Ohm’s Law: V = IR
Ohm’s Law is to electrical engineering what F = ma is to mechanical. Three variables, one equation, and an enormous amount of practical power.
What It Means
- V — Voltage (volts, V) — the “pressure” pushing electrons through a circuit
- I — Current (amps, A) — the flow rate of electrons
- R — Resistance (ohms, Ω) — how much the circuit resists that flow
Think of it like water in a pipe. Voltage is the water pressure, current is the flow rate, and resistance is how narrow the pipe is. More pressure (voltage) pushes more water (current) through the same pipe. A narrower pipe (higher resistance) reduces flow for the same pressure.
Three Ways to Write It
V = I × R | I = V / R | R = V / I
Know any two, calculate the third. This is the most-used equation in electronics.
Power: Where It Gets Useful
Electrical power (watts) is voltage times current:
P = V × I
Combine with Ohm’s Law and you get three equivalent power equations:
- P = V × I — know voltage and current
- P = I² × R — know current and resistance (substitute V = IR)
- P = V² / R — know voltage and resistance (substitute I = V/R)
P = I²R is especially important because it tells you that power loss in a wire increases with the square of the current. This is why power lines run at high voltage — reducing current dramatically reduces transmission losses.
Practical Examples
Example 1: LED Resistor Sizing
You want to power a red LED (2V forward voltage, 20mA) from a 12V supply. What resistor do you need?
- Voltage across resistor: 12 – 2 = 10V
- R = V / I = 10 / 0.020 = 500Ω (use standard 470Ω or 510Ω)
- Power dissipated: P = I²R = 0.020² × 500 = 0.2W — a ¼W resistor works
Example 2: Wire Sizing
A 12V pump draws 10A through 50 feet of wire (100 ft total round-trip). 14 AWG wire has 2.525 Ω/1000ft resistance.
- Wire resistance: 100 × 2.525/1000 = 0.253 Ω
- Voltage drop: V = IR = 10 × 0.253 = 2.53V drop (21% loss!)
- Power wasted as heat: P = I²R = 100 × 0.253 = 25.3W
- Solution: Use 10 AWG (1.0 Ω/1000ft) → 1.0V drop (8%), 10W loss
Example 3: Household Circuit
A 120V circuit with a 15A breaker. What’s the maximum load?
- P = V × I = 120 × 15 = 1,800W maximum
- NEC recommends loading to 80%: 1,440W continuous
- That’s why a 1,500W space heater trips a shared circuit — it’s already at the limit
Series vs. Parallel
Series: Resistances add. Rtotal = R₁ + R₂ + R₃. Current is the same through each. Voltage divides.
Parallel: Conductances add. 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃. Voltage is the same across each. Current divides.
Quick trick for two parallel resistors: Rtotal = (R₁ × R₂) / (R₁ + R₂)
Key Takeaways
- V = IR relates voltage, current, and resistance — know two, find the third
- P = I²R means power loss grows with the square of current — doubling current quadruples heat
- This is why long wire runs need thicker gauge and why power transmission uses high voltage
- Ohm’s Law applies to DC circuits directly; AC adds impedance (resistance + reactance) but the concept is identical