2.9 The response of circuits containing resistors, inductors, and capacitors depends upon the relative values of the resistors and the way they are con- nected. 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. W C=1 uF L=100 m Figure P2.9 Series circuit The equation that identifies the response of a particular series circuit (Figure P2.9) is s= @ (a) Determine the values of s for a resistance of 800 12. (b) Create a vector of values for R ranging from 600 to 7002 with a step of 5 and evaluate s. find the approximate size of resistor that yields a pure real value of s. Hint: 1 uF = le-6F 1 mH = le-3H 1 % Problem 2.9 2 % a) 3 Resee %ohms 4 L=1e8e-3 %H 5 Cele-6 %F 6% s_plus is the value of s using the + in the +- portion of the equation 75_plus_a= 8 % s_minus is the value of s using the - in the +- portion of the equation s_minus_a = 10 % b) 11 % Repeat for R between 600 to 700 in increments of 5 RE 13 s_plus = 14 s_minus = 15 % you can use this table and plot to help you table_values = [R',s_plus',s_minus'] figure plot3(real(s_plus), imag(s_plus),R,':ok') hold on 20 grid on plot(real(s_minus), imag (s_minus),R,':or') title('Roots as a function of R (z-axis)') xlabel('Real') 24 ylabel('Imaginary') zlabel('R (ohms)) legend('S-plus', 's-minus) % Assign the value of R that first makes s pure real to R_pure below R_pure