Conductivity Thermal And Electrical

The conductivity of a metal depends on the number of free electrons available and the nature of the bonding. Conductivity generally increases with the number of free electrons and atomic structure. Based on their conductivity: - Silver (Ag) is the best conductor of electricity because it has the highest number of free electrons. - Copper (Cu) also has high conductivity, but slightly lower than silver. - Iron (Fe) has relatively fewer free electrons, so its conductivity is lower than copper and silver. - Sodium (Na), being an alkali metal, is a good conductor but not as good as the transition metals like copper and silver. Thus, the order of conductivity is Ag > Cu > Fe > Na.

Step 1: Understanding the Concept:
It is crucial to distinguish between resistance ( ) and resistivity ( ).
- Resistance is an \textit{extensive} property; it depends on the physical dimensions of the object (length, cross-sectional area).
- Resistivity is an \textit{intensive} property; it is an intrinsic characteristic of the material itself (e.g., copper vs. iron) and depends only on the temperature and the microscopic structure of the material.
Step 2: Key Formula or Approach:
The formula relating the two is . While resistance changes with length and area , the resistivity is the constant of proportionality that describes the material.
Step 3: Detailed Explanation:
The problem states that the physical dimensions of the wire are altered:
- Radius doubles ( )
- Length reduces by half ( )
If the question asked for the new resistance, we would calculate it using the new dimensions.
However, the question specifically asks for the new resistivity.
Because cutting, stretching, or reshaping a material does not change what the material is made of, its intrinsic properties remain identical (assuming temperature stays constant). A piece of copper has the same resistivity whether it is a long thin wire or a short thick block.
Therefore, the resistivity does not change with changes in physical dimensions.
Step 4: Final Answer:
The resistivity remains unchanged.