Question

A 60W-100V tungsten lamp has a resistance of 20 ohms at air temperature (0◦C). What is the rise in temperature of the filament under normal working conditions? The temperature coefficient of resistance of tungsten is 0.0052/◦C.

Answer 1

The initial resistance

$$R_0=20\:\Omega$$

The resistance of the filament at the normal working condition

$$R=\frac{V^2}{P}=\frac{100^2}{60}=167\:\Omega$$

$$R=R_0(1+\alpha t)$$

$$t=\frac{R-R_0}{\alpha}=\frac{167-20}{0.052}=2820\:\rm K$$