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(C) The resistance at temperature $t$ is given by $R_t = R_0 [1 + \alpha t]$,where $R_0$ is the resistance at $0^{\circ}C$ and $\alpha$ is the tempera

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$4$

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(C) The resistance at temperature $t$ is given by $R_t = R_0 [1 + \alpha t]$,where $R_0$ is the resistance at $0^{\circ}C$ and $\alpha$ is the temperature coefficient of resistance.For $t = 50^{\circ}C$,$R_{50} = R_0 [1 + 50\alpha] = 5 \quad \dots(1)$For $t = 100^{\circ}C$,$R_{100} = R_0 [1 + 100\alpha] = 6 \quad \dots(2)$Dividing equation $(1)$ by $(2)$:$\frac{5}{6} = \frac{1 + 50\alpha}{1 + 100\alpha}$$5(1 + 100\alpha) = 6(1 + 50\alpha)$$5 + 500\alpha = 6 + 300\alpha$$200\alpha = 1 \implies \alpha = \frac{1}{200} \, ^{\circ}C^{-1}$Substituting $\alpha$ into equation $(1)$:$5 = R_0 [1 + 50 	imes \frac{1}{200}]$$5 = R_0 [1 + \frac{1}{4}]$$5 = R_0 [\frac{5}{4}]$$R_0 = 4 \, \Omega$

The resistance of a resistor wire is $5 \, \Omega$ at $50^{\circ}C$ and $6 \, \Omega$ at $100^{\circ}C$. What is its resistance at $0^{\circ}C$ in $\Omega$?

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