Resistors in series and parallel combination.In the series case, the resistance R is calculated as the sum of the individual resistances. In a parallel combination, the conductance, which is the reciprocal of the resistance, is summed.(Created using Inkscape.) |

Resistance formula for a conductor with resistivity, ρ.(Illustration by the author using Inkscape.) |

Y-Delta resistor networks and their equivalent resistor values. (Created using Inkscape.) |

RA = 996 | R1 = 1315 | ||

RB = 2202 | R2 = 595 | ||

RC = 4740 | R3 = 276 |

Nodes | Resistance (calc) | Δ (meas) | Y (meas) | Error Δ (%) | Error Y (%) | |

1-2 | 1909.6 | 1909 | 1902 | 0.0 | -0.4 | |

2-3 | 871.0 | 871 | 873 | 0.0 | 0.2 | |

3-1 | 1591.2 | 1540 | 1590 | -3.2 | -0.1 |

An infinite lattice of resistors in two dimensions, connected at each crossing. The resistance between some of the nodes will give an experimental value of pi (π). (Illustration by the author using Inkscape.) |

(i,j) | R | (i,j) | R | |

0,0 | 0 | || | 2,2 | (8/3π) |

0,1 | 1/2 | || | 3,3 | (46/15π) |

1,0 | 1/2 | || | 4,4 | (352/105π) |

1,1 | 2/π | || | 5,5 | (1126/315π) |

Modeling electrical conductivity in a rectangular array of particles.The model has resistive links to nearest neighbors. Fig. 1 of ref. 12, via arXiv |

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