ladder: Jacob's ladder of resistors

In RobinHankin/ResistorArray: Electrical Properties of Resistor Networks

Jacob's ladder of resistors

Description

A potentially infinite resistor network. Consider node 1 to be Earth. Nodes 2,\ldots, n are each connected to node 1 by a resistor. For 1<i<n, node i is connected to node i+1.

Usage

ladder(n, x = 1, y = 1, z = NULL)

Arguments

n	Number of nodes
x	Resistance of resistors connected to node 1 (earth). Standard recycling rules are used
y	Resistance of the other resistors (ie those not connected to earth). Standard recycling rules are used
z	Resistance of all resistors in the network. If non-NULL, x and y are discarded

Value

Returns a standard conductance matrix

Author(s)

Robin K. S. Hankin

See Also

cube, series

Examples

#  Resistance of an infinite Jacob's ladder with unit resistors is known
#  to be (sqrt(5)-1)/2:

 phi <- (sqrt(5)-1)/2
 resistance(ladder(20),1,2) - phi
 resistance(ladder(60),1,2) - phi

 Wu(ladder(20))[1,2]-phi


# z is the resistance of all the resistors:

 ladder(n=8,z=1/(1:13))

# See how node 1 is the "earth", with resistors of conductance 1,2,...,7
#  connecting to nodes 2-8.  Then nodes 5 & 6, say, are connected by a
#  resistor of conductance 11.

RobinHankin/ResistorArray documentation built on Jan. 17, 2024, 5:05 p.m.