Ohm’s Law Formulas and Power Wheel
Ohm’s law formulas for voltage, current, resistance and power: all twelve forms in one table, worked examples, and values at 12 V.
The twelve formulas
| To find | Formula 1 | Formula 2 | Formula 3 |
|---|---|---|---|
| Voltage | V = I × R | V = P / I | V = √(P × R) |
| Current | I = V / R | I = P / V | I = √(P / R) |
| Resistance | R = V / I | R = V² / P | R = P / I² |
| Power | P = V × I | P = I² × R | P = V² / R |
Read across: each row gives the quantity three ways. V is voltage in volts, I current in amperes, R resistance in ohms and P power in watts.
Worked example: 12 V across 4 Ω
- I = V / R = 12 / 4 = 3 A
- P = V × I = 12 × 3 = 36 W
- Check: I² × R = 9 × 4 = 36 W, and V² / R = 144 / 4 = 36 W
Worked example: a 60 W lamp on 230 V
- I = P / V = 60 / 230 = 0.2609 A
- R = V² / P = 52,900 / 60 = 881.7 Ω (hot)
A filament lamp measures much less when cold, because its resistance rises with temperature.
Current and power at 12 V
| Resistance | Current | Power |
|---|---|---|
| 1 Ω | 12 A | 144 W |
| 10 Ω | 1.2 A | 14.4 W |
| 100 Ω | 0.12 A | 1.44 W |
| 1,000 Ω | 0.012 A | 0.144 W |
| 10,000 Ω | 0.0012 A | 0.0144 W |
Series and parallel
In series the same current flows through every resistor and the resistances add. In parallel every resistor has the same voltage and the conductances (1/R) add. Both follow from Kirchhoff’s laws.
Frequently asked questions
What is Ohm’s law?
The current through a resistor is proportional to the voltage across it: V = I × R. With volts, amperes and ohms, 12 V across 4 Ω drives 3 A.
How do I find power from voltage and resistance?
P = V² / R. For 12 V across 4 Ω that is 144 / 4 = 36 W. The same power is V × I = 12 × 3 and I² × R = 9 × 4.
Does Ohm’s law work for AC?
For a purely resistive load, yes, with RMS values. For loads with inductance or capacitance, resistance becomes impedance Z and the power also depends on the power factor.
Which materials do not follow Ohm’s law?
Diodes, LEDs, lamp filaments (whose resistance rises as they heat) and other non-linear parts. Their current is not proportional to voltage.
Related
Kirchhoff’s LawsResistor Color CodeOhm’s Law CalculatorVoltage Divider CalculatorConversion Centre