A certain lightbulb has a tungsten filament with a resistance of 19.0 Ωwhen cold and 140 Ωwhen h

step 1 In this program we are given initial temperature is equal to 20 degree centigrade and initial re

A certain lightbulb has a tungsten filament with a...

A certain lightbulb has a tungsten filament with a resistance of $19.0 \Omega$ when cold and $140 \Omega$ when hot. Assume that the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here, and find the temperature of the hot filament. Assume the initial temperature is $20.0^{\circ} \mathrm{C}$.

Key Concepts

Temperature Coefficient of Resistance

This concept refers to the factor by which a material’s resistance changes with temperature. It quantifies the degree to which the resistivity of a conductive material increases (or decreases) as the temperature rises, typically expressed in units of 1/°C. Understanding this coefficient is crucial as it allows the prediction of resistance values at different temperatures based on a known reference temperature.

Linear Relationship of Resistivity with Temperature

When the resistivity of a material is assumed to vary linearly with temperature, it implies that the relationship between temperature and resistance can be described by a straight-line equation. This simplification means the change in resistance is proportional to the change in temperature, making it easier to model and calculate scenarios where the material heats up from a known base temperature.

Electrical Resistance and its Dependence on Material Properties

Electrical resistance is inherently linked to the physical properties of the material, including its resistivity, length, and cross-sectional area. As temperature changes, the intrinsic resistivity of the material changes, which in turn directly affects the resistance of the component. This concept is fundamental when analyzing how devices like filaments behave under different thermal conditions.

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