The resistance of a conductor at 15 ° C is 16 Ω and at 100 ° C is 20 Ω. What will be the temperature coefficient of resistance of the conductor? (a) 0.010 ⁻ 1 (b) 0.033 ⁻ 1 (c) 0.003 ° C ⁻¹ (d) 0.042 ° C ⁻¹

Answer: (c). Use Rt = R₀(1 + α t): 20/16 = (1 + 100α)/(1 + 15α) 20 + 300α = 16 + 1600α ⇒ 1300α = 4 α ≈ 0.003 ⁻¹ So the answer is (c) 0.003 ⁻¹.

The resistance of a conductor at 15 ° C is 16 Ω and at 100 ° C is 20… | JEE Main 2021 (27 Jul, Shift 2)

Q32JEE Main 2021 · 27 JUL · SHIFT 2Easy

Ohm's Law, Resistivity & Temperature

The resistance of a conductor at 15 $^\circ$ C is 16 $\Omega$ and at 100 $^\circ$ C is 20 $\Omega$ . What will be the temperature coefficient of resistance of the conductor?

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Answer: (c)

Use $R_t = R_0(1 + \alpha t)$ : $\dfrac{20}{16} = \dfrac{1 + 100\alpha}{1 + 15\alpha}$
$20 + 300\alpha = 16 + 1600\alpha \Rightarrow 1300\alpha = 4$
$\alpha \approx 0.003\ ^\circ\text{C}^{-1}$
So the answer is (c) $0.003\ ^\circ\text{C}^{-1}$ .

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