Ohm's Law is the single most useful equation in electronics. It ties together the three quantities you measure most often: the voltage across a component, the current through it, and its resistance. Almost every DC calculation you will ever do starts here.
The equation
For an ideal resistor, the current is directly proportional to the voltage across it. The constant of proportionality is the resistance:
V = I × R
You can rearrange it to solve for whichever quantity you are missing. All three forms describe the same relationship:
I = V / R R = V / I
- V is voltage in volts (V) — the potential difference across the resistor.
- I is current in amperes (A) — the flow of charge through it.
- R is resistance in ohms (Ω) — how strongly the component opposes that flow.
A worked example
Put 9 V across a 470 Ω resistor. How much current flows? Rearrange to I = V / R:
I = 9 V / 470 Ω ≈ 0.0191 A ≈ 19.1 mA
The relationship is inverse in R: if you halve the resistance to 235 Ω, the current doubles to about 38 mA. If you double the voltage to 18 V, the current also doubles. This proportional intuition is worth more than the algebra — most of the time you just need to know which way a number moves.
Power dissipation
A resistor turns electrical energy into heat. The power it dissipates follows directly from Ohm's Law:
P = V × I = I² × R = V² / R
For our example, P = 9 V × 0.0191 A ≈ 0.172 W, or about 172 mW. That comfortably fits a standard 1/4 W (250 mW) resistor. Sizing for power is exactly how components get destroyed when it is overlooked.
Where it breaks down
Ohm's Law applies cleanly to resistors and other ohmic elements. Diodes, LEDs, transistors and other semiconductors are non-linear — their current does not scale linearly with voltage — so you cannot treat them as a fixed resistance. You will still use V = I × R for the resistors surrounding them, which is exactly how a current-limiting resistor for an LED gets sized.