Did you know you can compute square roots using a supply of resistors and an ohmmeter? Here's how.

If you have an infinite array of resistors

it is straightforward to show that the effective equivalent resistance, *R _{eq}*, of the
combination is given by the expression

.

Furthermore, by considering the array truncated after

R_{2}/R_{1} | N for 1% | N for 0.1% |
---|---|---|

0.1 | 1 | 1 |

1 | 2 | 2 |

5 | 4 | 6 |

10 | 5 | 8 |

20 | 8 | 12 |

50 | 13 | 19 |

100 | 18 | 26 |

Hence, you can create an array with an equivalent resistance which is the
square root of *Y* kiloohms, *Y* > 1, by choosing *R _{1}* = 1 kiloohm and

Example: This array uses *N* = 3 and has a resistance equal to the square root of 3 kiloohms
(to better than 0.1% if ideal resistors are used).

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