Ohm's Law Explained: V = IR and the Power Wheel

Twelve volts across a four-ohm resistor pushes three amps through it and turns thirty-six watts into heat — and every one of those numbers can be found from any other two. That compactness is why Ohm's law is the first thing electricians, hobbyists and physics classes learn: a circuit's entire electrical behaviour hides inside two short equations.

One law, two equations

The law itself is a single proportionality. The voltage V across a component equals the current I flowing through it times its resistance R:

V = I × R

Double the push — the voltage, in volts — and the flow, the current in amps, doubles with it. Double the opposition — the resistance in ohms — and the flow halves. The relationship is linear, which is what makes circuits so predictable. Power enters through a second equation, P = V × I: the rate at which electrical energy is converted into heat, light or motion, measured in watts. Substitute Ohm's law into the power equation and two further identities fall out:

P = V × I     P = I² × R     P = V² / R

Three power formulas, one physical reality. Which of them is most convenient depends entirely on what you already know — and that is the whole genius of the arrangement.

The power wheel: any two give the rest

Four quantities bound by two independent equations means any two knowns determine the other two. Twelve pairs, twelve exact routes. The four routes worth memorising:

given V, R  →  I = V / R      P = V² / R
given I, R  →  V = I × R      P = I² × R
given V, I  →  R = V / I      P = V × I
given P, R  →  V = √(P × R)   I = √(P / R)

The wheel is why a multimeter and a nameplate are enough to describe a whole load. A heater labelled 2000 W at 230 V is also 8.7 A through 26.5 Ω — one physical object wearing three interchangeable descriptions. Meter readings, ratings and part labels rarely arrive in matching pairs, so the real skill is picking the route that starts from what you actually have.

Worked examples worth memorising

A phone charger supplies 5 V and its cable carries 2 A, so the load behaves like 2.5 Ω and draws 10 W. A 60 W bulb on 230 V mains draws 60 / 230 ≈ 0.26 A through 230 / 0.26 ≈ 882 Ω. A textbook 100 W, 25 Ω resistor must be running at V = √(100 × 25) = 50 V with I = √(100 / 25) = 2 A — and that is exactly what its rating means: the conditions under which it dissipates 100 W without cooking. Notice the pattern in every example: power is never an extra independent fact about a circuit. It is a consequence of any two of the other three quantities, which is why half-burnt resistors and tripped breakers are usually arithmetic failures, not mystery failures.

Where Ohm's law bends

V = I × R is exact for ohmic materials — metals at constant temperature, ordinary resistors — and approximate everywhere else. A filament bulb's resistance climbs several-fold as it heats, so its cold resistance understates its operating draw. Diodes and LEDs are not ohmic at all: their current grows exponentially with voltage, so no single constant R exists. In AC circuits containing coils and capacitors, impedance Z replaces resistance and carries phase angles with it — a motor's V/I ratio measured while spinning is its impedance, not the resistance you would read with it disconnected. And within an ohmic material, resistance itself depends on length, cross-section and temperature: R = ρL/A, with ρ the material's resistivity. None of this dethrones the law; it just says the R you plug in must be the right R for the conditions.

Try it yourself

Open the Ohm's Law Calculator and enter 12 V and 4 Ω: it returns I = 3 A and P = 36 W with the formulas it used on display. Then try the backwards route — 100 W and 25 Ω should return 50 V and 2 A exactly. To juggle watts, kilowatts and horsepower once the solver has finished, use the Power Converter, and for the story behind those units read power units explained. When the question becomes "what does this load cost to run?", hand its watts to the Electricity Cost Calculator.