5.1.3 Resistivity

Resistivity $(\rho)$

• Definition: Resistivity is a property that measures how well a material can conduct electricity. It is calculated using the formula:

$$\rho = \frac{RA}{L}$$

Where:

• $R$ is the resistance of the material,
• $A$ is the cross-sectional area, and
• $L$ is the length of the material.
• Resistivity helps in comparing materials regardless of their size by giving the resistance for a sample of 1m length and 1m² cross-sectional area.
• Environmental Factors: Resistivity is influenced by conditions like temperature, which impacts how easily current flows.

Effect of Temperature on Resistivity

• Metal Conductors: As the temperature of a metal conductor rises, its resistance increases. This happens because, with more kinetic energy, metal atoms vibrate more, causing more frequent collisions with charge carriers (electrons). These collisions slow down electron flow, which reduces current and thus increases resistance.

$$R \propto \text{temperature}$$

• Thermistors: In contrast, a thermistor's resistance decreases as its temperature increases. Higher temperatures lead to more electrons being released from atoms, which increases the number of charge carriers, enhancing current flow and decreasing resistance.
  • Application of Thermistors: Thermistors are often used as temperature sensors in circuits. For example, they can turn on a heater if the temperature falls below a certain threshold, or control a fan when the temperature rises above a set value.

Superconductors

• Definition: A superconductor is a material that, below a critical temperature (specific to each material), exhibits zero resistivity. This critical temperature is often very low, close to absolute zero (-273°C).
• Applications of Superconductors:
  • Power Cables: Superconducting cables can transmit electricity with no energy lost to heat, making them extremely efficient.
  • Magnetic Levitation (Maglev) Trains: These trains use powerful magnetic fields generated by superconductors, allowing frictionless motion along the rails.
  • Medical Applications: Superconductors are essential in devices such as MRI machines due to their ability to maintain strong magnetic fields without continuous energy input.

Graphical Representations

1. Resistance vs Temperature for Metals: Typically, resistance increases linearly with temperature.

   

2. Resistance vs Temperature for Thermistors: Shows a downward curve, indicating decreasing resistance with increasing temperature.

   

3. Superconductor Graph: Shows a sudden drop to zero resistance at the material's critical temperature.