| cube {ResistorArray} | R Documentation |
Various conductance matrices for simple resistor configurations
cube(x=1) octahedron(x=1) tetrahedron(x=1) dodecahedron(x=1) icosahedron(x=1)
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.
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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.
Robin K. S. Hankin
F. J. van Steenwijk “Equivalent resistors of polyhedral resistive structures”, American Journal of Physics, 66(1), January 1988.
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)