Resistors
Simple Explanation
A resistor is a component specifically designed to provide a known, controlled amount of resistance in a circuit. A conductor's resistance depends on the material it's made from (resistivity), as well as its length and cross-sectional area.
Why Do We Need It?
Resistors are among the most fundamental components in electronics, used to control current, divide voltage, and protect other components from excessive current.
Formula
Resistance from Resistivity
R = ρL / A
A conductor's resistance depends on its material (resistivity), its length, and its cross-sectional area — longer and thinner conductors have higher resistance.
- R
- — Resistance, in ohms (Ω)
- ρ
- — Resistivity of the material (a property of the material itself), in Ω·m
- L
- — Length of the conductor, in metres
- A
- — Cross-sectional area of the conductor, in m²
When to use it: Use to find a conductor's resistance from its material, length, and cross-sectional area, or to design a resistor with a specific target resistance.
Worked Example
Finding a wire's resistance
A wire has a resistivity of 1.7 × 10⁻⁸ Ω·m, a length of 2 m, and a cross-sectional area of 1 × 10⁻⁶ m². Find its resistance.
Why Does This Work?
A longer conductor gives charge carriers more material to travel through (more resistance), while a wider cross-section gives them more 'room' to flow through simultaneously (less resistance) — resistivity itself captures how strongly a specific material inherently resists current flow, independent of its shape.
Real-Life Example
Why thick electrical cables are used for high-current appliances
High-power appliances (like electric ovens) use thicker cables than low-power devices (like phone chargers).
Since resistance is inversely proportional to cross-sectional area, thicker cables have lower resistance — this reduces unwanted heating (and energy loss) in the cable itself when carrying the large currents that high-power appliances need.
Practice
A wire has resistivity 2.8 × 10⁻⁸ Ω·m, length 5 m, and area 2 × 10⁻⁶ m². Find its resistance.
MediumCommon mistake
Confusing resistivity (a property of the material, independent of shape) with resistance (a property of a specific object, dependent on both material AND shape/dimensions) — this mirrors the specific heat capacity vs. thermal capacity distinction from an earlier chapter.
Quick Review
- R = ρL/A: resistance depends on material (resistivity), length, and cross-sectional area.
- Longer conductors have more resistance; wider conductors have less.
- Resistivity is a material property; resistance depends on both material and shape.