Could you please write the matlab code for these two problems thank you

Homework 1 Note: Please label your plots and add legend. Upload a single PDF file containing your answers, MATLAB code and figures for both problems. Due Date: 09/12/2017, 2:30 PM Problem 1 The response of circuits containing resistors, inductors, and capacitors depends upon the relative values of the resistors and the way they are connected. An important intermediate quantity used in describing the response of such circuits is s. Depending on the values of R, L, and C, the values of s will be either both real values, a pair of complex values, or a duplicated value L = 100 mH C=1uF The equation that identifies the response of a series circuit shown above is (a) Determine the values of s for a resistance of 800 Ω. (b) Create a vector of values of R between 100 to 1000 Ω with a step size of 5, Evaluate s at all values of R. (c) Plot value of real and imaginary parts of s vs. R. (Hint: See help for MATLAB functions real and imag) (d) What is the minimum value of R that yields pure real value of s. (e) The resonant frequency of a series RLC circuit is given by Compute the resonant frequency of the above circuit.

PROBLEM-1

(a)

MATLAB CODE:

R = 800;
L = 100e-3;
C = 1e-6;
s = [(-R/L)+sqrt((R/(2*L))^2 – (1/(L*C))),(-R/L)-sqrt((R/(2*L))^2 – (1/(L*C)))];

OUTPUT:

(b)

MATLAB CODE:

R = 100:5:1000;
L = 100e-3;
C = 1e-6;
for i = 1 : length(R)
s(i,:) = [(-R(i)/L)+sqrt((R(i)/(2*L))^2 – (1/(L*C))),(-R(i)/L)-sqrt((R(i)/(2*L))^2 – (1/(L*C)))];
end

OUTPUT:

(c)

MATLAB CODE:

plot(R,real(s));
hold on;
plot(R,imag(s),’r’);
xlabel(‘Resistor, R’);
ylabel(‘Circuit response, s’);
legend(‘real(s)’,’real(s)’,’imag(s)’);
hold off;

OUTPUT:

(d)

s yields pure real values if :

$\left ( \frac{R}{2L} \right )^{2} - \frac{1}{LC} \geq 0$

$=> R^{2} \geq \frac{4L}{C} => 2\sqrt{\frac{L}{C}}$

$Minimum\ value\ of\ R\ = 2\sqrt{\frac{L}{C}} = 2\sqrt{\frac{10^{-1}}{10^{-6}}} = 632.45\ ohms$

(e)

$Resonant\ frequency,\ f = \frac{1}{2\pi \sqrt{LC}} = 503.29 Hz$

PROBLEM-2

Note: All the problems in this section can be solved similar to corresponding problem in PROBLEM-1 section just by changing values of equation of circuit reaction ,L,C and R.

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