cube {ResistorArray}R Documentation

Specimen conductance matrices

Description

Various conductance matrices for simple resistor configurations

Usage

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

Arguments

x In diamond(), vector of five (positive) elements, each of which specifies the resistance of the five resistors in the classic diamond resistor configuration: r is R_12, R_13, R_23, R_24, and R_34 (in order).
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.
In series(), x is a vector of two elements corresponding to the resistance of two resistors in series. The elements of x are R_12 and R_23 respectively. It is a very instructive exercise to derive R=R_12 + R_23 using matrices.

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.

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 1.0-5 Index]