At room temperature (27.0^{circ} C),the resis | vedclass

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Question

(C) Given:Room temperature,$T = 27.0^{\circ} C$Resistance at room temperature,$R = 100\; \Omega$Final resistance,$R_1 = 117\; \Omega$Temperature coeff

Vedclass · Accepted Answer

$1027$

Vedclass · Answer

(C) Given:Room temperature,$T = 27.0^{\circ} C$Resistance at room temperature,$R = 100\; \Omega$Final resistance,$R_1 = 117\; \Omega$Temperature coefficient,$\alpha = 1.70 	imes 10^{-4}\; ^{\circ} C^{-1}$The formula for temperature dependence of resistance is:$R_1 = R[1 + \alpha(T_1 - T)]$Rearranging for the final temperature $T_1$:$T_1 - T = \frac{R_1 - R}{R \alpha}$Substituting the values:$T_1 - 27 = \frac{117 - 100}{100 	imes 1.70 	imes 10^{-4}}$$T_1 - 27 = \frac{17}{1.70 	imes 10^{-2}}$$T_1 - 27 = \frac{17}{0.017} = 1000$$T_1 = 1000 + 27 = 1027^{\circ} C$Thus,the temperature of the element is $1027^{\circ} C$.

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