Find the resistance of `240 V - 200` watt electric bulb when glowing. If this resistance is `10` times the resistance at `0^(@)C` and the temperature of the glowing filament is `2000^(@)C`, then find the temperature coefficient of resistance of the filament.

Explanation

Resistance of hot bulb,
`R_(t) = V^(2)/P = (200 xx 200)/100 = 400 Omega`
Resistance of bulb at room temperature,
`R_(0) = 400/10 = 40 Omega`
Now, `R_(t) = R_(0) ( 1 +alpha t)`
`:. 400 = 40 (1 +alpha xx 2000)`
or `10 = 1 + alpha xx 2000`
On solving, we get
`alpha = 9/2000 = 4.5 xx 10^(-3).^(@)C^(-1)`