1. What Determines the Resistance of a Conductor
The resistance of a conductor tells us how strongly it opposes the motion of electric charges. But this resistance is not fixed—it depends on several physical factors. Changing any of these factors changes how easily electrons can flow.
The main factors are: length, area of cross-section, type of material and temperature.
2. Effect of Length
A longer conductor means charges must travel a greater distance. This increases the number of collisions with atoms and increases resistance.
So,
\( R \propto L \)
2.1. Reason Behind the Relation
When the length doubles, electrons collide twice as many times. This increased opposition shows up as higher resistance.
3. Effect of Area of Cross-Section
A thick conductor allows more electrons to flow side by side. This reduces collisions and decreases resistance.
So,
\( R \propto \dfrac{1}{A} \)
3.1. Simple Way to Remember
Think of a wide pipe vs a narrow pipe. More water can flow through the wide pipe. Similarly, a thicker wire allows more electrons to pass with less opposition.
4. Effect of the Material
Different materials oppose the movement of electrons differently. This property is captured by a constant called resistivity \( (\rho) \).
Materials with low resistivity (like copper and aluminium) are good conductors. Materials with high resistivity (like rubber or plastic) are poor conductors.
4.1. Material Determines the Value of Resistivity
Even if two wires have the same length and thickness, the one with lower resistivity will have lower resistance. That is why copper wires are used in most circuits.
5. Effect of Temperature
Temperature has a strong effect on resistance. As temperature increases, atoms vibrate more, making it harder for electrons to move. This increases resistance in most conductors.
5.1. Behaviour in Different Types of Materials
- Metals: resistance increases with temperature
- Semiconductors: resistance decreases with temperature
- Insulators: resistivity decreases slightly at higher temperatures
5.1.1. Reason for Metals
In metals, electrons are abundant and mobile. When temperature rises, atoms vibrate more strongly, increasing collisions. This increases resistance.
6. Combined Formula for Resistance
The combined effect of length, area and material is given by:
\( R = \rho \dfrac{L}{A} \)
This relation shows clearly how resistance changes when dimensions or material change.
6.1. Quick Visualisation
To reduce resistance:
- use a shorter conductor
- choose a thicker conductor
- use a material with lower resistivity