The Ohm's law wheel

Ohm's lawpower triangleV = IRP = VIwatts lawohms law pie chart

Ohm's law and the three power equations, arranged so that each one omits exactly one of voltage, current, resistance and power.

Which one do I use? Pick the equation missing what you neither have nor want

Equation	Leaves out
$V = I R$	Power
$P = V I$	Resistance
$P = I^{2} R$	Voltage
$P = \frac{V^{2}}{R}$	Current

Ohm's Law

V = I R

Relates the voltage across a conductor to the current through it and its resistance.

Electrical Power (P = VI)

P = V I

Power delivered to a component as the product of the voltage across it and the current through it.

Electrical Power (P = I²R)

P = I^{2} R

Power dissipated as heat in a resistance carrying a current (Joule heating).

Electrical Power (P = V²/R)

P = \frac{V^{2}}{R}

Power dissipated in a resistance held at a fixed voltage.

How they fit together

Four quantities, four equations, and each equation uses three of them. That is the whole structure, and it is why the wheel or pie chart is printed inside the cover of every electrical text: V = IR is the only one without power, P = VI is the only one without resistance, P = I²R is the only one without voltage, and P = V²/R is the only one without current. Substitute Ohm's law into P = VI and you generate the other two, so there are really only two independent facts here.

Choose exactly the way you choose a kinematic equation: list what you have, note what you want, and the quantity that is neither is the one to leave out — that names your equation. The two traps are physical rather than algebraic. First, resistance is rarely constant: a lamp filament's resistance climbs by a factor of ten as it heats, so an inrush current calculated from the hot resistance is badly wrong. Second, these are DC relations. On AC with a motor or a transformer, P = VI gives apparent power in volt-amperes, and you need the power factor to get real watts.