Question

ONLY NEED SOLUTION TO QUESTION 4 PLEASE, THANK YOU

(PLEASE MAKE SURE TO PLOT THE SOLUTION IN MATLAB)

Part A (Based off week 7 Workshop content) Consider the RLC circuit where R = 5, C = 1, L = 4 and Vs = 8. 1. Use circuit analysis laws to show that the resistor's voltage and induc tor's voltage can be modelled as the system of ODEs: L RC i the system of ODEs 3. Verify your answer for question (2) by using the eig function in MAT- LAB (make sure you comment on whether your solutions are equivalent to MATLAB's) 4. Solve for VR(t) and VL(t) given VR(O)8 and VL(0)0. Plot your solution in MATLAB from t 0 to t 30

Answer 1

for a sernes RL Ci C we hare hesC di 6 vs is DC So Constant di.R dt s ol of t ,2 t-

石-o 32 15 15 I5 る2 . e-oast

o.25 dl t -0.25 니 v, 32

#MATLAB CODE#

t=0:0.01:30;
Vr=(((32/3).*exp(-0.25.*t))-((8/3).*exp(-t)));
Vl=((32/15).*((exp(-t))-exp(-0.25.*t)));
subplot(2,1,1)
plot(t,Vr,'k')
xlabel('t')
ylabel('Vr(t)')
legend('Vr(t)')
title('Voltage across register')
subplot(2,1,2)
plot(t,Vl)
xlabel('t')
ylabel('Vl(t)')
legend('Vl(t)')
title('Voltage across capacitor')

Voltage acrass register し0 et し0 : θ.01 :38 ; 812 vr-(((32/3).*exp(-0.25.t))-((8/3).*exp(-t))) Vl-((32/15). ((exp(-t))-ex (-0.25.*t))): subplot(2,1,1) S plot(t,vr,'k') xlabel(t) Legend Vr()') title Voltage across register') subplot (2,1,2) 1 plot(t,vu) xlabel(t') ylabel'VI(t) Legend'Vl(t)) title(Voltage across capacitor') 15 Voltage across capacitor vilt) 0.2 0.6- 12- 5.10. 15 20 14L 25 30 16 col: 1 encoding: UTF-8 eol: LF mand Window Editor Documentatiorn (11.61, -0.1909)