Ohm's Law Formula
Ohm's Law relates voltage, current, and resistance: V = IR.
Includes power variations and practical examples for circuit analysis.
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.
Variables
| Symbol | Meaning |
|---|---|
| V | Voltage (measured in volts, V) |
| I | Current (measured in amperes, A) |
| R | Resistance (measured in ohms, Ω) |
Power Variations
P = I² × R
P = V² / R
By combining Ohm's Law with the power formula (P = VI), you can express electrical power in three different ways. This is useful when you only know two of the three quantities.
Rearranged Forms
| To Find | Formula |
|---|---|
| Voltage | V = I × R |
| Current | I = V / R |
| Resistance | R = V / I |
Example 1
A 12V battery is connected to a 4Ω resistor. What current flows through it?
Identify the values: V = 12 V, R = 4 Ω
Rearrange for current: I = V / R
I = 12 / 4
I = 3 A
Example 2
A heater draws 10 A from a 230 V supply. What is its resistance and power?
Resistance: R = V / I = 230 / 10 = 23 Ω
Power: P = V × I = 230 × 10
R = 23 Ω, P = 2,300 W (2.3 kW)
When to Use It
Use Ohm's Law whenever you need to analyze electrical circuits:
- Calculating current draw for a given voltage and resistance
- Sizing resistors for LED circuits or voltage dividers
- Determining power consumption of electrical devices
- Troubleshooting circuits by comparing measured and expected values
Key Notes
- Formula: V = IR; I = V/R; R = V/I: Ohm's law holds for ohmic materials at constant temperature. A graph of V vs I is a straight line through the origin; the slope equals resistance R.
- Microscopic form: J = σE: Current density J (A/m²) equals conductivity σ times electric field E. This connects the macroscopic (circuit) and microscopic (material) descriptions of conduction. Resistivity ρ = 1/σ; R = ρL/A.
- Temperature dependence: Resistance of metals increases with temperature: R(T) = R₀(1 + αΔT), where α is the temperature coefficient. Semiconductors behave oppositely — resistance decreases with temperature. This is why thermistors (temperature-sensitive resistors) are used as temperature sensors.
- Non-ohmic devices: Diodes, LED lights, and thermistors do not obey Ohm's law — their V-I relationship is nonlinear. The "resistance" of such devices varies with voltage or current and must be read from a characteristic curve rather than calculated from a fixed R.
- Applications: Ohm's law is the foundation of circuit analysis: calculating current through resistors, sizing fuses and circuit breakers, designing voltage regulators, analyzing sensor output voltages, and understanding power dissipation in electronic components.