In the circuit, Vs1 = 13 V, Vs2 = 23 V, R1 = 2.5 Ohm, R2 = 9 Ohm, R3 = 5 Ohm, R4
ID: 2079580 • Letter: I
Question
In the circuit, Vs1 = 13 V, Vs2 = 23 V, R1 = 2.5 Ohm, R2 = 9 Ohm, R3 = 5 Ohm, R4 = 6 Ohm, R5 = 4 Ohm, R6 = 5.5 Ohm.
A. Assume that the mesh currents for the three meshes shown in the circuit diagram are defined as i1, i2 and i3 correspondingly.
Using the notations of the caption below circuit diagram (case sensitive!), write the mesh equations for the circuit keeping all the terms on the left-hand side (LHS), so that the equation appears as " LHS = 0"
Enter the left-hand side of mesh equation for the mesh "1"
Vs1-i1*R1-(i1-i3)*R4-(i1-i2)*R2 = 0;
Enter the left-hand side of mesh equation for the mesh "2"
Vs2-(i2-i1)*R2-(i2-i3)*R5-i2*R3 = 0;
Enter the left-hand side of mesh equation for the mesh "3"
-(i3-i2)*R5-(i3-i1)*R4-i3*R6 = 0;
B. Using mesh analysis, answer the following questions.
1) Find the current through the resistor R1 in the direction from left to right. (Unit: A)
3.1670 A
2) Find the current through the resistor R2 in the direction from right to left. (Unit: A)
-0.157366563740626 A
3) Find the current through the resistor R3 in the direction from right to left. (Unit: A)
3.3243 A
4) Find the potential of the node "a" with respect to the ground node indicated in the circuit diagram. (Unit: V)
5.0826 V
5) Find the potential of the node "b" with respect to the ground node indicated in the circuit diagram. (Unit: V)
-1.41629907366564 V
6) Find the potential of the node "c" with respect to the ground node indicated in the circuit diagram. (Unit: V)
-6.37836347595942 V
Explanation / Answer
Ans) Matlab code here
----------------------------------------
format long
Vs1=13;
Vs2=23;
R1=2.5;
R2=9;
R3=5;
R4=6;
R5=4;
R6=5.5;
syms i1 i2 i3
eqn1=Vs1-i1*R1-(i1-i3)*R4-(i1-i2)*R2==0;
eqn2=Vs2-(i2-i1)*R2-(i2-i3)*R5-i2*R3==0;
eqn3=-(i3-i2)*R5-(i3-i1)*R4-i3*R6==0;
% equationsToMatrix to convert the equations into the form AX = B.
[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [i1, i2, i3]);
X = linsolve(A,B);
I=double(X); %converts symbolic result to numeric
i1=I(1);
i2=I(2);
i3=I(3);
%1.current through R1
iR1=i1
%2.current through R2 from right to left
iR2=i1-i2
%3.current through R3 from right to left
iR3=i2
%4.potential of node a
Va=Vs1-i1*R1
%5.potential of node b
Vb=Va-(i1-i3)*R4
%6 potential of node c
Vc=Vb-(i2-i3)*R5
---------------------------------------------------------------------------
===============================================
Result in command window
iR1 =
3.166960741067490
iR2 =
-0.157366563740626
iR3 =
3.324327304808116
Va =
5.082598147331275
Vb =
-1.416299073665638
Vc =
-6.378363475959418
>>