The law
For a resistor, the current is proportional to the voltage across it, and the constant of proportionality is the resistance. Rearranged, it answers any of three questions: the current a voltage drives, the voltage a current needs, or the resistance a measurement implies.
V = I·R I = V / R R = V / I
Power
The power a resistor turns into heat is the voltage times the current. Substituting Ohm’s law gives two more forms; pick the one that uses the quantities you know.
P = V·I = I²·R = V² / R
Reading the I-V graph
Plot current against voltage for a resistor and you get a straight line through the origin with slope 1/R: a steeper line is a smaller resistance. The operating point is where the present voltage sits on that line. Components whose I-V curve is not straight, such as diodes and lamps, are non-ohmic.
Worked example (the simulator’s default values)
- V = 9 V across R = 220 Ω.
- I = 9/220 = 40.9 mA.
- P = 9 × 0.0409 = 0.368 W: a standard ¼ W resistor would overheat, so use a ½ W part.
Common mistakes
- Mixing units: 9 V / 220 kΩ is 40.9 µA, not 40.9 mA. Convert kΩ and mA before dividing.
- Forgetting the power rating. The value can be right and the resistor still burn out.
- Applying Ohm’s law to a whole circuit with the wrong R: use the voltage across, and the current through, the same component.
Common questions
What is Ohm's law?
V = I·R: the voltage across a resistor equals the current through it times its resistance. Doubling the voltage doubles the current; doubling the resistance halves it.
How do you calculate power in a resistor?
P = V·I, or equivalently I²·R or V²/R. A 220 Ω resistor on 9 V dissipates 0.368 W.