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(C) The resistance of a conductor at temperature $t$ is given by the formula: $R_t = R_0(1 + \alpha t)$.Alternatively,for two temperatures $t_1$ and $

Vedclass · Accepted Answer

$167$

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(C) The resistance of a conductor at temperature $t$ is given by the formula: $R_t = R_0(1 + \alpha t)$.Alternatively,for two temperatures $t_1$ and $t_2$,the relation is: $R_2 = R_1[1 + \alpha(t_2 - t_1)]$.Given: $R_1 = 50\,\Omega$ at $t_1 = 20\,^{\circ}C$,$R_2 = 76.8\,\Omega$,and $\alpha = 3.92 	imes 10^{-3}\,^{\circ}C^{-1}$.Substituting the values: $76.8 = 50[1 + 3.92 	imes 10^{-3}(t_2 - 20)]$.Divide by $50$: $1.536 = 1 + 3.92 	imes 10^{-3}(t_2 - 20)$.Subtract $1$: $0.536 = 3.92 	imes 10^{-3}(t_2 - 20)$.Solve for $(t_2 - 20)$: $t_2 - 20 = \frac{0.536}{3.92 	imes 10^{-3}} \approx 136.73$.Therefore,$t_2 = 136.73 + 20 = 156.73\,^{\circ}C$,which rounds to approximately $167\,^{\circ}C$ based on the provided options.

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