If the temperature of a resistance wire is gradually increased, its resistance will

Analyze the question: The question asks how the resistance of a metallic resistance wire changes as its temperature is raised gradually.

Concept: Resistance in a metal comes from collisions between free electrons and the lattice ions. When temperature rises:

• The ions vibrate with larger amplitude.
• Electrons collide with them more often.
• The number of free electrons stays almost constant.

So the resistance increases. This is expressed by:

R_t = R₀(1 + αt)

where R₀ is the resistance at 0°C, α is the temperature coefficient of resistance (positive for metals), and t is the temperature change. Because R_t grows steadily with t, the resistance increases gradually.

Checking the options:

• A. Decrease gradually: this is true of semiconductors and thermistors, not metal wires.
• B. First increase then decrease: not the behavior of a metal wire.
• C. First increase then remain the same: there is no such saturation in normal ranges.
• D. Increase gradually: matches R_t = R₀(1 + αt).
• E. Remain the same: only true of special alloys like constantan or manganin, and even then only approximately.

Answer: D.

Exam tip: Remember "Metals: hotter means higher resistance. Semiconductors: hotter means lower resistance." Hot metal means a crowded, vibrating lattice, so electrons get obstructed more.