The temperature coefficient of resistance for a wire is 0-00125- C-1- At 300 K- its resistance is 1 - The temperature at which the resistance becomes 1-5 -

Rt_2/Rt_1=R_0[1+α t_2]/R_0[1+α t_1 1.5/1=1+α t_2/1+α t_2=1+α t_2/1+α 27 3/2=1+α t_2/1+27 α;3+81 α=2+2α t_2 1=α[2t_2 81] t_2=440.5^∘ C T_2=440.5+273=713.5 ...

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Standard XIII

Physics

Dependence of Resistance on Temperature

The temperatu...

Question

The temperature coefficient of resistance for a wire is ${0.00125}^{\circ} C^{- 1}$ . At 300 K, its resistance is $1 Ω$ . The temperature at which the resistance becomes $1.5 Ω$ .

450 K

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713 K

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454 K

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900 K

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Solution

The correct option is B 713 K
$\frac{R t_{2}}{R t_{1}} = \frac{R_{0} [1 + α t_{2}]}{R_{0} [1 + α t_{1}} \frac{1.5}{1} = \frac{1 + α t_{2}}{1 + α t_{2}} = \frac{1 + α t_{2}}{1 + α 27} \frac{3}{2} = \frac{1 + α t_{2}}{1 + 27 α}; 3 + 81 α = 2 + 2 α t_{2} 1 = α [2 t_{2} - 81] t_{2} = {440.5}^{\circ} C T_{2} = 440.5 + 273 = 713.5 K$

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The temperature coefficient of resistance for a wire is 0.00125∘C−1. At 300 K, its resistance is 1Ω. The temperature at which the resistance becomes 1.5Ω.

The correct option is B 713 KRt2Rt1=R0[1+αt2]R0[1+αt11.51=1+αt21+αt2=1+αt21+α2732=1+αt21+27α;3+81α=2+2αt21=α[2t2−81]t2=440.5∘CT2=440.5+273=713.5 K

The temperature coefficient of resistance for a wire is ${0.00125}^{\circ} C^{- 1}$ . At 300 K, its resistance is $1 Ω$ . The temperature at which the resistance becomes $1.5 Ω$ .