# Problem solving transient response in matlab

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Israt Jahan on 7 Sep 2016
I have RL circuit in series with ac source.
my question 1 is 1.Find an expression (analytic) for i(t). Try remembering basic circuits: transient responseof LR circuit to a sinusoidal forcing function with initial conditions.
I have answered it like below
i=e(-Rt/L)[(-V/sqrt(R^2+(wL)^2))*sin(phi-atan(wL/R)))+((V/sqrt(R^2+(wL)^2))*sin(wt+phi-atan(wL/R)))
now my 2nd question is
2.Use the above expression, e.g. in Matlab/Octave, to plot the resulting i(t) if:
V = 325 V, w = 2 ·ph. 50 Hz, wL = 0.1,
R = {0.01, 0.3} (two different values to try)
wt0 = {0, pi/4 , Pi/2 } rad (three values).
The above provide 6 combinations. Study the equation and compare plots with different parameter choices, to get a good feel for what situations of the fault-inception angle (wt0) andL/R ratio give the smallest and largest deviations from a pure sinusoid. “Sinusoid” in this case means the shape: I consider e.g. sin(wt) and sin(wt + pi/4 ) and cos(wt) all to be sinusoids, but sin(wt) + exp(−t/tau) is not purely sinusoidal. For submitting, plot just the two most extremecases (i.e. the most and least similar to a pure sinusoid) over five cycles.
I have coded matlab like following but get no sinusoidal wave. i have got value of zero
I have RL circuit in series with ac source.
my question 1 is 1.Find an expression (analytic) for i(t). Try remembering basic circuits: transient responseof LR circuit to a sinusoidal forcing function with initial conditions.
I have answered it like below
i=e(-Rt/L)[(-V/sqrt(R^2+(wL)^2))*sin(phi-atan(wL/R)))+((V/sqrt(R^2+(wL)^2))*sin(wt+phi-atan(wL/R)))
now my 2nd question is
2.Use the above expression, e.g. in Matlab/Octave, to plot the resulting i(t) if:
V = 325 V, w = 2 ·ph. 50 Hz, wL = 0.1,
R = {0.01, 0.3} (two different values to try)
wt0 = {0, pi/4 , Pi/2 } rad (three values).
The above provide 6 combinations. Study the equation and compare plots with different parameter choices, to get a good feel for what situations of the fault-inception angle (wt0) andL/R ratio give the smallest and largest deviations from a pure sinusoid. “Sinusoid” in this case means the shape: I consider e.g. sin(wt) and sin(wt + pi/4 ) and cos(wt) all to be sinusoids, but sin(wt) + exp(−t/tau) is not purely sinusoidal. For submitting, plot just the two most extremecases (i.e. the most and least similar to a pure sinusoid) over five cycles.
I have coded matlab like following but get no sinusoidal wave. i have got value of zero
close all;
clc;
%%% value of parameters
V=325;
wL=0.1; R=0.01; wt=0;
phi=atan(wL/R)
coswt=cos(pi/4);sinwt=sin(pi/4);
%%% equation of the current
i=((cos(wt)-jsin(wt))((-V/sqrt(R^2+(wL)^2))*sin(phi-atan(wL/R)))+((V/sqrt(R^2+(wL)^2))*sin(wt+phi-atan(wL/R))))
plot(i)
Would anyone help me to find the problem in matlab why i did not get any waveform.