Thermal Properties of Matter

JEE Main level, single correct, medium

96 of 126

Question 96 of 126

Resistance of the wire is measured as 2Ω2\Omega and 3Ω3\Omega at 10∘C10^{\circ}C and 30∘C30^{\circ}C respectively. Temperature coefficient of resistance of the material of the wire is

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Answer: (A) 0.033C∘−10.033{C^{\circ}}^{-1}

Resistance of a material is related to temperature by expression R=R0(1+αΔT)R={R}_{0}\left(1+\alpha \Delta T\right)
Here, at 10∘C10^{\circ}C, we have 2=R0(1+10α)...(i)2={R}_{0}\left(1+10\alpha \right)...\left(i\right)
And at 30∘C30^{\circ}C, we have 3=R0(1+30α)...(ii)3={R}_{0}\left(1+30\alpha \right)...\left(ii\right)
From equation (i)\left(i\right), R0=2(1+10α){R}_{0}=\dfrac{2}{\left(1+10\alpha \right)}
Putting this value in equation (ii)\left(ii\right),
3=21+10α(1+30α)⇒3+30α=2+60α3=\dfrac{2}{1+10\alpha }\left(1+30\alpha \right) \Rightarrow 3+30\alpha =2+60\alpha
⇒1=30α\Rightarrow 1=30\alpha
Hence, temperature coefficient of the material of wire is α=130=0.033∘C−1\alpha =\dfrac{1}{30}=0.033^{\circ}{C}^{-1}

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