: at 90% instead of 40%, they run cool in a closed plastic case.
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.
“Where the watts go” is lesson 6 of 6 in Solar Sound, Power & Energy World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.
Or start from the very first lesson, no account neededWork it out
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: Steals volts from the load and turns them into heat. Wire is a resistor too. A copper trace is just a flat wire.
- Why not “Stores energy”? A straight wire stores almost nothing. The volts it takes are turned into heat.
- Why not “Has no effect”? Wire has resistance, so the load current makes a drop across it, and that drop times the current is heat.
- Why not “Adds volts”? A passive wire can only lose voltage, never add it.
Show the answer
Answer: The square of the current. P = I² × R.
- Why not “Nothing”? A neck has resistance, so any current through it makes heat.
- Why not “The current”? Twice the current through the same resistance makes four times the heat, not twice: P = I² × R.
- Why not “The voltage”? The supply voltage doesn't set a trace's heat. The current through it and its resistance do.
Show the answer
Answer: 0.44 V: most of it on the return. The current flows through both. 2 A × 0.02 is 0.04 V out, 2 A × 0.2 is 0.4 V back. The return trace is where the volts went.
- Why not “0.04 V”? 0.04 V is only the power trace's share. The current comes back through the 0.2 Ω return too.
- Why not “0.4 V on the power trace”? The power trace is the 0.02 Ω one, and it drops only 0.04 V. The 0.4 V is lost on the return.
- Why not “Nothing: ground is ground”? Ground copper has resistance like any other, and the full 2 A flows back through it.
“Where the watts go” is lesson 6 of 6 in Solar Sound, Power & Energy World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.
Questions people ask
How do you calculate efficiency?
Divide the useful output power by the input power. A charger that takes 10 W from the wall and puts 8 W into a battery is 8 ÷ 10 = 80% efficient. The missing 2 W leaves as heat.
Why are linear regulators inefficient?
They drop the spare voltage across a transistor, and that voltage times the load current is heat. Their efficiency can't beat V out ÷ V in: 5 V from 12 V is at best 42%. A buck converter switches instead, and typically reaches 85 to 95%.
Why does a power bank deliver less than its rating?
Its mAh rating is for its 3.7 V cell. A 10,000 mAh bank holds about 37 Wh; boosting to 5 V at about 90% leaves 33 Wh, and the phone's own charger loses about another tenth. So it fills a 4000 mAh phone about twice, not two and a half times.
Related topics
- Electrical power explained: P = V × IP = V × I: how fast energy turns into heat, and why a resistor has a power rating.
- Linear regulator vs buck converterBrakes or gears: a linear regulator burns the spare volts, a buck trades them for amps. When each wins.
- How does a diode work?A one-way valve for current: anode, cathode, the 0.7 V forward drop and Schottky diodes.
- How to calculate battery life from mAhRuntime = capacity ÷ current: mAh, watt-hours, C-rate, and why real batteries give a little less.