The resistance of a conductor is 5,Omega at 5 | vedclass

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(D) 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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(D) 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.Given:$R_1 = 5\,\Omega$ at $t_1 = 50\,^{\circ}C$$R_2 = 6\,\Omega$ at $t_2 = 100\,^{\circ}C$Using the ratio: $\frac{R_1}{R_2} = \frac{1 + \alpha t_1}{1 + \alpha t_2} \Rightarrow \frac{5}{6} = \frac{1 + 50\alpha}{1 + 100\alpha}$$5(1 + 100\alpha) = 6(1 + 50\alpha) \Rightarrow 5 + 500\alpha = 6 + 300\alpha$$200\alpha = 1 \Rightarrow \alpha = \frac{1}{200}\,^{\circ}C^{-1}$Now,substitute $\alpha$ into the equation for $R_1$: $5 = R_0(1 + \frac{1}{200} 	imes 50)$$5 = R_0(1 + 0.25) \Rightarrow 5 = R_0(1.25)$$R_0 = \frac{5}{1.25} = 4\,\Omega$.

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

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