VP 10 RLC oscillation and transient behavior simulation An RLC circuit, with R=30 (W) , L=200 (mH) ,
C = 20 (μF) . The driving voltage source is
i
~
R L
C
0
𝑣(𝑡) = &36 ∙ sin(2𝜋𝑓 𝑡)
0
if 𝑡 < 0
if 0 ≤ 𝑡 < 12𝑇
if 12T ≤ 𝑡
where𝑓 =120(Hz),𝑇=1/𝑓 . !!
!
(1) Solve this circuit numerically and plot the voltage v(t), and current i(t) as a function of t for𝑡=0to20𝑇in scene1 and the total energy E(t) stored in the system in scene2.
- (2) You will see a transient behavior of the current i(t) before it reaches a steady-state oscillation around 𝑡 =
9𝑇. Find I , the amplitude of the oscillating current, and f the phase constant of the oscillating current
relative to the voltage source during the 9-th period. Compare them to the theoretical values.
- (3) After the voltage is turned off at 𝑡 = 12𝑇, you will see both the current and the total energy decays. Find the time t such that the energy decays to 10% of the energy at the time the voltage is just turned off, i.e.
0.1𝐸(𝑡 = 12𝑇).
from vpython import*
fd = 120 # 120Hz
#(Your Parameters here)
t=0
dt = 1.0/(fd * 5000) # 5000 simulation points per cycle
scene1 = graph(align = ‘left’, xtitle=’t’, ytitle=’i (A) blue, v (100V) red,’, background=vector(0.2, 0.6, 0.2)) scene2 = graph(align = ‘left’, xtitle=’t’, ytitle=’Energy (J)’, background=vector(0.2, 0.6, 0.2))
i_t = gcurve(color=color.blue, graph = scene1) v_t = gcurve(color=color.red, graph = scene1) E_t = gcurve(color=color.red, graph = scene2)
#(Your program here)
