array.resistance {ResistorArray}

Resistance between two arbitrary points on a regular lattice of unit resistors

Description

Given two points on a regular lattice of electrical nodes joined by unit resistors (as created by makefullmatrix()), returns the resistance between the two points, or (optionally) the potentials of each lattice point when unit current is fed into the first node, and the second is earthed.

Usage

array.resistance(x.offset, y.offset, rows.of.resistors,
  cols.of.resistors, give.pots = FALSE)

Arguments

x.offset

Earthed node is at (0,0), second node is at (x.offset, y.offset)

y.offset

Earthed node is at (0,0), second node is at (x.offset, y.offset)

rows.of.resistors

Number of rows of resistors in the network (positive integer)

cols.of.resistors

Number of columns of resistors in the network (positive integer)

give.pots

Boolean, with TRUE meaning to return a matrix of potentials of the electrical nodes, and FALSE meaning to return the resistance between the origin and the current input node

Details

Note that the electrical network is effectively toroidal.

Author(s)

Robin K. S. Hankin

See Also

makefullmatrix

Examples

jj.approximate <-  array.resistance(1,2,15,17,give=FALSE)
jj.exact <- 4/pi-1/2
print(jj.exact - jj.approximate)

persp(array.resistance(4,0,14,16,give=TRUE),theta=50,r=1e9,expand=0.6)