Resistance of a tungsten wire at 150,^{circ}C | 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

Vedclass · Accepted Answer

$258$

Vedclass · Answer

(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.Given:$R_{150} = 133\,\Omega$$\alpha = 0.0045\,^{\circ}C^{-1}$$T_1 = 150\,^{\circ}C$,$T_2 = 500\,^{\circ}C$Using the ratio formula:$\frac{R_{500}}{R_{150}} = \frac{1 + \alpha T_2}{1 + \alpha T_1}$$\frac{R_{500}}{133} = \frac{1 + (0.0045 	imes 500)}{1 + (0.0045 	imes 150)}$$\frac{R_{500}}{133} = \frac{1 + 2.25}{1 + 0.675} = \frac{3.25}{1.675}$$R_{500} = 133 	imes \frac{3.25}{1.675} \approx 133 	imes 1.9403 \approx 258.06\,\Omega$Thus,the resistance at $500\,^{\circ}C$ is approximately $258\,\Omega$.

Resistance of a tungsten wire at $150\,^{\circ}C$ is $133\,\Omega$. Its resistance temperature coefficient is $0.0045\,^{\circ}C^{-1}$. The resistance of this wire at $500\,^{\circ}C$ will be .............. $\Omega$.

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