### Resistance of a rectangular block

Metal | Resistivity - Ωm |
---|---|

Silver | 1.59x10^{-8} |

Nickel | 6.99x10^{-7} |

Iron | 1.0x10^{-7} |

Copper | 1.68x10^{-8} |

Lead | 2.2x10^{-7} |

Tungsten | 5.69x10^{-8} |

**E.g.1**

The dimensions of a metal cuboid are 6cm, 4cm and 2cm respectively. Find its resistance, if the resistivity is 1.2 X 10^{-8}Ωm and the current enters through the smallest surface.

R = ρl/A

A = 8 x 10^{-4}m^{2}

l= 6 x 10^{-2}m

R = 1.2 X 10^{-8} x 6 x 10^{-2} / 8 x 10^{-4}

R = 9 X 10^{-7}Ω

E.g.2

The radius of a wire is 2cm and the length is 8cm. If the resistivity is 3x10^{-6}

A = πr^{2} = 3.142*2^{2}*10^{-4} = 12.562*10^{-4}

R = ρl/A = 3X10^{-6}*8*10^{-2}/12.562*10^{-4} = 1.9x10^{-4}Ω.

E.g.3

The resistance of a wire is 4Ω. It is folded up and then twisted in the middle. What is its new resistance?

When it is folded up and then twisted, the cross sectional area gets doubled and length gets halved.

So, 4 = ρl/A for the first wire

R = ρ(l/2)/2A for the second wire

4/R = 4

R = 1Ω.

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