Two different conductors have the same resist | vedclass

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(D) Let $R_0$ be the resistance of both conductors at $0\,^{\circ}C.$The resistance of the first conductor at $t_1\,^{\circ}C$ is given by $R_1 = R_0(

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$\frac{t_2}{t_1}$

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(D) Let $R_0$ be the resistance of both conductors at $0\,^{\circ}C.$The resistance of the first conductor at $t_1\,^{\circ}C$ is given by $R_1 = R_0(1 + \alpha_1 t_1).$The resistance of the second conductor at $t_2\,^{\circ}C$ is given by $R_2 = R_0(1 + \alpha_2 t_2).$Given that $R_1 = R_2,$ we have:$R_0(1 + \alpha_1 t_1) = R_0(1 + \alpha_2 t_2)$Dividing both sides by $R_0$:$1 + \alpha_1 t_1 = 1 + \alpha_2 t_2$Subtracting $1$ from both sides:$\alpha_1 t_1 = \alpha_2 t_2$Therefore,the ratio of the temperature coefficients is:$\frac{\alpha_1}{\alpha_2} = \frac{t_2}{t_1}$

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