Labo Élec

electrical lab simulator
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Reminder sheet

Power, energy, efficiency

Bastaya

Power tells how fast energy is spent; energy is power multiplied by time. The kWh on your bill is an energy, not a power.

Power P = U·I is the energy exchanged per second, in watts. In a resistor it is entirely turned into heat (Joule heating): P = R·I² = U²/R.

Energy W = P·t is measured in joules; the utility bills in kilowatt-hours (1 kWh = 3.6 × 10⁶ J). A machine absorbs a power Pa and returns a useful part Pu: its efficiency is η = Pu / Pa, always below 1.

Formulas

Electrical powerP = U · I
QuantitySymbolUnit
PowerPW
VoltageUV
CurrentIA
Joule heatingP = R · I² = U²R
QuantitySymbolUnit
PowerPW
ResistanceRΩ
CurrentIA
EnergyW = P · t
QuantitySymbolUnit
EnergyWJ
PowerPW
Timets

In kWh: power in kW × time in hours.

Efficiencyη = PuPa
QuantitySymbolUnit
Efficiencyη-
Useful powerPuW
Absorbed powerPaW

Worked example

A 2 000 W heater runs at 230 V. What current does it draw, what is its resistance? It heats 3 h a day for 30 days: what energy, and what cost at €0.30/kWh? A motor draws 1 500 W and delivers 1 200 W: what efficiency?

I = P / U = 2 000 / 230 = 8.7 A. R = U² / P = 230² / 2 000 = 26.5 Ω.

W = P · t = 2 kW × 90 h = 180 kWh, i.e. 180 × 0.30 = €54 (in joules: 180 × 3.6 × 10⁶ = 6.48 × 10⁸ J).

η = Pu / Pa = 1 200 / 1 500 = 0.8, i.e. 80 %; the remaining 300 W are lost as heat.

Common mistakes

  • Confusing power P (watts, a rate of energy) with energy W (joules or kWh, an amount): the meter bills kWh, not kW.
  • W = P · t with P in watts and t in hours gives watt-hours, not joules: for joules, t must be in seconds.
  • Finding an efficiency greater than 1: the useful power is always less than the absorbed power.

IEC symbols

Lamp
MMotor
WWattmeter

Mini circuit

Open in the sandbox

Frequently asked questions

What is the difference between a kW and a kWh?
The kilowatt is a power (what the appliance draws at each instant), the kilowatt-hour an energy (what it has consumed after some time). A 1 kW appliance running for 1 h uses 1 kWh.
Why do P = R·I² and P = U²/R give the same result?
They are two ways of writing P = U·I, replacing U by R·I or I by U/R (Ohm's law). Choose the one whose data you know.

34 exercises in this topic

This chapter is covered by the paths: General electricity, ISL-oriented exercises

All sheets · All formulas · Glossary of electrical quantities · Standard electrical symbols (IEC 60617)

Practise this topic
Simulated time00:00:00
Q = I·t-
W = P·t-

Workbench

Circuit diagram CEI 60617

How does it work?

The perfboard: each big hole is a circuit node. You push a single leg of a component (resistor, lamp...) into it. The 4 small holes around it are connected to it: that is where chips and leads plug in.

  1. Drag a component onto the board: it snaps onto the grid. R rotates it.
  2. To join neighbouring big holes, click Jumper chip in the palette (or C) then drag on the board: a line of chips is laid at once. Bridged holes become a single node.
  3. For long links and for the power supply (placed next to the board), drag a lead from one big hole to another (or to a terminal).
  4. As soon as a loop is closed, the circuit is solved in real time (Ohm + Kirchhoff) and the diagram follows.
  5. Zoom with the wheel (or + / −, two-finger pinch); drag the background to pan, 0 fits the board. The + buttons around the board add a row or a column.

Del delete · R rotate · C chip brush · Esc cancel · wheel zoom · drag the background to pan

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