VP 10 RLC oscillation and transient behavior simulation
An RLC circuit, with R=30 ( )W , L=200 (mH) , i
C=20 (μF). The driving voltage source is
0 if 𝑡 < 0
𝑣 𝑇
𝑡
where 𝑓! . ~ C
(1) Solve this circuit numerically and plot the voltage v t( ), and current i t( ) as a function of t for 𝑡 = 0 to 20𝑇 in 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)
