The resistance of a platinum wire is to be calibrated for low-temperature work.A platinum wire with resistance 1.5 Ω at 30°C is immersed in liquid nitrogen at 93 K (−180°C).If the temperature response of the platinum wire is linear,what is the expected resistance of the platinum wire at −180°C? [α_platinum = 3.92 × 10−³ (°C)−¹]. A)0.265 Ω B)2.38 Ω C)2.73 Ω D)8.48 Ω E)0.618 Ω

Question

Quizplus · Accepted Answer

The resistance of a metal wire is given by the equation:R = R0(1 + αΔT)where:R is the resistance at temperature TR0 is the resistance at temperature T0α is the temperature coefficient of resistanceΔT = T - T0In this problem, we are given the following information:R0 = 1.5 ΩT0 = 30°CT = -180°Cα = 3.92 × 10−3 (°C)−1We can use this information to solve for R:R = R0(1 + αΔT)R = 1.5 Ω(1 + 3.92 × 10−3 (°C)−1(-180°C - 30°C))R = 1.5 Ω(1 - 0.826)R = 0.265 ΩTherefore, the expected resistance of the platinum wire at -180°C is 0.265 Ω.

The Resistance of a Platinum Wire Is to Be Calibrated