# Why does resistance increase with temperature in a filament lamp?

## Why does resistance increase with temperature in a filament lamp?

What is the relationship between resistance and temperature in a filament lamp?

## Answer:

Resistance increases with temperature in a filament lamp due to the temperature coefficient of resistance, α.

Resistance increasing with temperature in a filament lamp is a common phenomenon observed in electrical circuits. The resistance of a material is a measure of how much it opposes the flow of electric current. In a filament lamp, this resistance increases as the temperature of the lamp increases.

The relationship between resistance and temperature in a filament lamp is governed by the temperature coefficient of resistance, denoted by the symbol α. The temperature coefficient of resistance measures how the resistance of a material changes with temperature. In the case of a filament lamp, as the temperature of the wire filament increases, so does its resistance.

One of the main reasons for this increase in resistance with temperature is the increased vibrational motion of the atoms in the filament as the temperature rises. This heightened vibration causes more collisions between the free electrons moving through the wire and the atoms in the wire. These collisions impede the flow of electrons, resulting in a higher resistance to the current.

The relationship between resistance and temperature in a filament lamp can be described by the equation: R = R₀(1 + αΔT), where R is the resistance at temperature T, R₀ is the resistance at a reference temperature, α is the temperature coefficient of resistance, and ΔT is the change in temperature.

Understanding this relationship is crucial for designing and analyzing electrical circuits that include filament lamps. By knowing how resistance changes with temperature, engineers and designers can optimize the performance and efficiency of their circuits.