An experiment is conducted to measure the electrical resistivity of Nichrome in the form of wires with different lengths and cross-sectional areas. For one set of measurements, a student uses 30 gauge wire, which has a cross-sectional area of 7.30 ✕ 10−8 m2. The student measures the potential difference across the wire and the current in the wire with a voltmeter and an ammeter, respectively. For each of the measurements given in the following table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding value of the resistivity. What is the average value of the resistivity? Ω · m By what percent does this differ from the value given in this table (1.50 ✕ 10−6 Ω · m)? % The table presents data for electrical measurements across different lengths of a conductor. It includes columns for length (\(L\)), voltage (\(\Delta V\)), current (\(I\)), resistance (\(R\)), and resistivity (\(\rho\)).- **\(L\) (m):** The length of the conductor measured in meters. - 0.540 - 1.028 - 1.543- **\(\Delta V\) (V):** The voltage across the conductor in volts. - 5.23 - 5.75 - 5.96- **\(I\) (A):** The current through the conductor in amperes. - 0.502 - 0.272 - 0.185- **\(R\) (\(\Omega\)):** The resistance of the conductor in ohms. (Values to be calculated)- **\(\rho\) (\(\Omega \cdot \text{m}\)):** The resistivity of the material. (Values to be calculated)The resistance \(R\) can be calculated using Ohm's law: \(R = \frac{\Delta V}{I}\).The resistivity \(\rho\) can be calculated using the formula: \(\rho = R \cdot \frac{A}{L}\), where \(A\) is the cross-sectional area (not provided in the table).The table leaves the columns for resistance and resistivity blank, indicating a need for further calculation by the user.

The resistance of the wire can be expressed as V=IRR=VI

Answered: An experiment is conducted to measure…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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An experiment is conducted to measure the electrical resistivity of Nichrome in the form of wires with different lengths and cross-sectional areas. For one set of measurements, a student uses 30 gauge wire, which has a cross-sectional area of 7.30 ✕ 10⁻⁸ m². The student measures the potential difference across the wire and the current in the wire with a voltmeter and an ammeter, respectively. For each of the measurements given in the following table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding value of the resistivity.

What is the average value of the resistivity?
Ω · m

By what percent does this differ from the value given in this table (1.50 ✕ 10⁻⁶ Ω · m)?
%

The table presents data for electrical measurements across different lengths of a conductor. It includes columns for length (\(L\)), voltage (\(\Delta V\)), current (\(I\)), resistance (\(R\)), and resistivity (\(\rho\)).

- **\(L\) (m):** The length of the conductor measured in meters.
- 0.540
- 1.028
- 1.543

- **\(\Delta V\) (V):** The voltage across the conductor in volts.
- 5.23
- 5.75
- 5.96

- **\(I\) (A):** The current through the conductor in amperes.
- 0.502
- 0.272
- 0.185

- **\(R\) (\(\Omega\)):** The resistance of the conductor in ohms. (Values to be calculated)

- **\(\rho\) (\(\Omega \cdot \text{m}\)):** The resistivity of the material. (Values to be calculated)

The resistance \(R\) can be calculated using Ohm's law: \(R = \frac{\Delta V}{I}\).

The resistivity \(\rho\) can be calculated using the formula: \(\rho = R \cdot \frac{A}{L}\), where \(A\) is the cross-sectional area (not provided in the table).

The table leaves the columns for resistance and resistivity blank, indicating a need for further calculation by the user.

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