A 22-$\Omega$ platinum wire at 20°C with a temperature coefficient of resistivity of 3.9 *10 ^- ³ (°C) ^- ¹ will have what resistance at 100°C? A) 29 $\Omega$ B) 20 $\Omega$ C) 26 $\Omega$ D) 14 $\Omega$

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Quizplus · Accepted Answer

The resistance of a wire is given by the equation:R = ρL/Awhere:R is the resistance in ohmsρ is the resistivity in ohm-metersL is the length of the wire in metersA is the cross-sectional area of the wire in square metersThe temperature coefficient of resistivity is given by the equation:α = (1/ρ)(dρ/dT)where:α is the temperature coefficient of resistivity in 1/°Cρ is the resistivity in ohm-metersT is the temperature in °CThe change in resistance due to a change in temperature is given by the equation:ΔR = RαΔTwhere:ΔR is the change in resistance in ohmsR is the original resistance in ohmsα is the temperature coefficient of resistivity in 1/°CΔT is the change in temperature in °CIn this problem, we have:R = 22 ohmsρ = 1.68 × 10^-8 ohm-metersL = 1 meterA = 1 × 10^-6 square metersα = 3.9 × 10^-3 1/°CΔT = 100°C - 20°C = 80°CPlugging these values into the equations above, we get:ΔR = (22 ohms)(3.9 × 10^-3 1/°C)(80°C) = 6.64 ohmsR + ΔR = 22 ohms + 6.64 ohms = 28.64 ohmsTherefore, the resistance of the wire at 100°C will be 28.64 ohms, which is closest to choice A, 29 ohms.

A 22- Ω\OmegaΩ Platinum Wire at 20°C with a Temperature Coefficient of Resistivity

A 22- $\Omega$ Platinum Wire at 20°C with a Temperature Coefficient of Resistivity