When an incandescent light bulb is switched on, it can take a few moments for the filament to fully heat up and reach its equilibrium temperature. Assume the filament of a given light bulb is made of Tungsten, and also
assume the potential difference across the filament is maintained at a constant value during this short warm up
period. If the ‘steady state’ current is measured to be only 1/6 of the current drawn when the lamp is first turned on, then what is the final operating temperature of the filament? Assume the initial temperature of the filament is 20 °C, and assume the resistivity increases linearly with increasing temperature.
R = Ro[1+∝(T-To)]
The Attempt at a Solution
So im not given the resistance here but i am told the voltage is constant throughout this warm up. So i can use
R = V/I
Plug into R = Ro[1+∝(T-To)]
V/I = V/Io [1+∝(T-To)]
Since voltage is constant i can divide both sides to cancel them out, also multiply both sides by I and Io leaving me with
Io = I [1+∝(T-To)]
Im told the steady state current is only 1/6 of the initial current when the bulb is first turned on so i can say
I= 1/6 Io and plug it into the equation.
Io = 1/6 Io [1+∝(T-To)]
From here i cancel out Io from both sides and solve for T. The answer is get is
1131 oC, is this correct?