Modeling Circuit Behavior and Exponential Temperature Decay
School
University of Guelph**We aren't endorsed by this school
Course
MATH 2270
Subject
Mathematics
Date
Dec 12, 2024
Pages
1
Uploaded by ChancellorSeaLion4237
Lab Test 2Math*2270, Fall 2023Week of November 13, 2023Q1. Consider the following circuit diagram:A mad scientist named Dr. Nerbert (“Nerr-Nerr”, according to her final remainingcolleague) is designing a Very Important Machine, whose main circuit somehowhappens to be a simple closed loop. She has a battery that she has designed togradually increase the applied voltage, givingE(t) = 6tvolts (wheretis the time inseconds); the resistance in this circuit isR= 90 Ω, and there is also aL= 1.2 Hinductor. Assume that the current at timet= 0 is zero, whereupon the switch isclosed and the loop is completed.Set up and solve an IVP modelling Nerr-Nerr’s machine, with the dependentvariablei(t) representing the current in amperes at timet.(6 marks)Q2. Your parents refuse to turn on the heat to save money, but now thetemperature in your basement bedroom is falling exponentially toward 0◦C. Whenyou arrive downstairs at 11:00 pm, the temperature is 12◦, but by 1:00 am, thetemperature has fallen to 10◦. If this exponential pattern continues, predict:•a) The temperature at 7:00 am;•b) The amount of time it would take for the temp to be cut in half.You do not need to set up or solve a DE to answer this problem, but show at leasta little work. (4 marks)
