physics help

Question

A certain lightbulb has a tungsten filament with a resistance of 21.0 when cold and 142 when hot. Assume the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here. Find the temperature of the hot filament. Assume an initial temperature of 20.0°C.

Answer 1

Hi Porcia!

 

You should have a table in whatever textbook or class material you have for something called the "temperature coefficient of resistivity (or resistance)," usually symbolized α.  You can also probably find it online.  That coefficient is usually quoted for T = 20^o C, or some similar temperature, and has a minor temperature variation -- but we are told to assume it is constant.  So once you look it up for tungsten, you can insert it into the following formula:

 

R(T) = R_o(1 + α(T - T_o))

 

where R(T) is the resistance at temperature T (temperatures are often quoted in Celsius, as is the case here), and  R_o is the resistance at temperature T_o.  Here, the initial state is "cold" and the final state is "hot."  Just take:

 

R(T) = 142 Ω

R_o = 21 Ω

T_o = 20 ^oC

 

and put in the value for α you look up for tungsten, then go to town solving for T.

 

I hope this helps!  If you have further questions, or would like to check an answer, just let me know.