1. A motor coil can be modeled as a hollow copper cylinder with an outer diameter of 50 mm, an inner diameter of 40 mm, and a length of 60 mm. The motor stalls at time t = 0 and, at this point, the copper experiences a step input in electrical heating of Po⚫u(t), where Po is 350 W. Assume that there is little time for significant heat loss to the environment so that the copper cylinder can be considered to be insulated. If the initial temperature is 30 °C, find the temperature as a function of time, T(t), analytically using Laplace transforms. Calculate the time required to reach the breakdown temperature of the wire insulation, which is approximately 250 °C. Write a script file in MATLAB® to: (a) determine the time for the copper to reach 250 °C using the command find; and (b) plot T(t) over this time interval. Copper has a density of 8960 kg/m³ and a specific heat of 390 J/kg-°C.

1. A motor coil can be modeled as a hollow copper cylinder with an outer diameter of 50 mm, an inner diameter of 40 mm, and a length of 60 mm. The motor stalls at time t = 0 and, at this point, the copper experiences a step input in electrical heating of Po⚫u(t), where Po is 350 W. Assume that there is little time for significant heat loss to the environment so that the copper cylinder can be considered to be insulated. If the initial temperature is 30 °C, find the temperature as a function of time, T(t), analytically using Laplace transforms. Calculate the time required to reach the breakdown temperature of the wire insulation, which is approximately 250 °C. Write a script file in MATLAB® to: (a) determine the time for the copper to reach 250 °C using the command find; and (b) plot T(t) over this time interval. Copper has a density of 8960 kg/m³ and a specific heat of 390 J/kg-°C.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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