The resistance of a wire at 50^{circ}C is 5, | vedclass

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

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$4$

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(C) The resistance of a conductor 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 $t = 50^{\circ}C$, $R_{50} = R_0(1 + 50\alpha) = 5$ --- $(1)$For $t = 100^{\circ}C$, $R_{100} = R_0(1 + 100\alpha) = 6$ --- $(2)$Dividing equation $(2)$ by equation $(1)$:$\frac{R_0(1 + 100\alpha)}{R_0(1 + 50\alpha)} = \frac{6}{5}$$5(1 + 100\alpha) = 6(1 + 50\alpha)$$5 + 500\alpha = 6 + 300\alpha$$200\alpha = 1$$\alpha = \frac{1}{200} = 0.005^{\circ}C^{-1}$Substituting $\alpha$ into equation $(1)$:$5 = R_0(1 + 50 	imes 0.005)$$5 = R_0(1 + 0.25)$$5 = R_0(1.25)$$R_0 = \frac{5}{1.25} = 4\, \Omega$.

The resistance of a wire at $50^{\circ}C$ is $5\, \Omega$ and at $100^{\circ}C$ is $6\, \Omega$. The resistance of the wire at $0^{\circ}C$ is ............... $\Omega$.

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