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The resistance of platinum wire at 0°C is 2 Ω and 6.8 Ω at 80°C. The temperature coefficient of resistance of the wire is

Asked in NEET 2023 · Temperature dependence of resistance

(1) 3×10⁻⁴ °C⁻¹
(2) 3×10⁻³ °C⁻¹
(3) 3×10⁻² °C⁻¹
(4) 3×10⁻¹ °C⁻¹

Answer: (3) 3×10⁻² °C⁻¹

Step-by-step solution

R=R₀(1+αΔ T).

6.8=2(1+80α), so 1+80α=3.4.

α=(2.4)/(80)=0.03=3×10⁻² °C⁻¹.

Why the other options are wrong

(1) Two powers of ten low: with α=3×10⁻⁴ the resistance would rise by only 0.048 Ω over 80°C, not 4.8 Ω.
(2) A power of ten low: with α=3×10⁻³ the resistance would rise by only 0.48 Ω over 80°C, not 4.8 Ω.
(4) A power of ten high: with α=0.3 the resistance would rise by 48 Ω over 80°C.

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