3. (LO4) The rate of change in resistance of a conductive wire (R(0)) with respect to its temperature (0), is found to be equal to the product of the temperature coefficient of resistance (k) and the resistance at that temperature. If the variation of the resistance R(0) is continuous with respect to the temperature, a. formulate a first-order differential equation to describe the situation. b. Solve the differential equation formulated in (a) to find a formula for the resistance of the wire at a given temperature, given that its resistance is (50.22) N at 0°C. Assume k = 4.04 x 10-3 °C-1. c. Verify your answer in (b) by using another method of solving the differential equation (e.g. Laplace transforms). d. This conductor is being considered for use in wiring a circuit that is to be installed in a system prone to high temperatures. In order for this system to maintain stable operation in its environment, it is determined that the resistance of the wire should never go above 112 N. If the maximum temperature the system can reach is 195 °C, comment on the applicability of this wire in the system.

3. (LO4) The rate of change in resistance of a conductive wire (R(0)) with respect to its temperature (0), is found to be equal to the product of the temperature coefficient of resistance (k) and the resistance at that temperature. If the variation of the resistance R(0) is continuous with respect to the temperature, a. formulate a first-order differential equation to describe the situation. b. Solve the differential equation formulated in (a) to find a formula for the resistance of the wire at a given temperature, given that its resistance is (50.22) N at 0°C. Assume k = 4.04 x 10-3 °C-1. c. Verify your answer in (b) by using another method of solving the differential equation (e.g. Laplace transforms). d. This conductor is being considered for use in wiring a circuit that is to be installed in a system prone to high temperatures. In order for this system to maintain stable operation in its environment, it is determined that the resistance of the wire should never go above 112 N. If the maximum temperature the system can reach is 195 °C, comment on the applicability of this wire in the system.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

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