The resistance of a tungsten filament at `150^@C` is `133Omega`.What will be its resistance at `500^@C`? The temperaturecoefficient of resistance of tungsten at `0^@C` is `0.0045^@C^-1`

Explanation

Let `R_1 = 133 Omega` at temperature `theta_1= 150^@C` and `R_2` = Resistance of tungsten filament at `theta_2 = 500^@C`
`R_2 = ?`
Temperature co-efficient of resistance at `0^@C = alpha = 0.0045""^@C^(-1)`
Now `R_1 = R_0 (1 + alpha theta_1)`
`implies 133 = R_0 (1 + 150 alpha) " "...(1) `
where `R_0` = Resistance of tungsten filament at `0^@C`.
Also `R_2 = R_0 (1 + alphatheta_2)`
`R_2 = R_0 (1 + 500 alpha) " "....(2)`
Divide (2) by (1),
`R_2/(133)=(R_0(1+500alpha))/(R_0(1+150alpha))`
`implies R_2/133=(1+500(0.0045))/(1+150(0.0045))=(3.25)/(1.675)=1.94`
`implies R_2=1.94xx133`
`:. R_2 = 258.1Omega`