Chapter 8 Solutions - Soln0814 110224

Transcript

Chapter 8, Solution 14. When the switch is in position A, v(0-)= 0 and i L (0) = 80/40 = 2 A. When the switch is in position B, we have a source-free series RCL circuit. R 10    1.25 2L 2 x4 1 1 o   1 LC 1 x4 4 When the switch is in position A, v(0–)= 0. When the switch is in position B, we have a source-free series RCL circuit. R 10    1.25 2L 2 x4 1 1 o   1 LC 1 x4 4 Since   o , we have overdamped case. –2 64, 0.9336 s1,2     2  o2  1.25  1.5625–0.5  1 and 1.56 v(t) = Ae–2t + Be–0.5t (1) v(0) = 0 = A + B (2) i C (0) = C(dv(0)/dt) = –2 or dv(0)/dt = –2/C = –8. But dv( t )  2Ae  2 t  0.5Be  0.5t dt dv(0)  2 A  0.5B  8 dt Solving (2) and (3) gives A= 1.3333 and B = –1.3333 v(t) = 5.333e–2t–5.333e–0.5t V. (3)