The formula
Ohm's law links the three basic quantities of a circuit:
V = I × R
V is the voltage in volts, I the current in amps and R the resistance in ohms (Ω). Rearranged, I = V ÷ R and R = V ÷ I, so knowing any two gives the third.
Power
The power turned into heat, in watts, follows from the same quantities:
P = V × I = I² × R = V² ÷ R
A worked example
A 220 Ω resistor sits across a 12 V supply.
- Current: I = 12 ÷ 220 = 0.0545 A, or 54.5 mA.
- Power: P = 12 × 0.0545 = 0.65 W.
A common ¼ W resistor would overheat here. Choose a resistor rated for at least about twice the power it dissipates, so a 1 W part or larger.
Calculating a voltage
A current of 20 mA through a 470 Ω resistor drops V = 0.020 × 470 = 9.4 V across it. This is how a series resistor sets the current through an LED: R = (supply voltage − LED voltage) ÷ current.
Resistors in series and parallel
- Series: resistances add. 100 Ω + 220 Ω = 320 Ω.
- Parallel: 1 ÷ R = 1 ÷ R1 + 1 ÷ R2. Two 100 Ω resistors in parallel make 50 Ω.
Where it applies
Ohm's law holds for resistors and wires at a steady temperature. LEDs, diodes and lamps do not follow it in a straight line, and in AC circuits with coils or capacitors the resistance becomes impedance, which also depends on frequency.
Calculators
The Ohm's Law Calculator finds the missing value and the power from any two. The Voltage Divider Calculator, LED Resistor Calculator and Series and Parallel Resistor Calculator cover the most common circuits built on it.