# Transient response of LCR circuit

We study the time evolution of the voltage across the capacitor in an LCR circuit by applying a 5 to 0 volt step. Depending on the values of the parameters L,C and R, there are three different cases: Underdamped, Critically damped and Overdampped.

Connect the Inductor from OD1 to A1 and capacitor from A1 to GND. To change the damping factor add a resistor in series with the inductor, or change the value of the capacitor. The python program to plot the response is shown below

from pylab import *
import expeyes.eyesj, expeyes.eyemath as em
p = expeyes.eyesj.open()

NP = 150   # number of readings
tg = 10    # time gap between them, keep NP*tg around 3*RC

p.set_state(10,1)
p.enable_set_low(10)         # OD1 go LOW before capture
t,v = p.capture_hr(1,NP,tg)    # choose NP*tg according to RC

p.save( [[t,v]], 'lcr.dat')    # save data to a file
plot(t,v)
show()

The plots shown are for L=140 mH and C = 0.01 uF and C = 1 uF. The graph can be fitted with a damped exponential to extract the frequency and damping factor. The figure below shows the experimental data and the fit, along with the extracted parameters.