Q. 45

Expert-verifiedFound in: Page 763

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

You've been asked to determine whether a new material your company has made is ohmic and, if so, to measure its electrical conductivity. Taking a sample, you wire the ends of the long axis to a power supply and then measure the current for several different potential differences. Your data are as follows:

Voltage (V) | Current (A) |

0.200 | 0.47 |

0.400 | 1.06 |

0.600 | 1.53 |

0.800 | 1.97 |

Use an appropriate graph of the data to determine whether the material is ohmic and, if so, its conductivity.

The conductor is Ohmic, and its conductivity is .

Sample wire dimension

Voltage (V) | Current (A) |

0.200 | 0.47 |

0.400 | 1.06 |

0.600 | 1.53 |

0.800 | 1.97 |

The best way to determine whether a material is Ohmic is to fit the graph for the current through the material in proportion to the potential difference; in other words, if the increase in current is proportional to the increase in potential difference.

If the parameter is close to , then the fitting will well describe the data. If not, we can scatter the points and find the parameter of the fitting.

While more professional programs can surely be used instead of Excel, the data were scattered and fitted in Excel. Following are the results.

I | U |

0.47 | 0.2 |

1.06 | 0.4 |

1.53 | 0.6 |

1.97 | 0.8 |

In view of the close proximity of to 1, we can conclude that the linear fit indeed does a good job of fitting the scattered data. This implies that our conductor is Ohmic.

Using Ohm's law, find the resistance

The slope of our line, in our case, is about . Now let us measure its resistivity:

The conductivity is just the multiplicative inverse of the resistivity,

Substitute the values,

Hence, the conductor is Ohmic, and its conductivity is

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