Ohm's Law Formula
Reference for Ohm's law (V=IR) — the fundamental relationship between voltage, current, and resistance.
Covers power forms P=IV and P=I^2*R with examples.
The Formula
Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it.
The constant of proportionality is the resistance.
This is the most fundamental formula in electrical engineering.
Variables
| Symbol | Meaning |
|---|---|
| V | Voltage (Volts, V) |
| I | Current (Amperes, A) |
| R | Resistance (Ohms, Ω) |
Rearranged Forms
- V = I × R — find voltage when you know current and resistance
- I = V / R — find current when you know voltage and resistance
- R = V / I — find resistance when you know voltage and current
Example 1
A 12 V battery drives current through a 4 Ω resistor. What is the current?
I = V / R
I = 12 V / 4 Ω
I = 3 A
Example 2
A circuit carries 0.5 A through a 220 Ω resistor. What is the voltage drop across the resistor?
V = I × R
V = 0.5 A × 220 Ω
V = 110 V
When to Use It
Use Ohm's law when you need to:
- Calculate any one of voltage, current, or resistance when you know the other two
- Analyse simple DC circuits
- Size resistors for LED circuits or voltage dividers
- Troubleshoot electrical faults by measuring and comparing values
Ohm's law applies to resistive (ohmic) components where resistance is constant.
It does not directly apply to non-linear components like diodes or transistors.
Key Notes
- Formula: V = IR (I = V/R; R = V/I): Voltage (V) equals current (I) times resistance (R). Ohm's law holds only for ohmic conductors at constant temperature. Most metals are ohmic; diodes, LEDs, and transistors are not.
- Non-ohmic devices: A diode passes current in one direction only and has an exponential V-I relationship, not a straight line. A light bulb's filament has increasing resistance as it heats — its resistance when lit is ~10× higher than when cold.
- Three power formulas: P = VI = I²R = V²/R: All derived by combining P = VI with V = IR. These are used to calculate heat dissipation in resistors, power loss in cables (P = I²R — the reason high-voltage transmission minimizes I), and maximum component ratings.
- Resistivity: R = ρL/A: Resistance increases with material resistivity ρ and wire length L, and decreases with cross-sectional area A. Copper (ρ ≈ 1.7×10⁻⁸ Ω·m) and silver (ρ ≈ 1.6×10⁻⁸ Ω·m) are the best common conductors.
- Applications: Ohm's law is used to size resistors in circuits, calculate fuse ratings (maximum safe I = V/R), design voltage dividers, determine cable gauge for safe current-carrying capacity, and troubleshoot electrical faults.