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ResistorArray (version 1.0-7)

cube: 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 $R_{12}$, $R_{13}$, $R_{14}$, $R_{15}$, $R_{23}$, $R_{25}$, $R_{26}$, $R_{34}$, $R_{36}$, $R_{45}$, $R_{46}$, $R_{56}$.

References

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

Examples

Run this code
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)

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