Current Electricity

JEE Main level, single correct, medium

74 of 380

Question 74 of 380

The resistance of a conductor at 15∘C15^{\circ}C is 16Ω16\Omega and at 100∘C100^{\circ}C is 20Ω.20\Omega . What will be the temperature coefficient of resistance of the conductor?

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Answer: (C) 0.003∘C−10.003^{\circ}{C}^{-1}

16=R0[1+α(15−To)]16={R}_{0}\left[1+\alpha \left(15-{T}_{o}\right)\right]
20=R0[1+α(100−T0)]20={R}_{0}\left[1+\alpha \left(100-{T}_{0}\right)\right]
Assuming To=0∘C{T}_{o}=0^{\circ}C, as a general convention.
⇒1620=1+α×151+α×100\Rightarrow \dfrac{16}{20}=\dfrac{1+\alpha \times 15}{1+\alpha \times 100}
⇒α=0.003C∘−1\Rightarrow \alpha =0.003{C^{\circ}}^{-1}

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