MATH 307 Midterm: MATH 307 UW 307 Su09 Sol2
Document Summary
Math 307, sections a and b, summer 2009, solutions to midterm ii: a series circuit has a capacitor of 10 5 farad, a resistor of 3 102 ohms, and an inductor of 0. 2 henry. The initial charge on the capacitor is 10 6 coulomb and there is no initial current. (a) set up an initial value problem modeling this circuit. (2 points) Q (0) = 0 where q(t) is the charge. (b) find the charge on the capacitor and the current through the resistance at any time t. The characteristic equation has roots r = 300 p(300)2 4(0. 2)105. = 1000 or 500 so the solution is of the form. To nd the constants c1 and c2 we use the initial conditions: and the current is so giving us therefor the charge is and the current is. C1 = 10 6 and c2 = 2 10 6.
