Ohm’s law is the single most useful relationship in electronics. It ties together the three quantities you measure most often — voltage, current, and resistance — so that if you know any two, you can find the third.
The three quantities
Before the formula makes intuitive sense, it helps to picture what each term actually describes. The classic analogy is water flowing through a pipe.
| Quantity | Symbol | Unit | Water analogy |
|---|---|---|---|
| Voltage | V | volts (V) | Water pressure pushing the flow |
| Current | I | amperes (A) | How much water flows per second |
| Resistance | R | ohms (Ω) | How narrow the pipe is |
Raise the pressure (voltage) and more water flows (current). Narrow the pipe (more resistance) and less water flows. That is Ohm’s law in plain language: current is proportional to voltage and inversely proportional to resistance.
Rearranging the formula
You will rarely solve for voltage every time — sometimes you know the voltage and resistance and want the current. The same equation rearranges three ways:
- Find voltage:
V = I × R - Find current:
I = V ÷ R - Find resistance:
R = V ÷ I
A worked example
Say you are driving an LED that needs about 20 mA from a 9 V battery, and you want the series resistor value. First convert 20 mA to amps: 0.02 A. Then:
A 470 Ω resistor (the nearest standard value) is the safe choice. In practice you would subtract the LED’s forward voltage first, but the calculation method is identical — that is the whole point of the law.
Power: the fourth quantity
Ohm’s law pairs naturally with the power equation, P = V × I. Substituting Ohm’s law gives two more handy forms — useful for picking a resistor’s wattage rating so it doesn’t overheat:
P = I² × RP = V² ÷ R
When it doesn’t apply
Ohm’s law assumes a linear relationship between voltage and current. That holds for resistors and most wiring at a stable temperature. It breaks down for components whose resistance changes with conditions — diodes, transistors, thermistors, and incandescent bulbs. For those, the instantaneous V/I ratio still exists, but it is not a fixed constant you can plug into a single calculation.
Resistors in series and parallel
Real circuits rarely have a single resistor, so two rules let you reduce a network to one equivalent value and then apply Ohm’s law to the whole thing.
- In series (one after another), resistances simply add:
R_total = R₁ + R₂ + R₃…. The same current flows through each, and the supply voltage divides between them in proportion to their size — the idea behind a voltage divider. - In parallel (side by side), the reciprocals add:
1/R_total = 1/R₁ + 1/R₂…. Every branch sees the full voltage, and the total resistance is always smaller than the smallest branch, because you have given the current more paths to flow through.
A quick sanity check: two equal resistors in series double the resistance; the same two in parallel halve it. Once you have the equivalent resistance, the current the source delivers is just I = V ÷ R_total.
Common mistakes to avoid
Three slip-ups account for most wrong answers. First, mixing up units — milliamps and amps, or kilohms and ohms — throws the result off by a factor of a thousand; convert everything to volts, amps and ohms before calculating. Second, using the wrong voltage: Ohm’s law uses the voltage across the specific component, not always the full supply voltage. Third, forgetting power: a resistor that is electrically correct can still overheat if you do not check that its wattage rating comfortably exceeds the P = V × I it will dissipate.
Frequently asked questions
What are the three forms of Ohm’s law?
V = I × R to find voltage, I = V ÷ R to find current, and R = V ÷ I to find resistance. They are the same equation rearranged.
Does Ohm’s law work for every component?
No. It holds for ohmic (linear) components like resistors at a fixed temperature. Diodes, transistors, and lamps are non-ohmic — their resistance changes with voltage or temperature.
What units do I use?
Volts (V) for voltage, amperes (A) for current, and ohms (Ω) for resistance. Keep units consistent — convert milliamps to amps before calculating.
How do resistors add up in series and parallel?
In series they simply add: R_total = R₁ + R₂ + … In parallel the reciprocals add: 1/R_total = 1/R₁ + 1/R₂ + …, so the total is always smaller than the smallest branch. Reduce the network to one value, then apply Ohm’s law to the whole circuit.
How is Ohm’s law related to power?
Power is voltage times current: P = V × I. Combining it with Ohm’s law gives two more handy forms, P = I² × R and P = V² ÷ R, which let you find the heat a resistor dissipates so you can pick one with a high enough wattage rating.