/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 A copper wire and an aluminum ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 18: Problem 23

A copper wire and an aluminum wire of the same length have the same resistance. What is the ratio of the diameter of the copper wire to that of the aluminum wire?

Short Answer

Expert verified
Answer: The approximate ratio of the diameter of the copper wire to that of the aluminum wire is 1.30.

Step by step solution

01

Find the formula for resistance of a wire

To find the resistance of a wire, we use the formula: Resistance (R) = (Resistivity (蟻) 脳 Length (L)) / Cross-sectional Area (A) Since both wires have the same length and resistance, we can write the equation as: R_copper = R_aluminum (蟻_copper 脳 L) / A_copper = (蟻_aluminum 脳 L) / A_aluminum
02

Use the resistivity values for copper and aluminum

The standard resistivity values for copper and aluminum at room temperature are: 蟻_copper = 1.68 脳 10^{-8} ohm路m 蟻_aluminum = 2.82 脳 10^{-8} ohm路m Using the formula from step 1, we get: (1.68 脳 10^{-8}) / A_copper = (2.82 脳 10^{-8}) / A_aluminum
03

Solve for the ratio of cross-sectional areas

To find the ratio of cross-sectional areas, we can rearrange the equation from step 2: A_copper / A_aluminum = (2.82 脳 10^{-8}) / (1.68 脳 10^{-8}) = 1.67857 A_copper / A_aluminum 鈮� 1.68
04

Convert the cross-sectional area ratio to a diameter ratio

Since both wires are cylindrical, we can use the formula for the cross-sectional area of a circle (A = 蟺 * (diameter^2) / 4) and set up a proportion for their diameters: (A_copper / A_aluminum) = (d_copper^2 / d_aluminum^2) 1.68 = (d_copper^2 / d_aluminum^2) Now, take the square root of both sides: sqrt(1.68) = (d_copper / d_aluminum) d_copper / d_aluminum 鈮� 1.30 The ratio of the diameter of the copper wire to that of the aluminum wire is approximately 1.30.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the resistance of a \(40.0-\mathrm{W}, 120-\mathrm{V}\) lightbulb?
An ammeter with a full scale deflection for \(I=10.0 \mathrm{A}\) has an internal resistance of \(24 \Omega .\) We need to use this ammeter to measure currents up to 12.0 A. The lab instructor advises that we get a resistor and use it to protect the ammeter. (a) What size resistor do we need and how should it be connected to the ammeter, in series or in parallel? (b) How do we interpret the ammeter readings?
Near Earth's surface the air contains both negative and positive ions, due to radioactivity in the soil and cosmic rays from space. As a simplified model, assume there are 600.0 singly charged positive ions per \(\mathrm{cm}^{3}\) and 500.0 singly charged negative ions per \(\mathrm{cm}^{3} ;\) ignore the presence of multiply charged ions. The electric field is $100.0 \mathrm{V} / \mathrm{m},$ directed downward. (a) In which direction do the positive ions move? The negative ions? (b) What is the direction of the current due to these ions? (c) The measured resistivity of the air in the region is $4.0 \times 10^{13} \Omega \cdot \mathrm{m} .$ Calculate the drift speed of the ions, assuming it to be the same for positive and negative ions. [Hint: Consider a vertical tube of air of length \(L\) and cross-sectional area \(A\) How is the potential difference across the tube related to the electric field strength?] (d) If these conditions existed over the entire surface of the Earth, what is the total current due to the movement of ions in the air?
A solar cell provides an emf of \(0.45 \mathrm{V}\). (a) If the cell supplies a constant current of \(18.0 \mathrm{mA}\) for \(9.0 \mathrm{h},\) how much electric energy does it supply? (b) What is the power-the rate at which it supplies electric energy?
(a) What is the resistance of the heater element in a \(1500-\mathrm{W}\) hair dryer that plugs into a \(120-\mathrm{V}\) outlet? (b) What is the current through the hair dryer when it is turned on? (c) At a cost of \(\$ 0.10\) per kW .h, how much does it cost to run the hair dryer for 5.00 min? (d) If you were to take the hair dryer to Europe where the voltage is \(240 \mathrm{V},\) how much power would your hair dryer be using in the brief time before it is ruined? (e) What current would be flowing through the hair dryer during this time?
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Waves Physics

Read Explanation

Radiation

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.