Question

Q 3. In an LRC series circuit, the impressed voltage Elt) and the charge q(t) on the capacitor are related to cach other hy the linear socond-order ordinary differential equation, dey + R 1 g= E(t) . T dt df where L is the inductaice. R is the resistauce and C is the capacitance. Suppose we Icasure the charge on rhe capacitor for several valnes of t and obtain 1.4 1.0 1.1 1.2 1.3 32 22 24 28 21 where t is in seconds, a is in coulombs, the inductance L is a constant 0.8h, the resistance R is 0.752 and the Capacitance is 0.001f. Approximate the voltage E(t) when t=1.1. 1.2 and 1.3. 10 points

Answer 1

2 1 2 E g.19 38 t"-1-1 856 t t 1.9794 21 24 1-2 2 B 13 3 2 then dq - 1 856 2 X 9.993 8 t dt da dt g.58 6 t - 'lg56 19.S876 dt2 E L olt dt2 +0. 19.586 t- l1856) (0.(1.5836) (t13 とー 18 SGヒ + E L I4.690 t -D 3892 + 949 3.8 t2 156 1185.6 t 119494 19 9 4 18 1190909 七 9A93.8 t2 t 3 at 2-96 X10 volk 01メむいて volk E