a) Write the stiffness matrix [K] for a single resistor element
1
1
−
𝑅𝑗
𝑅𝑗 𝑉1
𝐼𝑗
{ }=⌈ ⌉
1
1
𝑉2
−𝐼𝑗
−
𝑅𝑗 ]
[ 𝑅𝑗
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.
𝑘1
−𝑘1
0
0
0
0
[ 0
−𝑘1
𝑘1 + 𝑘2 + 𝑘5
−𝑘2
0
−𝑘5
0
0
0
0
0
0
−𝑘5
0
−𝑘3
−𝑘4
0
𝑘3 + 𝑘6 + 𝑘7 + 𝑘8
−𝑘6
−𝑘7
−𝑘6
−𝑘4 + 𝑘5 + 𝑘6 + 𝑘9
0
−𝑘7
0
𝑘7 + 𝑘10
−𝑘8
−𝑘9
−𝑘10
𝐼
𝑢1
1
−𝐼1 + 𝐼2 + 𝐼5
𝑢2
𝑢3
−𝐼2 + 𝐼3 + 𝐼4
𝑢4 = −𝐼3 + 𝐼6 + 𝐼7 + 𝐼8
𝑢5
−𝐼4 − 𝐼5 − 𝐼6 + 𝐼9
𝑢6
−𝐼7 + 𝐼10
{𝑢7 } { −𝐼 − 𝐼 − 𝐼
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
−𝑘2
𝑘2 + 𝑘3 + 𝑘4
−𝑘3
−𝑘4
0
0
0
0
0
−𝑘8
−𝑘9
−𝑘10
𝑘8 + 𝑘9 + 𝑘10 ]
𝑘1
−𝑘1
0
0
0
[ 0
−𝑘1
𝑘1 + 𝑘2 + 𝑘5
−𝑘2
0
−𝑘5
0
0
−𝑘2
𝑘2 + 𝑘3 + 𝑘4
−𝑘3
−𝑘4
0
0
0
0
−𝑘5
−𝑘3
−𝑘4
𝑘3 + 𝑘6 + 𝑘7 + 𝑘8
−𝑘6
−𝑘6
−𝑘4 + 𝑘5 + 𝑘6 + 𝑘9
−𝑘8
−𝑘9
𝐼
𝑢1
1
−𝐼1 + 𝐼2 + 𝐼5
𝑢2
𝑢3
−𝐼2 + 𝐼3 + 𝐼4
𝑢4 = −𝐼3 + 𝐼6 + 𝐼7 + 𝐼8
𝑢5
−𝐼4 − 𝐼5 − 𝐼6 + 𝐼9
{𝑢7 } { −𝐼 − 𝐼 − 𝐼
8
9
10 }
0
0
0
−𝑘8
−𝑘9
𝑘8 + 𝑘9 + 𝑘10 ]
e) Solve the system of equations simultaneously to determine the voltages at all the nodes.
Assume Rj = 200  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
(𝑉 − 𝑉6 ) = 0.0545𝐴
𝐼7 =
200 4
1
(𝑉 − 𝑉7 ) = −.0454𝐴
𝐼10 =
200 6
𝐼6 = −𝐼7 + 𝐼10 = −0.099𝐴