Ohm’s law and power: U, I, R, P
U = R × I
The Ohm’s law wheel without the wheel: two relations, U = RI and P = UI, tie four quantities together, and any two determine the other two. The tool accepts any pair, a charger’s voltage and power, an LED’s current and resistance, a resistor’s value and dissipated power, and returns all four values with the relations shown. It refuses overabundant inputs rather than silently ignoring one: if three values contradict each other, saying so beats choosing. And it recalls where the law stops: ohmic components, direct current, constant temperature.
24
- Relations
- U = R × I and P = U × I, hence P = U²/R = I²R
- Given
- Voltage + Current
U = 12 V, I = 2 A, R = 6 Ω, P = 24 W.
Two relations, four quantities: any two determine the other two, and that is the whole "Ohm’s law wheel". The twelve formulas of the disc are just the six pairs of this calculation, read both ways.
The law holds for an ohmic component under direct current, at constant temperature: a hot filament’s resistance is not the cold one’s (a 100 W bulb reads 529 Ω lit, ten times less off), and under AC, impedance replaces resistance as soon as coils or capacitors join in. An LED, a diode or a transistor does not follow Ohm’s law.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasU = R × I
U = R × I
P = U × I
P = U² / R
P = I² × R
Two independent relations suffice: the twelve formulas of the classic "wheel" are just their recombinations. Giving two quantities fixes the whole operating point; giving three risks contradiction, and the tool prefers to flag it rather than settle it.
- U
- · voltage across the component, in volts.
- I
- · current through it, in amperes.
- R
- · resistance, in ohms: the ratio U/I, constant for an ohmic component.
- P
- · power dissipated as heat, in watts: it is what sizes the component.
Validity domainOhm’s law describes ohmic components, resistors and conductors, under direct current and at constant temperature.
Ohm’s law describes ohmic components, resistors and conductors, under direct current and at constant temperature. A bulb filament changes resistance tenfold between cold and hot; an LED, a diode or a transistor does not follow the law at all; and under AC, impedance replaces resistance as soon as coils or capacitors come into play. All four quantities are taken positive here, the component being passive: for sign conventions of full circuits, see the associations tool.
Reading the resultPower is often the quantity that matters in practice: a 100 Ω resistor under 10 V dissipates 1 W, and a quarter-watt part would burn there.
Power is often the quantity that matters in practice: a 100 Ω resistor under 10 V dissipates 1 W, and a quarter-watt part would burn there. The forms P = U²/R and P = I²R each tell their own story: at fixed voltage, the lower the resistance the hotter it runs; at fixed current, the reverse.