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 $27.2 .$ $$\begin{array}{lll} \hline {{L(\mathbf{m})}} & {\Delta V(\mathbf{V})} & {\mathbf{I}(\mathbf{A})} & {\mathbf{R}(\mathbf{\Omega})} & \rho(\Omega \cdot \mathrm{m})\\ \hline {0.540} & {5.22} & {0.72} \\ {1.028} & {5.82} & {0.414} \\ {1.543} & {5.94} & {0.281} \\ \hline\end{array}$$
Added by James C.
Step 1
For \( L = 0.540 \, \text{m} \): \( R = \frac{5.22}{0.72} = 7.25 \, \Omega \) For \( L = 1.028 \, \text{m} \): \( R = \frac{5.82}{0.414} = 14.09 \, \Omega \) For \( L = 1.543 \, \text{m} \): \( R = \frac{5.94}{0.281} = 21.14 \, \Omega \) Show more…
Show all steps
Your feedback will help us improve your experience
Ameer Said and 96 other Physics 102 Electricity and Magnetism educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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 x 10^-8 m^2. 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. L (m) ΔV (V) I (A) R (̦) ̑ (̦ ∙ m) 0.540 5.18 0.504 1.028 5.81 0.275 1.543 5.98 0.186 What is the average value of the resistivity? ̦ ∙ m By what percent does this differ from the value given in this table (1.50 ! 10^-6 ̦ ∙ m)? %
Vishal G.
A 2.0-m length of wire is made by welding the end of a 120-cm-long silver wire to the end of an 80-cm-long copper wire. Each piece of wire is 0.60 mm in diameter. The wire is at room temperature, so the resistivities are as given in Table 25.1. A potential difference of 9.0 V is maintained between the ends of the 2.0-m composite wire. What is (a) the current in the copper section; (b) the current in the silver section; (c) the magnitude of $\vec E$ in the copper; (d) the magnitude of $\vec E$ in the silver; (e) the potential difference between the ends of the silver section of wire?
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD