Filament Heating and Resistance

Steps:

• Current flows through the lamp's filament, generating heat via Joule's law (P = I²R).
• Rising current increases power dissipation, elevating filament temperature.
• In metal filaments, higher temperature increases resistivity due to intensified electron-phonon collisions.
• Greater resistivity raises overall resistance (R = ρL/A).

Why D is correct:

• Resistance in metals follows the temperature coefficient of resistance formula, ρ = ρ₀[1 + α(T - T₀)], where α > 0, so resistance rises with temperature.

Why the others are wrong:

• A: Charge of charge carriers (electrons) remains constant at -e, unaffected by current.
• B: Potential difference typically increases with current per Ohm's law (V = IR), not decreases.
• C: Power dissipated increases with current (P = I²R or VI), heating the filament more.

Final answer: D