Question

use MATLAB functions to solve this problem

The current, i, in a series RLC circuit when the switch is closed at t 0 can be determined from the solution of the V 2nd-order ODE to v t-0 d2i ndi 1 where R, L, and c are the resistance of the resistor, the inductance of the inductor, and the capacitance of the capacitor, respectively. (a) Solve the equation for i in terms of L, R, C, and t, assuming that at o (b) Use the subs command to substitute L-3 H. R 10 32, and C-80 μF nto the expression that were derived in part (a) Make a plot of i versus r for 0stsl s. (Underdamped response.) plot of i versus for Osts 2 s. (Overdamped response.) of i versus r for 0sts2 s. (Critically damped response.) (c) Use the subs command to substitute 1 3 H, R 200 Q, and C-1200 iFinto the expression that were derived in part (a) Make a (d) Use the subs command to substitute L-3 H. R-201 Ω, and 300 μ F into the expression that were derived in part (a). Make a plot

Answer 1

%part a syms y(t) R L C %defining variables %defining equations and conditions Dy diff (y); ode- diff (y, t, 2)-R/L) diff (y,t) -y/ (L*C); 1 5 6 cond2 = Dy ( 0 ) 8; %solving ODI conds - [condi cond2; ySol (t)-dsolve (ode, conds); %simplifying solution ySol simplify (ySol) 10 12 13 14 15 16-YS 17 18 19 20 21 %part b L-3:R-10:C-80 104-6; yso1=subs (ySol) ; fplot (ySol, [0,1]) title('Underdamped Response') xlabel ('t') ylabel ( ' i (t) ' ) %part c ysol (t) = dsolve (ode, conds); yso1 = simplify (ySol) ; L-3:R-200:C-1200 10-6; yso1=subs (ySol) ; figure fplot (ySol, [0,2]) title ('Overdamped Response') xlabel ('t') ylabel ( ' i (t) ' ) 23 - 24- 25 27 28 29 30 31 32

%part d ySol(t) = dsolve (ode, conds); ySol simplify (ySol) 35- 36 - 37- L-3 ; R-201:C-300*10^-б; 38- yso1=subs (ysol) ; 39-figure 40-fplot (ySol, [0,21) 41 42 43ylabel ('i (t)' title('Critically damped Response') xlabel('t')

Figure 1 File Edit View Insert Tools Desktop Window Help Underdamped Response 0.1 F 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.60.7 0.8 0.91

Figure 2 File Edit View Insert Tools Desktop Window Help Overdamped Response 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0 0.2 0.4 0.6 0.8 12 1.4 1.6 1.82