Here we consider a circuit containing only a resistor and a capacitor. Suppose t
ID: 2974741 • Letter: H
Question
Here we consider a circuit containing only a resistor and a capacitor. Suppose the circuit consist of a resistor with value R = 2 a capacitor with value C =1/2 and the EMF is a constant source of 12 Assume the initial charge is 0 (q(0) = 0 ) The DE which describes this situation is 2 q'(t) +1/(1/2) q(t) = 12 , q(0) = 0 a) Is the DE separable? If so, write down the DE in the separable form. b) Is the DE linear? If so, what is the integrating factor? c) Is the DE autonomous? If so, what is the equilibrium solution, if any? Is the equilibrium solution stable? The solution to the IVP is q(t) = 6 - 6e^-t d) Sketch the solution curve and the equilibrium solution. e) If the resistance were to increase, would the charge approach equilibrium faster or slower?Explanation / Answer
http://iweb.tntech.edu/murdock/books/bookv5.pdf