Filament lamp resistance increases nonlinearly with voltage due to heating

Steps:

• Recall that a filament lamp's resistance depends on temperature, unlike fixed resistors.
• As applied p.d. (V) increases, current flows, heating the tungsten filament.
• Higher temperature causes atoms to vibrate more, increasing collisions and thus resistance R.
• Therefore, R rises with V, starting low and curving upward to operating levels.

Why A is correct:

• Graph A shows R increasing nonlinearly with V, matching the positive temperature coefficient of resistance for metals like tungsten (R ∝ T).

Why the others are wrong:

• B: Linear increase implies constant resistance, typical of ohmic conductors, not lamps.
• C: Decreasing R suggests negative temperature coefficient, seen in semiconductors, not filaments.
• D: Constant R ignores heating effects, as in ideal resistors.

Final answer: A