Filament lamp resistance rises nonlinearly with voltage due to thermal effects

Steps:

• Recall that filament lamps are non-ohmic; resistance depends on temperature.
• As V increases, current heats the filament, raising its temperature.
• Higher temperature increases resistance in metals like tungsten.
• Thus, R vs V graph shows R increasing, steeper at higher V.

Why A is correct:

• Option A depicts R rising nonlinearly with V, matching the positive temperature coefficient of resistance for metals (R ∝ T).

Why the others are wrong:

• B shows constant R, typical of ohmic conductors like resistors, not lamps.
• C shows decreasing R, incorrect as lamp resistance only falls when cooling.
• D shows linear increase, oversimplifying the nonlinear heating effect.

Final answer: A