Description Usage Arguments Details Author(s) References Examples
Various conductance matrices for simple resistor configurations including a skeleton cube
1 2 3 4 5 | cube(x=1)
octahedron(x=1)
tetrahedron(x=1)
dodecahedron(x=1)
icosahedron(x=1)
|
x |
Resistance of each edge. See details section |
Function cube()
returns an eight-by-eight conductance matrix
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.
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). This series is obtainable by reading the rows given by
platonic("cube")
. 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 (again
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.
This may be read off from the rows of platonic("octahedron")
.
To do a Wheatstone bridge, use tetrahedron()
with one of the
resistances Inf
. As a worked example, let us determine the
resistance of a Wheatstone bridge with four resistances one ohm and
one of two ohms; the two-ohm resistor is one of the ones touching the
earthed node.
To do this, first draw a tetrahedron with four nodes. Then say we
want the resistance between node 1 and node 3; thus edge 1-3 is the
infinite one. platonic("tetrahedron")
gives us the order of
the edges: 12, 13, 14, 23, 24, 34. Thus the conductance matrix is
given by jj <- tetrahedron(c(2,Inf,1,1,1,1))
and the resistance
is given by resistance(jj,1,3)
[compare the analytical answer
of 117/99 ohms].
Robin K. S. Hankin
F. J. van Steenwijk “Equivalent resistors of polyhedral resistive structures”, American Journal of Physics, 66(1), January 1988.
1 2 3 4 5 6 7 | 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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