Ohm's Law Guide: The Complete Electrical Formula Reference
Ohm's Law: The Foundation of Electrical Engineering
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This fundamental relationship governs every electrical circuit from a flashlight to a power grid.
Three forms of Ohm's Law:
- V = I × R — Voltage (volts) = Current (amps) × Resistance (ohms)
- I = V / R — Current = Voltage ÷ Resistance
- R = V / I — Resistance = Voltage ÷ Current
The Ohm's Law Triangle
The triangle mnemonic helps remember all three forms. Cover the variable you want to find:
- Cover V → I × R remains
- Cover I → V / R remains
- Cover R → V / I remains
Power Formulas
Power (watts) combines voltage and current with Ohm's Law:
- P = V × I — Power = Voltage × Current
- P = I² × R — Power = Current² × Resistance
- P = V² / R — Power = Voltage² ÷ Resistance
Common Values Reference
| Circuit | Voltage | Current | Resistance | Power |
|---|---|---|---|---|
| 120V / 15A circuit | 120V | 15A | 8Ω | 1,800W |
| 120V / 20A circuit | 120V | 20A | 6Ω | 2,400W |
| 240V / 30A dryer | 240V | 30A | 8Ω | 7,200W |
| 240V / 50A range | 240V | 50A | 4.8Ω | 12,000W |
| 12V car battery | 12V | 100A (cranking) | 0.12Ω | 1,200W |
| 5V USB charger | 5V | 2.4A | 2.08Ω | 12W |
| LED bulb (10W equiv) | 120V | 0.083A | 1,440Ω | 10W |
DC vs AC: When Ohm's Law Applies
Ohm's Law works directly for:
- DC circuits: Always applicable. V, I, R are scalar values.
- AC resistive loads: Incandescent bulbs, electric heaters, toasters. Use RMS values.
- AC reactive loads: Motors, transformers, capacitors. Use impedance Z instead of R: V = I × Z, where Z = √(R² + (XL − XC)²)
NEC Wire Sizing with Ohm's Law
Ohm's Law determines wire size through ampacity and voltage drop:
Ampacity: Wire must handle I = P / V. A 2,400W load on 120V draws 20A → need 12 AWG (rated 20A at 60°C).
Voltage drop: Vdrop = I × R × 2 (round trip). NEC recommends <3% for branch circuits. For a 20A, 100-ft run on 12 AWG: Vdrop = 20 × 0.00193 × 200 = 7.72V (6.4% — too much, need 10 AWG).
Worked Examples
Example 1: Find Current
A 1,500W space heater operates on 120V. What current does it draw?
I = P / V = 1,500 / 120 = 12.5A. Needs a 15A circuit (12 AWG wire minimum).
Example 2: Find Resistance
A 100W bulb on 120V has what resistance?
R = V² / P = 120² / 100 = 14,400 / 100 = 144Ω
Example 3: Voltage Drop
A 15A load runs through 150 ft of 14 AWG copper (2.525Ω/1000ft). What's the voltage drop?
Rwire = 2.525 × 300/1000 = 0.7575Ω (300 ft round trip)
Vdrop = 15 × 0.7575 = 11.36V (9.5% — way over 3% limit, need 10 AWG)
Common Mistakes
- Confusing RMS and peak: Household 120V is RMS. Peak = 120 × √2 = 170V. Always use RMS for Ohm's Law in AC.
- Ignoring power factor: For motors, Pactual = V × I × PF. A motor drawing 10A at 120V with PF 0.8 uses 960W, not 1,200W.
- Using resistance at operating temp: Copper resistance increases 0.39% per °C. A wire at 75°C has 29% more resistance than at 20°C.
- Forgetting round-trip for voltage drop: Current flows out AND back. Double the one-way wire length.
Standards Reference
- NEC Article 310 — Conductors for General Wiring
- NEC Article 210 — Branch Circuits
- IEC 60364 — Low-voltage Electrical Installations
- IEEE Standard 141 — Electric Power Distribution
Frequently Asked Questions
What is Ohm's Law?
Ohm's Law states V = I × R: voltage equals current times resistance. It describes the relationship between voltage (electrical pressure), current (flow of electrons), and resistance (opposition to flow). It's the most fundamental equation in electrical engineering.
Does Ohm's Law apply to AC circuits?
Yes, but with a caveat. For purely resistive loads (heaters, incandescent bulbs), use V = IR directly with RMS values. For reactive loads (motors, transformers), use impedance Z instead of resistance R: V = I × Z, where Z = √(R² + (X_L − X_C)²).
What are the 12 formulas of Ohm's Law?
The 12 formulas combine the 4 quantities (V, I, R, P) in all useful ways: V=IR, V=P/I, V=√(PR); I=V/R, I=P/V, I=√(P/R); R=V/I, R=P/I², R=V²/P; P=VI, P=I²R, P=V²/R.
How do I use Ohm's Law for wire sizing?
First find current: I = P / V. Then check NEC ampacity tables (Table 310.16) for the wire gauge that handles that current. Finally verify voltage drop: V_drop = I × R × 2 × length / 1000. NEC limits voltage drop to 3% for branch circuits.
What happens if resistance is zero?
If R = 0, then I = V / 0 = infinity (in theory). In practice, this is a short circuit — massive current flows, limited only by the source impedance and wire resistance. This is why we need circuit breakers: to interrupt the circuit before the current causes a fire.