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A wire has resistance of 2.0 Omega at ...

A wire has resistance of ` 2.0 Omega` at ` 25^@ C` and `2.5 Omega` at `100^@ C`. Calculate the temperature coefficient of resistance of the wire.

Text Solution

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`R_t = R_0 (1+alpha t)`
When ` t = 25^@ C" "R_t = 2.0 Omega`
`:." 2.0 = R"_0 (1 + 25 alpha )" …(1)"`
When ` t = 100^@ C" R"_(100) = 2.5`
` :." 2.5 " = R_0 (1 + 100 alpha)" …(2)"`
`((1))/((2)) rArr (2.5)/(2.0) = (1+ 100 alpha)/(1+ 25 alpha)`
`:." 2.5"(1+ 25 alpha ) = 2 ( 1+ 100 alpha)`
`2.5 + 62.5 alpha = 2 + 200 alpha`
`2.5 - 2 = 200 alpha - 62.5 alpha`
` :." 137.5" alpha = 0.5 `
` alpha = (0.5)/(137.5) `
` alpha = 0.003636//^@ C`
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