Electric Current and Temperature Relationship - Physics?

Question

A battery-powered light bulb has a tungsten filament. Immediately after the switch connecting the bulb to the battery is turned on and the temperature of the bulb is still 20 degrees C, the current in the bulb is 0.860 A. After the bulb has warmed up to its operating temperature the current is 0.220 A.
What is the operating temperature of the filament?

Where do I go with this? Do I need the resistance of tungsten at 20 deg C (5.25x10^-8 ohm*meter)? Is there a simple formula or ratio I'm missing?

Answer 1

The temperature coefficient of resistance of Tungsten is 0.0051 Ohm/K at 20C.

At 293K (20C), the R_20 = 1.49 Ohms
so, V = 0.86 * 1.49 = 1.285

At high temp:
1.285 / 0.22 = R = 5.841 Ohm

5.841 / 0.0051 = 1145 K = 872 C

.

Answer 2

You may use the formular P=q*T^4
P1/P2=(T1/T2)^4 you should convert 20 degree C
to 293 k
( P1/P2)=(T1/T2)^4=(V*0.86A)/(V*0.22A)
( 293/T2)^4= (0.86/0.22)
you can do the rest