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 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 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 value of the minimum resistance, in ohms.
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