Chapter 8 Solutions - Soln0858

Transcript

Chapter 8, Solution 58. (a) Let i =inductor current, v = capacitor voltage i(0) =0, v(0) = 4 dv(0) [v(0)  Ri (0)] (4  0)     8 V/s dt RC 0.5 (b) For t  0 , the circuit is a source-free RLC parallel circuit.  1 1   1, 2 RC 2 x0.5 x1 o  1 LC  1 0.25 x1 2  d   2 o   2  4  1  1.732 Thus, v(t )  e t ( A1 cos1.732t  A2 sin 1.732t ) v(0) = 4 = A 1 dv  e t A1 cos1.732t  1.732e t A1 sin 1.732t  e t A2 sin 1.732t  1.732e t A2 cos1.732t dt dv(0)  8   A1  1.732 A2   A2  2.309 dt v ( t )  e  t (4 cos 1.732t  2.309 sin 1.732t ) V