The electrical resistance $“R”$ of a metal is given by the formula:

$$ R = p (l/A) $$

The table below shows the electrical resistance of a wire (made of metal “Z”) of length “l” and cross-sectional area “A”, at different temperatures.

__Table 3.1__

Temperature |
Resistance (in ohm) |
---|---|

20$^\circ$ C | 40 |

25$^\circ$ C | 41 |

30$^\circ$ C | 42 |

35$^\circ$ C | 43 |

The table below shows the resistances of wires of different lengths made out of the same metal (Z) at 20° C. The cross-sectional area of these wires is equal.

__Table 3.2__

Length (in meter) |
Resistance (in ohm) |
---|---|

1 | 40 |

1.05 | 42 |

1.1 | 44 |

1.15 | 46 |

The table below shows the resistances of wires of different cross-sectional areas made of the same metal (Z) at 20° C. The length of these wires is equal.

__Table 3.3__

Cross sectional area (in 10-8 m$^2$) |
Resistance (in ohm) |
---|---|

1 | 40 |

2 | 20 |

3 | 13.33 |

4 | 10 |

The resistance of a wire is given by the formula: $R = β l^xr^y$, where $“l”$ is the length of the wire, $“r”$ is the radius of the cross section and $“β”$ is a constant.

Find the values of $x$ and $y$ from the information given in the passage.