### Understanding Resistance and Volume of a Copper Wire#### Problem Statement:The resistivity of copper is \( 1.70 \times 10^{-8} \, \Omega \cdot \text{m} \).##### Hint:Apply the expression relating resistance to resistivity. Treat the wire as a cylinder with volume \( V = A\ell \) where \(A\) is the wire's cross-sectional area.**Click the hint button again to remove this hint.**---1. **Find the resistance of a copper wire (in ohms) with a radius of \(1.21 \, \text{mm}\) and a length of \(1.18 \, \text{m}\).** \( \boxed{\phantom{0}} \, \Omega \)2. **Calculate the volume (in m³) of copper in the wire.** \( \boxed{\phantom{0}} \, \text{m}^3 \)3. **Suppose that volume of copper is formed into a new wire with a length of \(2.92 \, \text{m}\). Find the new resistance of the wire (in ohms).** \( \boxed{\phantom{0}} \, \Omega \)---In this problem, you are required to apply the concepts of resistivity and geometric properties of cylindrical objects to solve for the resistance and volume of a copper wire and its transformation when the dimensions are altered. Here's a step-by-step method to solve the questions:- **Resistance Calculation:** The resistance \(R\) of a wire is calculated using the formula: \[ R = \rho \frac{\ell}{A} \] where: - \( \rho \) is the resistivity of the material (\( 1.70 \times 10^{-8} \, \Omega \cdot \text{m} \) for copper) - \( \ell \) is the length of the wire - \( A \) is the cross-sectional area of the wire - The cross-sectional area \( A \) of a wire with radius \( r \) is given by \( A = \pi r^2 \)- **Volume Calculation:** The volume \( V \) of the cylinder (wire) can be found using the formula: \[ V = A\ell = \

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The resistivity of copper is 1.70 x 10-8 2. m. HINT Apply the expression relating resistance to resistivity. Treat the wire as a cylinder with volume V = Al where A is the wire's cross-sectional area. Click the hint button again to remove this hint. (a) Find the resistance of a copper wire (in ohms) with a radius of 1.21 mm and a length of 1.18 m. Q (b) Calculate the volume (in m³) of copper in the wire. m3 (c) Suppose that volume of copper is formed into a new wire with a length of 2.92 m. Find the new resistance of the wire (in ohms). Ω

The resistivity of copper is 1.70 x 10-8 2. m. HINT Apply the expression relating resistance to resistivity. Treat the wire as a cylinder with volume V = Al where A is the wire's cross-sectional area. Click the hint button again to remove this hint. (a) Find the resistance of a copper wire (in ohms) with a radius of 1.21 mm and a length of 1.18 m. Q (b) Calculate the volume (in m³) of copper in the wire. m3 (c) Suppose that volume of copper is formed into a new wire with a length of 2.92 m. Find the new resistance of the wire (in ohms). Ω

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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