Incandescent lamp behavior: After switching on a lamp, how does the filament's resistance change as it quickly heats from room temperature to operating temperature?

Introduction / Context:
An incandescent lamp uses a metal filament (typically tungsten). When you first apply voltage, the filament is at room temperature and draws a large inrush current. As the filament heats up to a white-hot operating temperature, its electrical properties change. Understanding how filament resistance varies with temperature is important for surge analysis, fuse sizing, dimmer design, and lifetime prediction.

Given Data / Assumptions:

• Filament material has a positive temperature coefficient of resistance (typical for metals such as tungsten).
• Voltage is applied suddenly to a cold filament.
• Steady-state is reached within a fraction of a second as the filament becomes incandescent.

Concept / Approach:
For metals, resistance R increases with temperature T according to R ≈ R0 * (1 + α * ΔT), where α is the positive temperature coefficient. At the moment of switch-on, the filament is cold, so R is low and current is high. As temperature rises, the increased lattice vibrations impede electron flow, causing resistance to increase markedly, which in turn limits the current to its normal operating value.

Step-by-Step Solution:

Verification / Alternative check:
Practical measurements show cold resistance can be roughly 1/10 to 1/15 of the hot resistance in small lamps. The observable effect is a brief bright surge then stabilization, consistent with an increasing resistance as temperature climbs.

Why Other Options Are Wrong:

• Less resistive: Opposite of metallic behavior under heating.
• Cooler: Describes temperature, not resistance; in reality it gets hotter.
• Brighter: Illumination increases but this does not state the electrical resistance change.

Common Pitfalls:
Confusing semiconductors (often negative temperature coefficient) with metals. Also, assuming constant resistance when calculating startup current leads to underestimating surge stress on switches and power supplies.

Final Answer:
more resistive