Electrical resistance is the property of a component or material that opposes the flow of electric current, defined by R = V/I and measured in ohms. For a uniform conductor it depends on material resistivity, length and cross-sectional area.
Learning objectives
- Define resistance and state the meaning of one ohm.
- Calculate resistance from voltage and current.
- Calculate conductor resistance from resistivity, length and area.
- Explain how temperature and material affect resistance.
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
Resistance converts electrical energy into heat. That is how an electric heater, a incandescent lamp or a fuse works, and it is also why cables warm up when they carry current. In most circuits we want resistance to be predictable: resistors set currents and voltages, while unwanted resistance in connections and cables causes voltage drop and heat.
Intermediate How it behaves in a circuit
Resistance changes with temperature. For modest temperature changes, R ≈ R₀[1 + α(T − T₀)], where α is the temperature coefficient. Metals generally have a positive coefficient, so their resistance rises as they heat. Resistance also depends on frequency in some materials and geometries because of skin effect and proximity effect, but at DC and low frequencies these effects are usually small.
Advanced Limits, assumptions, engineering detail
Real resistors have tolerance, temperature coefficient, voltage coefficient and power rating. They also have parasitic inductance and capacitance, so their impedance becomes frequency-dependent. Four-terminal (Kelvin) measurement removes lead and contact resistance when measuring very low values, while guard techniques are used for very high values. In circuit analysis, resistance is treated as an ideal linear element, but a real resistor is a distributed, temperature-dependent component.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Resistance | R | ohm (Ω) |
| Resistivity | ρ | ohm-metre (Ω·m) |
| Conductance | G | siemens (S) |
| Temperature coefficient | α | per kelvin (1/K) |
Worked examples
Resistance from a voltage and current measurement
Problem. A component has 9.0 V across it while carrying 30 mA. What is its resistance?
Solution. R = V / I = 9.0 V / 0.030 A = 300 Ω.
Resistance of a copper conductor
Problem. Find the resistance of 20 m of copper wire with a cross-sectional area of 1.5 mm². Take ρ = 1.68 × 10⁻⁸ Ω·m.
Solution. A = 1.5 mm² = 1.5 × 10⁻⁶ m². R = ρL/A = 1.68 × 10⁻⁸ × 20 / 1.5 × 10⁻⁶ = 3.36 × 10⁻⁷ / 1.5 × 10⁻⁶ = 0.224 Ω.
Practical applications
- Current limiting and voltage division
- Heating elements and fuses
- Cable voltage-drop calculations
- Sensor and bridge circuits
Automotive applications
In a vehicle, resistance appears in every connection, cable and load. A corroded ground strap may have only a fraction of an ohm, but at 100 A that fraction produces several volts of drop and prevents the starter from turning. Resistance tests on injectors, ignition coils and sensors are compared with the manufacturer’s specification, and temperature must be considered because resistance changes with heat.
Industrial applications
Industrial resistance measurements are used for motor winding checks, heater element verification and insulation testing. Winding resistance is low, so a four-wire measurement is often needed to avoid lead resistance dominating the result. Insulation resistance is a different quantity and is measured with a dedicated insulation tester at a specified test voltage.
Measurement procedure
- De-energise the circuit and discharge capacitors before measuring resistance with an ohmmeter.
- Isolate the component or lift one end so parallel paths do not affect the reading.
- For low resistances, use a four-wire measurement to remove lead and contact resistance.
- Allow the component to reach a stable temperature; resistance of metals changes noticeably with heat.
Common mistakes
- Measuring resistance in a live circuit, which can damage the meter and give meaningless results.
- Confusing resistance with resistivity: resistance is a property of an object, resistivity of a material.
- Ignoring parallel paths that make an in-circuit resistance reading too low.
- Assuming a resistor’s value is exact; tolerance and temperature coefficient matter in precision work.
Safety considerations
- Check the power rating of a resistor; an undersized resistor can overheat and fail.
- Allow hot components to cool before touching them; heating elements and power resistors reach high temperatures.
- Never rely on an ohmmeter reading to prove a circuit is de-energised; test for voltage first.