Resistance of the wire is measured as 2,Omega | vedclass

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(A) The resistance $R$ at temperature $T$ is given by the formula $R = R_{T_0}[1 + \alpha(T - T_0)]$,where $R_{T_0}$ is the resistance at reference te

Vedclass · Accepted Answer

$0.033$

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(A) The resistance $R$ at temperature $T$ is given by the formula $R = R_{T_0}[1 + \alpha(T - T_0)]$,where $R_{T_0}$ is the resistance at reference temperature $T_0$ and $\alpha$ is the temperature coefficient of resistance.Given:$R_1 = 2\,\Omega$ at $T_1 = 10^{\circ}C$$R_2 = 3\,\Omega$ at $T_2 = 30^{\circ}C$Using the relation $R_T = R_0(1 + \alpha T)$,we have:$2 = R_0(1 + 10\alpha)$  --- (Equation $1$)$3 = R_0(1 + 30\alpha)$  --- (Equation $2$)Dividing Equation $2$ by Equation $1$:$\frac{3}{2} = \frac{1 + 30\alpha}{1 + 10\alpha}$Cross-multiplying:$3(1 + 10\alpha) = 2(1 + 30\alpha)$$3 + 30\alpha = 2 + 60\alpha$$3 - 2 = 60\alpha - 30\alpha$$1 = 30\alpha$$\alpha = \frac{1}{30} \approx 0.033\,^{\circ}C^{-1}$.

Resistance of the wire is measured as $2\,\Omega$ and $3\,\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. The temperature coefficient of resistance of the material of the wire is............$^{\circ}C^{-1}$.

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