Electrical Resistance
Electrical resistance is the opposition that a material offers to the flow of electric current, quantifying how much a conductor restricts charge flow for a given applied voltage. It depends on the material's resistivity, its length, and its cross-sectional area, and increases with temperature in most metals. Resistance is central to controlling current in circuits and forms the basis of Ohm's Law.
Key Formula
R = (rho × L) / A
LaTeX: R = \dfrac{\rho L}{A}
| Symbol | Meaning | Unit |
|---|---|---|
| R | Resistance | Ohm (Ω) |
| ρ | Resistivity of the material | Ohm·metre (Ω·m) |
| L | Length of the conductor | Metre (m) |
| A | Cross-sectional area | Square metre (m²) |
Worked Example
Problem
A copper wire (ρ = 1.7 × 10⁻⁸ Ω·m) is 2 m long and has a cross-sectional area of 1 × 10⁻⁶ m². Find its resistance.
Solution
Step 1: Identify values: ρ = 1.7 × 10⁻⁸, L = 2, A = 1 × 10⁻⁶. Step 2: R = ρL / A = (1.7 × 10⁻⁸ × 2) / (1 × 10⁻⁶) = 3.4 × 10⁻⁸ / 10⁻⁶ = 3.4 × 10⁻² Ω.
Answer
R = 0.034 Ω
Resistivity of Common Materials at 20 °C
| Material | Resistivity (Ω·m) | Classification | Typical Use |
|---|---|---|---|
| Silver | 1.59 × 10⁻⁸ | Conductor | High-precision electronics |
| Copper | 1.7 × 10⁻⁸ | Conductor | Electrical wiring |
| Aluminium | 2.82 × 10⁻⁸ | Conductor | Power cables |
| Silicon | 6.4 × 10² | Semiconductor | Transistors, diodes |
| Glass | 10¹⁰ – 10¹⁴ | Insulator | Electrical insulation |
Interactive Tools
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Related Terms
Electric Current
Electric current is the rate of flow of electric charge through a conductor, measured as the amount of charge passing a cross-section per unit time. It is the fundamental quantity that drives electrical circuits and powers all electronic devices. In metallic conductors, current arises from the drift of free electrons, while in electrolytes and plasma it involves the movement of ions.
Ohm's Law
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across those points, provided temperature and other physical conditions remain constant. It is one of the most fundamental relationships in electrical engineering and circuit analysis. The law applies to ohmic (linear) materials and is used to calculate unknown voltages, currents, or resistances in simple circuits.
Electrical Power
Electrical power is the rate at which electrical energy is transferred or consumed by a device, equal to the product of the voltage across it and the current through it. It determines how quickly a device does work or dissipates energy as heat, light, or motion. Power is critical in the design of electrical systems, from household appliances rated in watts to large industrial generators rated in megawatts.
From Latin "resistere" meaning "to withstand" or "to stand back". The unit Ohm honours German physicist Georg Simon Ohm (1789–1854) who formulated the relationship between voltage, current, and resistance. The concept was formalised in the early 19th century.