Resistance of a wire at 0^{circ} C, 100^{circ | vedclass

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(D) The resistance of a conductor at temperature $T$ is given by $R = R_0(1 + \alpha \Delta T)$,where $R_0$ is the resistance at $0^{\circ} C$ and $\a

Vedclass · Accepted Answer

$748$

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(D) The resistance of a conductor at temperature $T$ is given by $R = R_0(1 + \alpha \Delta T)$,where $R_0$ is the resistance at $0^{\circ} C$ and $\alpha$ is the temperature coefficient of resistance.For the first case,at $100^{\circ} C$:$10.2 = 10(1 + \alpha(100 - 0))$$10.2 = 10 + 1000\alpha$$0.2 = 1000\alpha \Rightarrow \alpha = \frac{0.2}{1000} = 2 	imes 10^{-4} /^{\circ} C$.For the second case,at $t^{\circ} C$:$10.95 = 10(1 + \alpha(t - 0))$$10.95 = 10 + 10\alpha t$$0.95 = 10 	imes (2 	imes 10^{-4}) 	imes t$$0.95 = 2 	imes 10^{-3} 	imes t$$t = \frac{0.95}{0.002} = 475^{\circ} C$.To convert the temperature to the Kelvin scale:$T(K) = t(^{\circ} C) + 273$$T(K) = 475 + 273 = 748 \ K$.

Resistance of a wire at $0^{\circ} C, 100^{\circ} C$ and $t^{\circ} C$ is found to be $10 \Omega, 10.2 \Omega$ and $10.95 \Omega$ respectively. The temperature $t$ in Kelvin scale is $\qquad$

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