Which of the following statements are true with regard to resistivity?

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Examoogle · Accepted Answer

Resistance depends on the temperature

Explanation: Resistance is a property of a material's shape and dimensions, defined by $R = \rho \frac{l}{A}$. It depends on the material's resistivity, its length, cross-sectional area, and, crucially, the temperature.

Working Principle: As temperature increases, the atomic vibrations (lattice vibrations) in a conductor increase. This leads to more frequent collisions between charge carriers (electrons) and the crystal lattice, thereby increasing the electrical resistance of the material.

Key Formulas: $R = \rho \frac{l}{A}$ — Resistance definition based on geometry; $R_t = R_0(1 + \alpha \Delta T)$ — Temperature dependency of resistance

Key Points: Resistivity ($\rho$) is an intrinsic property of the material and does not depend on length or cross-sectional area.; Resistance (R) is an extrinsic property dependent on dimensions (length, area) and temperature.; For most metals, resistance increases with temperature (positive temperature coefficient).

Advantages: Used in Resistance Temperature Detectors (RTDs) for accurate temperature sensing; Allows for precise control of current in electrical circuits

Disadvantages: Thermal instability in precision circuits; Power dissipation as heat (I^2R losses)

Applications: Heating elements; Temperature sensors (RTDs); Circuit protection (Fuses/PTC thermistors)

Additional Info: Resistivity depends only on material nature and temperature, not on geometric factors.. Option B is incorrect because resistance is highly sensitive to thermal energy. Options C and D are incorrect because they define resistivity as a geometric variable, which is fundamentally wrong.

Answer: A is correct — Resistance is physically defined by the material properties and geometric dimensions, and it changes as the temperature modifies the internal carrier dynamics.

Exam Tip: In competitive exams, remember that resistivity is an intensive property (independent of size), whereas resistance is an extensive property (dependent on size).

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