The correct option is 1 and 3 only
Explanation
Electrical resistivity (denoted by the Greek letter rho, ρ) is a fundamental property that quantifies how strongly a given material opposes the flow of electric current. Unlike resistance, which depends on the dimensions of the conductor, resistivity is an intrinsic property of the material itself.
Statement-wise Analysis
- Statement 1 is Correct: Resistivity is a characteristic property of the material. It depends on the nature of the material and its electronic structure, independent of the shape, length, or cross-sectional area of the specific specimen.
- Statement 2 is Incorrect: The relationship between resistance (R) and resistivity (ρ) is given by the formula \( R = \rho \frac{L}{A} \), where \( L \) is length and \( A \) is the area of cross-section. Rearranging for resistivity gives \( \rho = R \frac{A}{L} \).
The SI unit is calculated as:
\( \text{Ohm} (\Omega) \times \frac{\text{metre}^2 (m^2)}{\text{metre} (m)} = \text{Ohm-metre} (\Omega \cdot m) \).
The statement incorrectly mentions "ohm per metre" (\( \Omega/m \)). - Statement 3 is Correct: Resistivity is temperature-dependent. For metallic conductors, resistivity generally increases with a rise in temperature due to increased collision frequency of free electrons. In contrast, for semiconductors and insulators, resistivity typically decreases as temperature increases.
Key Takeaway
Resistivity (ρ) is an intrinsic material property measured in Ohm-metre (\( \Omega \cdot m \)). While resistance changes with the dimensions of the conductor (length and area), resistivity remains constant for a specific material at a specific temperature.