A potential difference is applied across the filament of a bulb at `t = 0` and it is maintained at a constant value while the filament gets heated to its equilibrium temperature. We find that final current in the filament is one fifth the current drawn at `t = 0`. If the temperature of filament at `t = 0` is `20^(@)C` and the temperature coefficient of resistivity at `20^(@)C` is `0.004(.^(@)C)^-1`, find the final temperature of the filament.

Explanation

At constant potential different, current becomes `1//5^th` i.e., resistance is five times of initial resistance.
`R_theta = 5 R_20`
`R_20[1 + alpha(theta - 20)]= 5 R_20`
`alpha(theta - 20) = 4`
`theta - 20 = (4)/(alpha) = (4)/(0.004) = 1000`
`theta = 1020.^@C`.