Question

On increasing the temperature, the resistance of conductors:

• A. Increases
• B. Decreases
• C. Becomes zero
• D. None of the above

Hint:

For most conductors, resistance increases with temperature due to increased lattice vibrations that impede electron flow. This behavior is described by the temperature dependence formula $ R(T) = R_0 \left[ 1 + \alpha (T - T_0) \right] $.

Answer 1

The Correct Option is A

Step 1: Understand Temperature Dependence of Resistance.
For most conductors, the resistance increases with an increase in temperature. This is due to increased lattice vibrations in the material, which hinder the flow of electrons. The relationship between resistance ($ R $) and temperature ($ T $) is often expressed as: $$ R(T) = R_0 \left[ 1 + \alpha (T - T_0) \right], $$ where:
$ R_0 $ is the resistance at a reference temperature $ T_0 $,
$ \alpha $ is the temperature coefficient of resistivity.
For metals, $ \alpha > 0 $, meaning resistance increases with temperature. Step 2: Analyze Each Option. Option (1): Increases — Correct, as resistance generally increases with temperature for conductors.
Option (2): Decreases — Incorrect, as resistance typically increases with temperature.
Option (3): Becomes zero — Incorrect, as resistance does not become zero unless the material becomes superconducting, which is not implied here.
Option (4): None of the above — Incorrect, as option (1) is correct. Step 3: Final Answer. $$ (1) \mathbf{\text{Increases}} $$