Chapter 8 Solutions - Soln0818 110618

Transcript

Chapter 8, Solution 18. When the switch is off, we have a source-free parallel RLC circuit. o    o 1 LC  1 0.25 x1    2,  1  0.5 2 RC underdamped case  d   o   2  4  0.25  1.936 2 I o (0) = i(0) = initial inductor current = 100/5 = 20 A V o (0) = v(0) = initial capacitor voltage = 0 V v(t )  e t ( A1 cos(d t )  A2 sin(d t ))  e 0.5t ( A1 cos(1.936t )  A2 sin(1.936t )) v(0) =0 = A 1 dv  e 0.5t (0.5)( A1 cos(1.936t )  A2 sin(1.936t ))  e 0.5t (1.936 A1 sin(1.936t )  1.936 A2 cos(1.936t )) dt (V  RI o ) (0  20) dv(0)  o   20  0.5 A1  1.936 A2 1 dt RC Thus, v ( t )  [10.333e 0.5 t sin(1.936t )]volts   A2  10.333