Although caution must be used in applying ρ = ρ0(1 + αΔT) and R = R0(1 + αΔT) for temperature changes greater than 100ºC , 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

Question

Although caution must be used in applying $\rho=\rho_{0}(1+\alpha \Delta T)$ and $R=R_{0}(1+\alpha \Delta T)$ for temperature changes greater than 100ºC , 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 2850ºC ?

Strategy
This is a straightforward application of $R=R_{0}(1+\alpha \Delta T)$ , since the original resistance of the filament was given to be $R_{0}=0.350 \Omega$ , and the temperature change is ΔT = 2830ºC .

Strategy
This is a straightforward application of [latex]R=R_{0}(1+\alpha \Delta T)[/latex], since the original resistance of the filament was given to be [latex]R_{0}=0.350 \Omega[/latex], and the temperature change is ΔT = 2830ºC .

Accepted Answer

The hot resistance R is obtained by entering known values into the above equation:

[latex]R=R_{0}(1+\alpha \Delta T)[/latex] (20.25)

[latex]=(0.350 \Omega)\left[1+\left(4.5 imes 10^{-3} /{ }^{\circ} C ight)\left(2830^{\circ} C ight) ight][/latex]

= 4.8 Ω.

Discussion
This value is consistent with the headlight resistance example in Ohm’s Law: Resistance and Simple Circuits.

Question 20.6: Although caution must be used in applying ρ = ρ0(1 + αΔT) an...

Related Answered Questions