Ohm’s law states that the current through a linear resistive element is directly proportional to the voltage across it and inversely proportional to its resistance, V = I × R, at constant temperature.
Learning objectives
- State Ohm’s law and write it in three equivalent forms.
- Use the formula triangle to calculate voltage, current or resistance.
- Apply the power relationships derived from Ohm’s law.
- Recognise the conditions and limits of the law.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
A useful memory aid is the triangle. Write V at the top, I and R below. Cover the quantity you want: covering V leaves I × R; covering I leaves V over R; covering R leaves V over I. For example, 12 V across 6 Ω gives 2 A, and 12 V across 24 Ω gives 0.5 A.
Intermediate How it behaves in a circuit
The law is used together with power relationships. Since P = V × I, substitution gives P = I²R and P = V²/R. These forms are useful when only one electrical quantity and the resistance are known. For example, a 12 Ω resistor carrying 2 A dissipates I²R = 4 × 12 = 48 W, and a 24 Ω resistor with 12 V across it dissipates V²/R = 144/24 = 6 W.
Advanced Limits, assumptions, engineering detail
For AC circuits, the resistance is replaced by impedance, V = I × Z, where Z includes reactance and the relationship involves phase. At high frequencies, skin effect and parasitic elements also change the effective opposition to current. Material resistivity and geometry still explain resistance, but the simple scalar equality V = IR becomes a phasor relationship for reactive circuits and a local field relationship when dimensions approach the signal wavelength.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | volt (V) |
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
| Power | P | watt (W) |
Worked examples
Current through a resistor
Problem. A 12 V source is connected across a 6 Ω resistor. Find the current.
Solution. I = V / R = 12 V / 6 Ω = 2 A. The power is P = V × I = 12 × 2 = 24 W.
Resistance from voltage and current
Problem. A component has 230 V across it and carries 5.0 A. Find its resistance and the power dissipated.
Solution. R = V / I = 230 / 5.0 = 46 Ω. P = V × I = 230 × 5.0 = 1,150 W.
Practical applications
- Selecting series resistors for LEDs and sensors
- Calculating cable and connector voltage drop
- Checking fuse and resistor power ratings
- Diagnosing circuits with voltage and current measurements
Automotive applications
Technicians use Ohm’s law constantly: a 12 V circuit feeding a 3 Ω load draws 4 A, and a 0.1 Ω connection carrying 20 A drops 2 V and dissipates 40 W. In diagnostics, measuring voltage across a known resistance, or current through a known load, allows the other quantity to be calculated. The law assumes the measured component is resistive and at a stable temperature, which is not true for lamps, motors and electronic modules.
Industrial applications
Ohm’s law underpins cable sizing and protection coordination. A long cable with resistance R drops I × R volts and dissipates I²R watts, heating the conductor. Industrial checks often combine the law with temperature derating: the resistance of a copper conductor rises with temperature, so the voltage drop at operating temperature is higher than at the reference temperature used in a simple calculation.
Measurement procedure
- Measure voltage across the component and current through it at the same operating point, then calculate R = V/I.
- Account for meter loading: a voltmeter in parallel draws a small current that can matter in high-resistance circuits.
- For non-linear components, record the voltage and current together; a single resistance value is not valid across the whole range.
- Verify the power rating of the resistor from P = V × I before testing, so the component is not overheated.
Common mistakes
- Applying Ohm’s law to non-ohmic devices such as diodes or lamps and expecting a constant resistance.
- Mixing units, for example using milliamperes with ohms and expecting volts.
- Using the voltage of the source instead of the voltage across the specific element.
- Ignoring temperature rise and self-heating, which change resistance under load.
Safety considerations
- Check the power rating of resistors; a resistor can reach high temperature or fail if undersized.
- Do not assume the law makes a circuit safe: a low resistance can produce a very high current from a low voltage source.
- Work de-energised where possible and use meters rated for the circuit voltage.