AmpSizerOhm's law explained
Ohm’s law says that the current through a conductor is proportional to the voltage across it and inversely proportional to its resistance: V = I × R. Volts, amps, ohms — know two and the third follows.
Pair it with the power law, P = V × I, and the two together generate the twelve formulas usually drawn as a wheel. There is nothing extra in the wheel; it is algebra on two statements.
The consequence worth understanding is what happens when you substitute one into the other: P = I² × R. Power dissipated rises with the square of current, which is why a 25% overload produces 56% more heat, and why almost every electrical failure is a heat failure.
The two statements
V = I × R. Push harder and more current flows. Add resistance and less does. Georg Ohm published it in 1827 after measuring wires of different lengths, which is the same experiment as measuring voltage drop.
P = V × I. Power is the rate of energy transfer: how much voltage, moved through how much current.
Everything else is substitution. Put the first into the second and you get P = I² × R. Put it in the other direction and you get P = V² ÷ R.
The wheel, written out
| To find | Formula | Formula | Formula |
|---|---|---|---|
| Volts | V = I × R | V = P ÷ I | V = √(P × R) |
| Amps | I = V ÷ R | I = P ÷ V | I = √(P ÷ R) |
| Ohms | R = V ÷ I | R = V² ÷ P | R = P ÷ I² |
| Watts | P = V × I | P = I² × R | P = V² ÷ R |
Why P = I²R explains everything
This one substitution is why the trade has ampacity tables, torque specifications and thermal imaging cameras.
A loose terminal. A slightly loose screw might add a tenth of an ohm. At 20 amps that is 0.1 × 400 = 40 watts in the volume of a screw head — comparable to a soldering iron. The connection gets hot, oxidises, resistance rises, and it accelerates. This is the mechanism behind almost every burnt receptacle.
An overloaded conductor. 25% more current is 56% more heating, not 25%. Nothing about overload is gentle, which is why a circuit can be fine for years and then fail in a week when one more load is added.
Voltage drop as wasted energy. The volts lost in a long run are I × R and the watts wasted are I²R, turned into heat along the way and paid for on the meter.
Why a fuse works at all. A fuse is a deliberately resistive element sized so that I²R melts it before the same current damages anything else. It is Ohm’s law used as a safety device.
Where it stops
Ohm’s law describes materials whose resistance is constant. Three common things are not:
Filament lamps. A cold tungsten filament has roughly a tenth of its hot resistance, which is why incandescent bulbs draw an inrush and fail at switch-on.
Semiconductors. An LED conducts almost nothing below its forward voltage and then almost anything above it, which is why LEDs need a current-limiting driver rather than a voltage.
Arcs. An arc’s resistance falls as current rises, which is why an arc fault escalates and why arc-fault detection is a separate technology from overcurrent protection.
Put your own numbers in on the Ohm’s law calculator — pick any two of the four and it returns the other two.
Frequently asked questions
What is the Ohm's law triangle?
A memory device. V sits at the top, I and R at the bottom: cover the quantity you want and the remaining arrangement is the formula. Cover V and you have I × R; cover I and you have V over R. The wheel is the same idea extended to four quadrants so watts are included.
What are the twelve Ohm's law formulas?
Three for each quantity. Volts: V = IR, V = P/I, V = √(PR). Amps: I = V/R, I = P/V, I = √(P/R). Ohms: R = V/I, R = V²/P, R = P/I². Watts: P = VI, P = I²R, P = V²/R. All twelve are rearrangements of V = IR and P = VI, so there are really two.
Does Ohm's law apply to AC?
For resistive loads, exactly. For circuits with inductance or capacitance, resistance is replaced by impedance and voltage and current stop peaking together, which is where power factor comes from. Ohm’s law still holds — it just needs complex numbers. On a heating element it is precise as written.
Why is it called a law if it does not always apply?
Because it describes ohmic materials, and most metals at ordinary temperatures are ohmic. Semiconductors, gas discharge lamps, arcs and batteries are not: their resistance changes with the current through them. It is a law about a class of material rather than about electricity in general, which is why an LED does not obey it and a resistor does.
How do I remember which formula to use?
Do not. Remember V = IR and P = VI, and rearrange. Two facts you can derive from are more reliable than twelve you have to recall correctly, and the derivation takes about four seconds once you have done it a dozen times.
How we calculate this
V = I × R and the power law is P = V × I; the twelve commonly quoted formulas are substitutions
between the two. All arithmetic on this page treats resistance as a real number, which is exact for direct current
and for purely resistive alternating-current loads. Circuits containing inductance or capacitance require
impedance in place of resistance, introducing a phase angle between voltage and current — the ratio of real to
apparent power that results is the power factor used in the
conversion calculators. Ohm’s law describes ohmic conductors; semiconductor junctions,
arcs and gas discharges have current-dependent resistance and do not follow it.Sources: