Example 20.6 from College Physics, 20.3 Resistance and Resistivity

Calculating Resistance: Hot-Filament Resistance

Although caution must be used in applying $ρ = ρ_{0} (1 + α Δ T)$ and $R = R_{0} (1 + α Δ T)$ for temperature changes greater than $100º C$ , for tungsten the equations work reasonably well for very large temperature changes. What, then, is the resistance of the tungsten filament in the previous example if its temperature is increased from room temperature ( $20ºC$ ) to a typical operating temperature of $2850º C$ ?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
This is a straightforward application of $R = R_{0} (1 + α Δ T)$ , since the original resistance of the filament was given to be $R_{0} = 0 . 350 Ω$ , and the temperature change is $Δ T = 2830º C$ .
Solution
The hot resistance $R$ is obtained by entering known values into the above equation:
$\begin{array}{l} R & = & R_{0} (1 + α Δ T) \\ = & (0 . 350 Ω) [1 + (4.5 \times 10^{–3} / ºC) (2830º C)] \\ = & 4.8 Ω. \end{array}$
20.25
Discussion
This value is consistent with the headlight resistance example in Ohm’s Law: Resistance and Simple Circuits.

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