cube {ResistorArray}R Documentation

Specimen conductance matrices

Description

Various conductance matrices for simple resistor configurations including a skeleton cube

Usage

cube(x=1)
octahedron(x=1)
tetrahedron(x=1)
dodecahedron(x=1)
icosahedron(x=1)

Arguments

x Reistance of each edge. See details section for details.

Details

cube() returns an eight-by-eight conductancematrix for a skeleton cube of 12 resistors. Each row/column corresponds to one of the 8 vertices that are the electrical nodes of the compound resistor.

In one orientation, node 1 has position 000, node 2 position 001, node 3 position 101, node 4 position 100, node 5 position 010, node 6 position 011, node 7 position 111, and node 8 position 110.

To do a Wheatstone bridge, use tetrahedron() with one of the resistances Inf.

In cube(), x is a vector of twelve elements (a scalar argument is interpreted as the resistance of each resistor) representing the twelve resistances of a skeleton cube. In the orientation described below, the elements of x correspond to R_12, R_14, R_15, R_23, R_26, R_34, R_37, R_48, R_56, R_58, R_67, R_78 (here R_ij is the resistancd between node i and j). The pattern is general: edges are ordered first by the row number i, then column number j.

In octahedron(), x is a vector of twelve elements (a scalar argument is interpreted as the resistance of each resistor) representing the twelve resistances of a skeleton octahedron. If node 1 is “top” and node 6 is “bottom”, the elements of x correspond to R_12, R_13, R_14, R_15, R_23, R_25, R_26, R_34, R_36, R_45, R_46, R_56.

Author(s)

Robin K. S. Hankin

References

F. J. van Steenwijk “Equivalent resistors of polyhedral resistive structures”, American Journal of Physics, 66(1), January 1988.

Examples


 resistance(cube(),1,7)  #known to be 5/6 ohm
 resistance(cube(),1,2)  #known to be 7/12 ohm

 resistance(octahedron(),1,6) #known to be 1/2 ohm
 resistance(octahedron(),1,5) #known to be 5/12 ohm

 resistance(dodecahedron(),1,5) 


[Package ResistorArray version 1.0-7 Index]