Ohm's Law Explained: Voltage, Current, and Resistance
The three-way relationship at the heart of every electrical circuit, explained with a worked example and power calculation.
Ohm's Law is the single most foundational relationship in electronics — nearly every basic circuit calculation eventually reduces to some rearrangement of this one equation.
The formula
V = I × R
where V is voltage (volts), I is current (amps), and R is resistance (ohms). Because it's a simple multiplicative relationship between three variables, knowing any two always lets you solve for the third: I = V/R, or R = V/I.
Worked example
A circuit with 2 amps of current flowing through a 10-ohm resistor: V = 2 × 10 = 20 volts dropped across that resistor. If instead you knew the voltage (20V) and resistance (10Ω) but not the current, you'd rearrange to I = V/R = 20/10 = 2A — same relationship, different starting point.
Power: the fourth variable
Power (in watts) follows directly from Ohm's Law: P = I²R (or equivalently P = VI = V²/R). That same 2A through 10Ω dissipates P = 2² × 10 = 40 watts as heat. This is why resistor power ratings matter in circuit design — a resistor rated for only 25 watts would overheat and likely fail carrying that same 40 watts, even though the voltage and current values alone seem unremarkable.
Why doubling current quadruples power, not just doubles it
Because power depends on current squared (P = I²R), doubling the current doesn't double power dissipation — it quadruples it. Push 4A instead of 2A through that same 10Ω resistor: P = 4² × 10 = 160 watts, four times the original 40W, despite only doubling the current. This squared relationship is exactly why even modest current increases in underrated wiring can cause dramatically more heating than expected.
A worked voltage divider example
Voltage dividers use Ohm's Law across two series resistors to produce a fraction of an input voltage: Vout = Vin × R2/(R1+R2). A 12V supply split across a 1kΩ and 2kΩ pair in series gives Vout = 12 × 2000/3000 = 8V measured at the junction between them — a simple, component-free way to scale a voltage down for a sensor or reference circuit.
Common mistakes to avoid
- Mixing up which resistor is R1 vs. R2 in a voltage divider — swapping them changes the output voltage entirely, since the formula isn't symmetric
- Forgetting that Ohm's Law in this simple form applies to resistive (not reactive/AC) circuits — inductors and capacitors need a more general impedance-based version
- Underestimating power dissipation because "the voltage and current both seem small" — always calculate power explicitly rather than eyeballing it, given its squared relationship to current
Solve your own circuit with the Ohm's Law calculator, voltage divider calculator, or power calculator.