When an incandescent light bulb is switched on, it can take a few moments for th

Question

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. (When the filament is fully heated, the bulb shines with its maximum brightness). 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 (current drawn when the equilibrium temperature is reached) 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 degreeC, and assume the resistivity increases linearly with increasing temperature.

Explanation / Answer

R = Ro[1 + 0.004403(T - 20)]
now, initially, V = IRo
finally, V = IR/6
so, R = 6Ro
6 = 1 + 0.004403(T - 20)
T = 1155.58 deg celcius

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