Electrical power is the rate at which electrical energy is transferred or converted, measured in watts. In a resistive element it equals the product of voltage and current, and it can also be expressed from current and resistance or from voltage and resistance.
Learning objectives
- State the three common power formulas
- Choose the formula that matches the known quantities
- Calculate energy from power and time
- Distinguish active power from apparent power
- Measure power in a practical circuit
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
In a simple resistive circuit, power is voltage times current. Double the voltage across a fixed resistor and the power quadruples, because the current also doubles.
Intermediate How it behaves in a circuit
Power is not the same as energy: power is the rate, energy is power multiplied by time. A 1000 W appliance running for one hour uses 1 kWh.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Power | P | watt (W) |
| Apparent power | S | volt-ampere (VA) |
| Energy | E | joule (J) or kilowatt-hour (kWh) |
| Resistance | R | ohm (Ω) |
Worked examples
Power from voltage and current
Problem. A 12 V supply delivers 5 A to a load. What power does the load dissipate?
Solution. P = V × I = 12 × 5.
Mains heater
Problem. A resistive heater draws 10 A from a 230 V supply. Find its power, resistance and the energy used in 2 hours.
Solution. P = 230 × 10 = 2300 W. R = V/I = 230/10 = 23 Ω. E = 2300 W × 2 h = 4600 Wh.
Using V²/R
Problem. A 6 Ω resistor has 12 V across it. Find the power without first calculating the current.
Solution. P = V²/R = 12²/6 = 144/6.
Practical applications
- Appliance and equipment ratings
- Electric heating and lighting
- Motor and generator power
- Cable and fuse sizing
- Energy cost estimation
- Power supply selection
Automotive applications
Alternator output is rated in amperes at a regulated voltage, which gives the available power, and starter motors draw very high power for a short time. Headlamp wattage, audio amplifier power and electric-vehicle motor power are all specified in watts or kilowatts.
Industrial applications
Motor nameplates give mechanical output power in kW, while the electrical input is higher because of losses. Transformers are rated in kVA because their heating depends on voltage and current, not on the phase relationship between them.
Measurement procedure
- Use a power meter or power analyser for direct readings; a wattmeter measures active power.
- Measure voltage and current and multiply only for DC or purely resistive AC loads.
- Use true-RMS instruments and include the power factor for AC loads.
- Check whether the reading is instantaneous, average or peak.
Common mistakes
- Using peak values instead of RMS values in AC power calculations.
- Confusing watts with volt-amperes; they are equal only for a purely resistive load.
- Confusing power with energy and ignoring the time factor.
- Ignoring power factor when calculating current from power.
Safety considerations
- High-power equipment produces heat and fire risk; respect ventilation and clearance requirements.
- Size cables and protective devices for the full load current, including continuous duty.
- Do not exceed the rated output of a power supply or generator.