The resistance of a resistance wire is 5,Omeg | vedclass

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(D) The resistance at temperature $	heta$ is given by $R_{	heta} = R_0(1 + \alpha	heta)$,where $R_0$ is the resistance at $0\,^{\circ}	ext{C}$.At

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$4$

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(D) The resistance at temperature $	heta$ is given by $R_{	heta} = R_0(1 + \alpha	heta)$,where $R_0$ is the resistance at $0\,^{\circ}	ext{C}$.At $50\,^{\circ}	ext{C}$,$5 = R_0(1 + 50\alpha)$ ... $(1)$At $100\,^{\circ}	ext{C}$,$6 = R_0(1 + 100\alpha)$ ... $(2)$Dividing equation $(1)$ by equation $(2)$:$\frac{5}{6} = \frac{1 + 50\alpha}{1 + 100\alpha}$$5(1 + 100\alpha) = 6(1 + 50\alpha)$$5 + 500\alpha = 6 + 300\alpha$$200\alpha = 1 \implies \alpha = \frac{1}{200}$Substituting $\alpha$ in equation $(1)$:$5 = R_0(1 + 50 	imes \frac{1}{200})$$5 = R_0(1 + \frac{1}{4})$$5 = R_0(\frac{5}{4})$$R_0 = 4\,\Omega$.

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

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