**Title: Understanding the Properties of Copper Wires****Introduction:**In this exercise, we explore the properties of two copper wires, A and B, which have the same length and are connected across the same battery. Given that the resistance of wire B ($R_B$) is four times the resistance of wire A ($R_A$), you will determine various ratios related to their physical and electrical characteristics. Use the hint provided to guide you through the problem.---**Exercise:****Hint:** [Explore the relationship between resistance, resistivity, and cross-sectional area.]1. **The Ratio of Their Cross-Sectional Areas** - $ \frac{A_B}{A_A} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ $2. **The Ratio of Their Resistivities** - $ \frac{\rho_B}{\rho_A} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ $3. **The Ratio of the Currents in Each Wire** - $ \frac{I_B}{I_A} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ $**Instructions:**- Use the formula for resistance in terms of resistivity ($\rho$), length (L), and cross-sectional area (A): \[ R = \rho \frac{L}{A} \]- Consider how changes in area affect the current given a constant voltage source.- Assume all materials involved are homogeneous and isotropic.**Discussion:**Reflect on why the change in cross-sectional area impacts the resistance disproportionately and how this ties into practical applications in electrical engineering and design. How can understanding these relationships assist in improving the efficiency of electrical systems?**Conclusion:**This exercise demonstrates the interconnectivity of physical and electrical properties in conductive materials, providing a fundamental understanding of how electrical systems can be manipulated to achieve desired outcomes. Analyze each step carefully and verify calculations.

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Two copper wires A and B have the same length and are connected across the same battery. If R. = 4R, determine the following. HINT (a) the ratio of their cross-sectional areas AB AA (b) the ratio of their resistivities PB = PA (c) the ratio of the currents in each wire IB IA

Two copper wires A and B have the same length and are connected across the same battery. If R. = 4R, determine the following. HINT (a) the ratio of their cross-sectional areas AB AA (b) the ratio of their resistivities PB = PA (c) the ratio of the currents in each wire IB IA

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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Two copper wires A and B have the same length and are connected across the same battery. If RB = 8RA, determine the following. HINT (a) the ratio of their cross-sectional areas AB AA = (b) the ratio of their resistivities ?B ?A = (c) the ratio of the currents in each wire IB IA =
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