1. What Resistance Really Means
Resistance tells us how much a conductor opposes the flow of electric charges. When charges move through a material, they collide with atoms, slowing down their motion. This opposition is what we call electrical resistance.
If resistance is high, only a small current flows for a given voltage. If resistance is low, a larger current flows.
1.1. Definition of Resistance
Resistance is defined as the ratio of the potential difference across a conductor to the current flowing through it.
\( R = \dfrac{V}{I} \)
It depends on the material, length, thickness and temperature of the conductor.
2. What Determines the Value of Resistance?
The resistance of a conductor depends on physical factors. Some materials let electrons move easily while others strongly oppose the motion.
2.1. Physical Factors
- Length: longer wire → more resistance
- Area of cross-section: thicker wire → less resistance
- Material: some materials are better conductors
- Temperature: in most metals, resistance increases with temperature
2.1.1. General Formula for Resistance
The resistance of a uniform conductor is given by:
\( R = \rho \dfrac{L}{A} \)
Here:
- R = resistance
- ρ = resistivity of the material
- L = length
- A = cross-sectional area
3. Understanding Resistivity
While resistance depends on the shape and size of the conductor, resistivity depends only on the nature of the material. Every material has its own characteristic resistivity.
Good conductors (like copper, aluminium) have very low resistivity, while insulators (like rubber, glass) have extremely high resistivity.
3.1. Definition of Resistivity
Resistivity is the measure of how strongly a material opposes the flow of electric current. It is a property of the material itself, independent of dimensions.
\( \rho = R \dfrac{A}{L} \)
3.1.1. Resistivity vs Resistance
Two wires made from the same material have the same resistivity, no matter their length or area. But their resistance will differ depending on their dimensions.
4. How Temperature Affects Resistance
As temperature increases, the atoms in a conductor vibrate more vigorously. Electrons collide more often with these vibrating atoms, increasing the resistance.
In most metals:
- temperature ↑ → resistance ↑
- temperature ↓ → resistance ↓
4.1. Behaviour in Different Materials
- Metals: resistance increases with temperature
- Semiconductors: resistance decreases with temperature
- Insulators: resistivity decreases slightly at high temperatures
5. Example to Visualise Resistance and Resistivity
Take two wires of equal length and area: one copper and one iron. Even though both have the same dimensions, the copper wire has much lower resistance because its resistivity is naturally low.
Now take two copper wires but make one twice as long. The longer one has double the resistance because of the formula:
\( R \propto L \)