Consider the following parallel RLC circuit: The equation that identifies the re
ID: 3877904 • Letter: C
Question
Consider the following parallel RLC circuit: The equation that identifies the response of a parallel circuit shown above is s = -1/2RC plusminus squareroot (1/2RC)^2 - 1/LC (a) Determine the values of s for a resistance of 200 ohm. (b) Create a vector of values of R between 50 to 900 ohm with a step size of 2. Evaluate s at all values of R. (c) Plot value of real and imaginary parts of s vs. R (d) What is the minimum value of R that yields pure real value of s. (e) The resonant frequency of a parallel RLC circuit is given by: f_r = 1/2 pi squareroot LC Compute the resonant frequency of the above circuit.Explanation / Answer
r = 200;
l = 0.64;
c = 0.000001;
% PART A
s1 = (-1)/(2*r*c) + sqrt( (1/(2*r*c)).^2 - 1/(l*c));
s2 = (-1)/(2*r*c) - sqrt( (1/(2*r*c)).^2 + 1/(l*c));
%PART B
for r = 50:2:900
s1 = (-1)/(2*r*c) + sqrt( (1/(2*r*c)).^2 - 1/(l*c));
s2 = (-1)/(2*r*c) - sqrt( (1/(2*r*c)).^2 + 1/(l*c));
end
%{
for real value of s , the sqrt part has to be 0 or positive
hence
1/4r*r*c*c - 1/l*c >= 0
1/4*r*r*c*c >= 1/l*c
1/4*r*r*c >= 1/l
4*r*r*c <= l
r*r <= l/4*c
r <= 1/2*sqrtc
%}
%PART D
min_r = 1/(2*sqrt(c));
% PART E
fr = 1/(2*pi*sqrt(l*c));