An experiment is conducted to measure the electrical...

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 $7.30 \times 10^{-8} \mathrm{~m}^{2}$. The student measures the potential difference across the wire and the current in the wire with a voltmeter and an ammeter, respectively. (a) For each set of measurements given in the table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding values of the resistivity. (b) What is the average value of the resistivity? (c) Explain how this value compares with the value given in Table 26.2 . $$ \begin{array}{lclll} \hline L(\mathrm{~m}) & \Delta V(\mathrm{~V}) & I(\mathrm{~A}) & R(\Omega) & \rho(\Omega \cdot \mathrm{m}) \\ \hline 0.540 & 5.22 & 0.72 & & \\ 1.028 & 5.82 & 0.414 & & \\ 1.543 & 5.94 & 0.281 & & \\ \hline \end{array} $$

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 $7.30 \times 10^{-8} \mathrm{~m}^{2}$. The student measures the potential difference across the wire and the current in the wire with a voltmeter and an ammeter, respectively. (a) For each set of measurements given in the table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding values of the resistivity. (b) What is the average value of the resistivity? (c) Explain how this value compares with the value given in Table 26.2 . $$
\begin{array}{lclll}
\hline L(\mathrm{~m}) & \Delta V(\mathrm{~V}) & I(\mathrm{~A}) & R(\Omega) & \rho(\Omega \cdot \mathrm{m}) \\
\hline 0.540 & 5.22 & 0.72 & & \\
1.028 & 5.82 & 0.414 & & \\
1.543 & 5.94 & 0.281 & & \\
\hline
\end{array}
$$

Key Concepts

Electrical Resistance

Electrical resistance is a property of a material or a component that quantifies how strongly it opposes the flow of electric current. In a uniform wire, resistance is directly proportional to the length of the wire and inversely proportional to its cross?sectional area. Understanding resistance is essential in experiments that involve varying the dimensions of the conductor to see its effect on the flow of current.

Electrical Resistivity

Electrical resistivity is an intrinsic property of materials that indicates how much they resist the flow of electric current. It is independent of the shape and size of the material and is calculated using the formula ? = (R · A) / L, where R is the measured resistance, A is the cross?sectional area, and L is the length of the material. This concept allows comparison between different materials and is key in determining if experimental measurements align with standard reference values.

Geometric Influence on Resistance

The geometry of a conductor, including its length and cross?sectional area, plays a crucial role in determining its resistance and, by extension, its resistivity. A longer conductor has higher resistance, whereas a larger cross?sectional area reduces resistance. This relationship is central in experiments that involve altering the geometry of wires to study the corresponding changes in electrical resistance and resistivity.

Data Averaging and Comparison

Averaging multiple measurements is a common practice in experimental physics to reduce random errors and obtain a more reliable estimate of a physical quantity. After calculating the resistivity from different sets of measurements, taking their average helps in comparing the experimental results with standard reference values, thereby assessing the accuracy and reliability of the procedure and instrumentation used.

Ohm's Law

Ohm’s Law is a fundamental principle in electric circuits that relates the voltage across an electrical component to the current flowing through it and the resistance of the component. It is expressed by the formula V = IR, where V is the potential difference, I is the current, and R is the resistance. This principle is critical in experiments involving electrical measurements as it provides the basis for determining the resistance when voltage and current are measured.

Transcript

00:02 Given the cross sectional area of the 30 gauge nichrome wire a is given to be equal to 7 .30 into 10 to the power minus 8 meter square.

00:19 The student measures the potential difference and the current through the wires through the nichrome wires of different length and it has been asked to find nichrome wires of different length.

00:44 It has been asked to find in part a the resistance of the wires of three different lengths, the resistance of the nichrome wires of three different lengths and their corresponding values of resistivity.

01:08 In part b it has been asked to determine the average value of the resistivity based on the measurements done on nichrome wires of different length.

01:21 And in part c to compare this average value with the standard value of nichrome given in table 26 .2 which according to which the resistivity of nichrome at 20 degree centigrade is 1 .00 into 10 to the power minus 6 ohm meters.

01:55 Nichrome is an alloy of nickel and chromium and its resistivity can vary between 1 .00 into 10 to the power minus 6 to 1 .50 into 10 to the power minus 6 ohm meters.

02:08 Now the resistivity of a metal wire is given by the relation r that is equal to delta v by i and the resistance of the metal wire is given by the relation r is delta v by i and the resistivity of the metal wire is related to its resistance r as rho is r a by l.

02:32 Now in the first set with the first set of data where the length of the nichrome wire is 0 .540 meters the potential difference measured was 5 .22 volts and the current determined by the emitter was 0 .72 amperes.

02:49 It is the same wire having the area of cross section 7 .30 into 10 to the power minus 8 meters square...

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