A wire has resistance of 3.1 `Omega ` at `30 ^@` C and `4.5 Omega` at `100 ^@ C` . The temperature coefficient of resistance of the wire is

Options

A. `0.0012 ^(@) C^(-1)`
B. `0.0024^(@)C^(-1)`
C. `0.0032 ^@ C^(-1)`
D. `0.0064^(@)C^(-1)`

Explanation

(* ) Given
` t_1 = 30 ^(@) C `
` R_1 = 3.1 Omega `
`t_2 = 100^@ C `
` R_2 = 4.5 Omega `
We know that ,
Temperature coefficient of resistance
` alpha = (R _2 -R_1)/(R_1 t_2 - R_2 t_1)=(4.5 - 3.1) /( (3.1)(100 ) -( 4.5xx30 ))`
` =( 14 ) /( 310-135 ) =( 14 ) /( 175 ) = 0.008 ^(@) C^(-1)`