Physics

Physics

Problem

A metal filament lamp is connected to a steady 6 V6\,\text{V} supply. The current through the lamp decreases from 0.50 A0.50\,\text{A} just after switching on to 0.25 A0.25\,\text{A} after the filament becomes white-hot. Which statement best explains this change? a) The supply voltage falls as the lamp warms, so with the filament’s constant resistance the current decreases. b) The resistance of the filament decreases when hot, therefore a smaller current flows after heating. c) The resistance of the filament rises sharply with temperature, so even at constant 6 V6\,\text{V} the current falls as the lamp heats up. d) Ohm’s law predicts the current should stay at 0.50 A0.50\,\text{A}; the drop to 0.25 A0.25\,\text{A} indicates the ammeter is faulty.
Intuitive explanation

The filament's resistance increases as it heats up—this is the key to understanding why current drops even though voltage stays constant. When you apply Ohm's law (V=IRV = IR), a constant voltage with rising resistance means current must fall. Most metals have positive temperature coefficients, so their resistivity grows significantly at high temperatures, and the white-hot filament is far hotter than the cool one just switched on.

Intuitive explanation

The filament's resistance increases as it heats up—this is the key to understanding why current drops even though voltage stays constant. When you apply Ohm's law (V=IRV = IR), a constant voltage with rising resistance means current must fall. Most metals have positive temperature coefficients, so their resistivity grows significantly at high temperatures, and the white-hot filament is far hotter than the cool one just switched on.

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