Bulb Temperature using resistance

[hoseA]

An incandescent bulb has a resistance of 12 *omega
when it is at room temperature (25 degrees C) and
400 omega * when it is hot and delivering light to
the room. The temperature coefficient of re-
sistivity of the filament is 0.008 (degrees C)^-1, where
the base resistance R0 is determined at 0 degrees C.
What is the temperature of the bulb when
in use? Answer in units of degrees C.

T = T0 + (1/alpha)[(R/R0)-1]

= 25 + (1/{1/.008})[(400/12)-1]

=25.25866 deg. C

This is wrong. What've I blundered this time?

Help is most appreciated.

 

[mezarashi]

Firstly could you verify the units for that resistivity coefficient? It is far too low to be reasonable in my opinion. The equations you need to set up from the word problem should look like:

$$R(25 C) = 12 \Omega$$
$$R(T_1) = 400 \Omega$$
$$R(T) = (R_0 + kT) \Omega$$


where T1 is the temperature of the bulb when in use, and k is the resistivity coefficient. See if these equations make sense with regard to the word problem.

 

[physicsprasanna]

0.008 degC^-1 is alpha ... its not 1/alpha ... that's what is wrong...

1/alpha will have the unit deg celsius. only then you can add it with T0 ..
What you have taken as alpha is actually 1/0.008 degC^-1 ... so your 1/alpha will have the units degC^-1 so you cannot add it to $$T_{0}$$

= 25 + (1/{1/.008})[(400/12)-1]

In a nutshell, change that thing to 0.008... you'll get the answer which seems to be correct.

And by the way, the value for the coefficent of resistivity isn't that low...Actually, its value for nichrome is 0.0004 per deg celsius and we know that nichrome materials are used as heating elements in many appliances ...