Library / Electrical / ELE-03
Electrical
Electrical power
Rate of energy transfer in an electrical component from its voltage and current.
- Ref
- ELE-03
- Rev
- v1
- Field
- Electrical
- Result
- P [W]
P in watts (W), V in volts, I in amperes, R in ohms. The three forms are the same relation combined with Ohm’s law. The calculator uses P = IV and shows the other two as checks.
Power is how fast energy is transferred. The current and the voltage across a component give P = IV directly. Substituting Ohm’s law gives the other two forms, which are handy when you know the resistance instead.
Calculator
- Resistance R = V/I2.4 Ω
- Check: V²/R60 W
- Check: I²R60 W
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At a fixed resistance, power goes as the square of the voltage or the current. Doubling the voltage across a resistor quadruples the heat it produces.
- At a fixed voltage (a power rail), power is proportional to current. Halving the current halves the power.
- The same power can be delivered at high voltage and low current or the other way round. Cable loss is I²R, so high voltage and low current wastes less power in the cables.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V Potential difference | 1 to 400 V | 5 | 2,000 | 1,995 | +10% | +10 % |
| I Current | 0.1 to 20 A | 1.2 | 240 | 238.8 | +10% | +10 % |
Sweep of Current
| Current (A) | Power (W) |
|---|---|
| 0.1 | 1.2 |
| 0.1939 | 2.327 |
| 0.3761 | 4.513 |
| 0.7293 | 8.751 |
| 1.414 | 16.97 |
| 2.742 | 32.91 |
| 5.318 | 63.82 |
| 10.31 | 123.8 |
| 20 | 240 |
Sweep one variable
Variables and how each one contributes
Power
What the equation gives you. Everything else feeds it.
Potential difference
Voltage across the component. With the current fixed, power rises in proportion to V. If the resistance is fixed instead, the current also rises with V and power rises as V².
Current
Current through the component. With the voltage fixed, power rises in proportion to I. If the resistance is fixed instead, power rises as I².
Worked example with the values above
- Resistance from Ohm’s law: R = V/I = 12 / 5 = 2.4 Ω.
- Power: P = IV = 5 A × 12 V = 60 W.
- Check the other forms: V²/R = 60 W and I²R = 60 W. They agree.
Assumptions and limits
- Direct current, or AC with RMS values and a purely resistive load (power factor 1).
- V is the voltage across the component, not the supply voltage.
- Steady values over the time considered.
Common mistakes
- Using V²/R with the supply voltage instead of the voltage across that resistor.
- Using peak AC values instead of RMS. Peak values give twice the mean power (see the AC peak and RMS page).
- Mixing up watts (power) and watt-hours (energy).
Statistics and uncertainty
The formula is deterministic. For independent errors, δP/P ≈ √[(δV/V)² + (δI/I)²]. In the V²/R form the voltage error counts twice: δP/P ≈ √[(2δV/V)² + (δR/R)²].
Where it is used
- Rating resistors and checking heat dissipation.
- Power-supply and battery load calculations.
- Estimating cable losses through I²R.
Maths you need
- Ohm’s law: V = IR links the three forms
- Squares: the V² and I² forms grow quickly