The resistance of a wire is 2.5 Omega at a te | vedclass

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(A) The formula for the temperature dependence of resistance is given by $R_T = R_0(1 + \alpha \Delta T)$,where $R_T$ is the resistance at temperature

Vedclass · Accepted Answer

$1.84$

Vedclass · Answer

(A) The formula for the temperature dependence of resistance is given by $R_T = R_0(1 + \alpha \Delta T)$,where $R_T$ is the resistance at temperature $T$,$R_0$ is the resistance at reference temperature $T_0$,and $\Delta T = T - T_0$.Given: $R_1 = 2.5 \ \Omega$ at $T_1 = 373 \ K$,$\alpha = 3.6 	imes 10^{-3} \ K^{-1}$,and $T_2 = 273 \ K$.We need to find $R_2$ at $T_2$. Using the relation $R_2 = R_1[1 + \alpha(T_2 - T_1)]$,we substitute the values:$R_2 = 2.5 	imes [1 + 3.6 	imes 10^{-3} 	imes (273 - 373)]$$R_2 = 2.5 	imes [1 + 3.6 	imes 10^{-3} 	imes (-100)]$$R_2 = 2.5 	imes [1 - 0.36]$$R_2 = 2.5 	imes 0.64 = 1.6 \ \Omega$.Wait,re-calculating: $2.5 	imes 0.64 = 1.6 \ \Omega$. Let us re-check the standard formula $R_2 = R_1 / (1 + \alpha \Delta T)$ if $R_1$ is at higher temperature. Using $R_2 = R_1 / (1 + \alpha \Delta T_{diff})$ where $\Delta T_{diff} = 100 \ K$:$R_2 = 2.5 / (1 + 3.6 	imes 10^{-3} 	imes 100) = 2.5 / (1 + 0.36) = 2.5 / 1.36 \approx 1.838 \ \Omega \approx 1.84 \ \Omega$.

The resistance of a wire is $2.5 \Omega$ at a temperature $373 \ K$. If the temperature coefficient of resistance of the material of the wire is $3.6 \times 10^{-3} \ K^{-1}$,its resistance at a temperature $273 \ K$ is nearly: (in $\Omega$)

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