The question asks to identify the material among the given options that exhibits a negative temperature coefficient of resistance. This property describes how the electrical resistance of a material changes with temperature.

Temperature Coefficient of Resistance Explained

The temperature coefficient of resistance ($\alpha$) indicates how much the electrical resistance of a material changes for each degree Celsius (or Kelvin) change in temperature. It is defined by the formula:

$$R_T = R_0 [1 + \alpha (T - T_0)]$$

Where:

• $R_T$ is the resistance at temperature $T$.
• $R_0$ is the resistance at reference temperature $T_0$.
• $\alpha$ is the temperature coefficient of resistance.

Based on the value of $\alpha$, materials can be broadly classified into three categories:

• Positive Temperature Coefficient (PTC): Materials with a positive $\alpha$ means their electrical resistance increases as their temperature increases. Most metals, like conductors, fall into this category.
• Negative Temperature Coefficient (NTC): Materials with a negative $\alpha$ means their electrical resistance decreases as their temperature increases. Semiconductors and insulators typically exhibit this behavior.
• Near-Zero Temperature Coefficient (NZTC): Some alloys have a very small temperature coefficient, meaning their resistance changes very little with temperature.

Negative Temperature Coefficient: Understanding Carbon

Let's analyze the given options in the context of their temperature coefficient of resistance:

• Aluminium: Aluminium is a good electrical conductor (metal). Like most metals, it has a positive temperature coefficient of resistance. As its temperature rises, its resistance increases due to increased thermal vibrations of atoms impeding electron flow.
• Copper: Copper is an excellent electrical conductor (metal), widely used in wiring. It also has a positive temperature coefficient of resistance. Its resistance increases with temperature.
• Brass: Brass is an alloy primarily composed of copper and zinc. Being metallic in nature, it also exhibits a positive temperature coefficient of resistance, meaning its resistance increases as its temperature increases.
• Carbon: Carbon, in its common forms (like graphite or amorphous carbon), behaves as a semiconductor or a poor conductor. Semiconductors are characterized by a negative temperature coefficient of resistance. As the temperature of carbon increases, more electrons gain enough thermal energy to break free from their covalent bonds and become available for conduction. This increase in the number of charge carriers (electrons and holes) leads to a decrease in the overall resistance of the material.

Carbon's Unique Electrical Behavior

The distinctive behavior of carbon having a negative temperature coefficient of resistance is a key characteristic of semiconductor materials. Unlike metals where the primary factor affecting resistance is increased scattering of existing free electrons, in semiconductors, the dominant effect of temperature increase is the generation of a significantly higher number of charge carriers. This increase in carrier concentration outweighs the effect of increased scattering, leading to a net decrease in resistance.

Therefore, out of the materials listed, Carbon is the one that has a negative temperature coefficient of resistance.