Resistance of tungsten wire at `150^(@)C` is `133 Omega`. Its resistance temperature coefficient is `0.0045//^(@)C`. The resistance of this wire at `500^(@)C` will be

Answer

`215 Omega`

Explanation

Here, `R_(160) = 132 Omega R_(400) = ?`
`alpha = 4.5 xx 10^(-3).^(@)C^(-1)`
Now `R_(t) = R_(0)(1 + alpha t)`
`:. R_(160) = R_(0) [1 + (4.5 xx 10^(-3))xx 100]`
or `132 = R_(0)[1+4.5 xx 10^(-3)xx 100]`……(i)
and `R_(400) = R_(0) [1 + 4.5 xx 10^(-3)xx400]`.....(ii)
Dividing (ii) by (i) we get
`(R_(400))/(132) = (1+ 4.5 xx 10^(-3) xx 400)/(1+ 4.5 xx 10^(-3) xx 400)`
`= (1+ 1.80)/(1+ 0.72) = (2.80)/(1.72) = 1.63`
`R_(400) = 132 xx 1.63 = 215 Omega`