Reference data and planning arithmetic. Does not apply ambient or bundling derating, motor rules, or local amendments. Not a substitute for the NEC edition your jurisdiction has adopted, an inspection, or a licensed electrician.
The four relationships
V = I × R I = V ÷ R R = V ÷ I P = V × I
Ohm's law proper is the first three — voltage equals current times resistance. The fourth is Joule's law and combines with it to give P = I²R and P = V²/R, both useful when you know the resistance and one other quantity.
| Known | Solving for | Formula | Result |
|---|---|---|---|
| 120 V across 12 Ω | Current | I = V ÷ R | 10.00 A |
| 10 A through 12 Ω | Voltage | V = I × R | 120 V |
| 120 V drawing 10 A | Resistance | R = V ÷ I | 12 Ω |
| 120 V drawing 10 A | Power | P = V × I | 1200 W |
| 20 A through 0.2 Ω of wire | Heat in the wire | P = I²R | 80 W |
| 40 A through the same wire | Heat in the wire | P = I²R | 320 W — four times |
Where P = I²R explains real behaviour
Power loss in a conductor is I²R, and the square is the interesting part: doubling the current quadruples the heat.
That single relationship explains a lot of practical electrical work. It is why a loose connection burns — contact resistance rises, and the heat at that point rises with it until something fails. It is why transmission runs at high voltage: for the same power, higher voltage means lower current, and lower current means far lower loss. It is why an undersized extension cord on a heater gets warm along its whole length rather than just at the ends.
Where Ohm's law stops being enough
Ohm's law describes resistive DC behaviour. Real AC circuits need more:
- Inductive and capacitive loads have reactance as well as resistance, and the combination is impedance. Motors and transformers are inductive.
- Power factor means V × I gives volt-amps rather than watts.
- Non-linear loads — electronics, LED drivers, variable-frequency drives — do not have a constant resistance at all, and draw current in pulses rather than smoothly.
For sizing conductors, calculating voltage drop and understanding heat in a resistive circuit, Ohm's law is exactly the right tool. For anything with a motor or a power supply in it, it is a first approximation.
Common questions
What is Ohm's law?
Voltage equals current times resistance: V = I x R. Rearranged, I = V/R and R = V/I. Power is a separate relationship, P = V x I.
How do I find amps from volts and ohms?
Divide volts by ohms. A 120 V supply across a 12 ohm load draws 10 A, which is 1,200 W.
Why does doubling current quadruple the heat?
Power loss in a conductor is I²R — proportional to the square of the current. Double the current and the I² term goes up four times. It is why loose connections burn and why undersized wire overheats.