Chapter 2, Problem 2.64P

We have a cube with 1- $\Omega$ resistances along each edge as illustrated in Figure P2.64 in which we are looking into the front face which has corners at nodes 1,2,7, and the reference node Nodes 3, 4, 5, and 6 are the corners on the rear face of the cube (Alternatively, you can consider it to be a planar network.) We want to find the resistance between adjacent nodes, such as node 1 and the reference node. We do this by connecting a 1-A current source as shown and solving for v1, which is equal in value to the resistance between any two adjacent nodes.

1. Use MATLAB to solve the matrix equation GV=1 for the node voltages and determine the resistance.

Modify your work to determine the resistance between nodes at the ends of a diagonal across a face, such as node 2 and the reference node.

Finally, find the resistance between opposite corners of the cube [Comment:Part (c) is the same as Problem 2.16, in which we suggested using symmetry to solve for the resistance. Parts (a) and (b) can also be solved by use of symmetry and the fact that nodes having the same value of voltage can be connected by short circuits without changing the currents and voltages. With the shorts in place, the resistances can be combined in series and parallel to obtain the answers. Of course, if the resistors have arbitrary values. the MATLAB approach will still work but considerations of symmetry will not.]

Figure P2.64