# HW1

```a) Write the stiffness matrix [K] for a single resistor element
1
1
−
ππ
ππ π1
πΌπ
{ }=⌈ ⌉
1
1
π2
−πΌπ
−
ππ ]
[ ππ
b) Write the connectivity table for the resistor network in Figure 2.
EN
1
2
3
4
5
6
7
8
9
10
LN1
1
2
3
3
2
4
4
4
5
6
LN2
2
3
4
5
5
5
6
7
7
7
c) Assemble the stiffness matrix for the system and write the corresponding system of linear
simultaneous equations.
π1
−π1
0
0
0
0
[ 0
−π1
π1 + π2 + π5
−π2
0
−π5
0
0
0
0
0
0
−π5
0
−π3
−π4
0
π3 + π6 + π7 + π8
−π6
−π7
−π6
−π4 + π5 + π6 + π9
0
−π7
0
π7 + π10
−π8
−π9
−π10
πΌ
π’1
1
−πΌ1 + πΌ2 + πΌ5
π’2
π’3
−πΌ2 + πΌ3 + πΌ4
π’4 = −πΌ3 + πΌ6 + πΌ7 + πΌ8
π’5
−πΌ4 − πΌ5 − πΌ6 + πΌ9
π’6
−πΌ7 + πΌ10
{π’7 } { −πΌ − πΌ − πΌ
8
9
10 }
d) Apply boundary conditions and write down the matrix equation that you would use to
solve this problem.
Assume V6 = 0
0
−π2
π2 + π3 + π4
−π3
−π4
0
0
0
0
0
−π8
−π9
−π10
π8 + π9 + π10 ]
π1
−π1
0
0
0
[ 0
−π1
π1 + π2 + π5
−π2
0
−π5
0
0
−π2
π2 + π3 + π4
−π3
−π4
0
0
0
0
−π5
−π3
−π4
π3 + π6 + π7 + π8
−π6
−π6
−π4 + π5 + π6 + π9
−π8
−π9
πΌ
π’1
1
−πΌ1 + πΌ2 + πΌ5
π’2
π’3
−πΌ2 + πΌ3 + πΌ4
π’4 = −πΌ3 + πΌ6 + πΌ7 + πΌ8
π’5
−πΌ4 − πΌ5 − πΌ6 + πΌ9
{π’7 } { −πΌ − πΌ − πΌ
8
9
10 }
0
0
0
−π8
−π9
π8 + π9 + π10 ]
e) Solve the system of equations simultaneously to determine the voltages at all the nodes.
Assume Rj = 200 ο for all the elements and I1 = 0.1A. Use an equation solver, Matlab or
your own program, to solve the equations.
clc;clear;
A= [0.005 -0.005 0 0 0 0;
-0.005 0.015 -0.005 0 -0.005 0;
0 -0.005 0.015 -0.005 -0.005 0;
0 0 -0.005 0.02 -0.005 -0.005;
0 -0.005 -0.005 -0.005 0.02 -0.005;
0 0 0 -0.005 -0.005 0.015];
B= [0.1;0;0;0;0;0]
X = linsolve(A,B)
X= [47.2727; 27.2727; 18.1818; 10.9091; 16.36; 9.0909]
f) Compute the current through elements 7 and 10. What is the current flowing to the
ground at node 6?
1
(π − π6 ) = 0.0545π΄
πΌ7 =
200 4
1
(π − π7 ) = −.0454π΄
πΌ10 =
200 6
πΌ6 = −πΌ7 + πΌ10 = −0.099π΄
```