A nichrome rod of length LN = 78 cm is connected in series (end to end) to a carbon rod of length LC = 5 cm. Both rods have cross-sectional areas of A = 85 mm2. At T0 = 20° C the restistivity of nichrome is ρN = 1.50 × 10-6 Ω⋅m and the resistivity of carbon is ρC = 3.50 × 10-5 Ω⋅m. The temperature coefficient of nichrome is positive with value αN = 0.4 × 10-3 °C-1. The temperature coefficient of carbon is negative with a value αC = -0.5 × 10-3 °C-1. The nonlinear dependence of the resistivity on temperature T can be written as ρ = ρ0eα(T-T0). A) Write an expression for the total resistance of the nichrome-carbon combination as a function of temperature in terms of quantities given in the introduction. Simplify your answer as much as possible. B) Calculate the temperature in degrees Celsius for which the resistance of the carbon-nichrome combination will be a minimum C) Calculate the value of the minimum resistance, in ohms.

A nichrome rod of length LN = 78 cm is connected in series (end to end) to a carbon rod of length LC = 5 cm. Both rods have cross-sectional areas of A = 85 mm2. At T0 = 20° C the restistivity of nichrome is ρN = 1.50 × 10-6 Ω⋅m and the resistivity of carbon is ρC = 3.50 × 10-5 Ω⋅m. The temperature coefficient of nichrome is positive with value αN = 0.4 × 10-3 °C-1. The temperature coefficient of carbon is negative with a value αC = -0.5 × 10-3 °C-1. The nonlinear dependence of the resistivity on temperature T can be written as ρ = ρ0eα(T-T0). A) Write an expression for the total resistance of the nichrome-carbon combination as a function of temperature in terms of quantities given in the introduction. Simplify your answer as much as possible. B) Calculate the temperature in degrees Celsius for which the resistance of the carbon-nichrome combination will be a minimum C) Calculate the value of the minimum resistance, in ohms.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter21: Current And Direct Current Circuits

Section: Chapter Questions

Problem 63P

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A nichrome rod of length LN = 78 cm is connected in series (end to end) to a carbon rod of length LC = 5 cm. Both rods have cross-sectional areas of A = 85 mm2. At T0 = 20° C the resistivity of nichrome is ρN = 1.50 × 10-6 Ω⋅m and the resistivity of carbon is ρC = 3.50 × 10-5 Ω⋅m. The temperature coefficient of nichrome is positive with a value αN = 0.4 × 10-3 °C-1. The temperature coefficient of carbon is negative with a value αC = -0.5 × 10-3 °C-1. The nonlinear dependence of the resistivity on temperature T can be written as ρ = ρ0eα(T-T0). A)Write an expression for the total resistance of the nichrome-carbon combination as a function of temperature in terms of quantities given in the introduction. Simplify your answer as much as possible. Answer to part A is r(t)= ( ( ρC LC )/A ) eαC ( T - T0 ) + ( ( ρN LN )/A ) eαN ( T - T0 ) B) Calculate the temperature in degrees Celsius for which the resistance of the carbon-nichrome combination will be a minimum. C) Calculate the…
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