The resistance of a tungsten wire at 150^{cir | vedclass

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(C) The resistance of a wire 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 t

Vedclass · Accepted Answer

$258$

Vedclass · Answer

(C) The resistance of a wire 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 $R_{150} = 133 \Omega$ and $\alpha = 0.0045^{\circ} C^{-1}$.For $t = 150^{\circ} C$:$133 = R_0(1 + 150 	imes 0.0045) = R_0(1 + 0.675) = 1.675 R_0$$R_0 = \frac{133}{1.675} \approx 79.403 \Omega$Now,for $t = 500^{\circ} C$:$R_{500} = R_0(1 + 500 	imes 0.0045) = R_0(1 + 2.25) = 3.25 R_0$Substituting $R_0$:$R_{500} = 3.25 	imes \frac{133}{1.675} = \frac{432.25}{1.675} \approx 258.06 \Omega$Thus,the resistance at $500^{\circ} C$ is approximately $258 \Omega$.

The resistance of a tungsten wire at $150^{\circ} C$ is $133 \Omega$. The temperature coefficient of resistance is $0.0045^{\circ} C^{-1}$. The resistance of this wire at $500^{\circ} C$ is: (in $\Omega$)

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