The temperature coefficient of resistance of a wire is 0.00125 per `""^(@)C`. At 300 K, its resistance is `1Omega`. The resistance of the wire will be `2Omega` at ………………. .

Options

A. 1154 K
B. 1100 K
C. 1400 K
D. 1127 K

Answer

D

Explanation

`alpha = 0.00125 //^(@)C`
`T_1 = 300 K " "R_1 = 1 Omega`
`T_2 = ?" "R_2 = 2 Omega`
` T = 27 + 273 = 300 K `
` T_1 ^(@) C = 300 - 273 = 27^@ C`
` :." "alpha = (R_2 - R_1)/(R_1 T_2 - R_2 T_1)`
`125 xx 10^(-5) = (2-1)/(1 xxT_2 - 2 xx 27) = 1/ (T_2 - 54)`
`T_2 - 54 = 1/(125 xx10^(-5) `
` = (100000)/(125) = 800 `
`T_2 = 800 + 54 = 854 ^@ C`
Required Temperature
`T_2 ^@C = 854 ^@C`
`T_2 K = 854 + 273`
` = 1127 K`