Explanation Given data: Mass of the copper ( m ) is 1.0 g. Resistance of the cooper wire ( R ) is 1.0 Ω . Density of the copper wire ( D ) is 8900 kg m 3 . Formula used: Write the expression for resistance of a material in terms of resistivity and dimensions. R = ρ L A (1) Here, ρ is the resistivity of material, L is the length of the material, and A is the cross-section area of the material. Write the expression for cross-section area of the material as follows. A = π 4 d 2 (2) Here, d is the diameter of the material. Write the expression for density of a material (copper wire). D = m v (3) Here, m is the mass of the copper, and v is the volume of the material. Write the expression for volume of the material (copper). v = A L (4) Explanation: From equation (4), substitute ( A L ) for v in equation (3), D = m A L From equation (2), substitute ( π 4 d 2 ) for A . D = m ( π 4 d 2 ) L = 4 m π d 2 L Rewrite the expression to find the diameter of the copper as follows. d 2 = 4 m π D L d = 4 m π D L Substitute 1.0 g for m , and 8900 kg m 3 for D , d = 4 ( 1.0 g ) π ( 8900 kg m 3 ) L = 4 ( 1.0 × 10 − 3 kg ) π ( 8900 kg m 3 ) L d = 0.14306 × 10 − 6 m 3 L (5) From equation (2), substitute ( π 4 d 2 ) for A in equation (1), R = ρ L ( π 4 d 2 ) = 4 ρ L π d 2 Rewrite the expression to find the diameter of the copper wire as follows. d 2 = 4 ρ L π R d = 4 ρ L π R (6) Refer to the Table 22.1 in the textbook for resistivity of various materials. From the table, the resistivity of the copper wire is ( 1.7 × 10 − 8 ) Ω ⋅ m . Substitute ( 1

College Physics: A Strategic Approach (3rd Edition)

3rd Edition

ISBN: 9780321902559

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

See similar textbooks

Concept explainers

Resistivity

Resistivity is a characteristic property of the conductor’s material that measures the extent to which the material opposes the flow of current. It is denoted by the Greek letter “rho”. Electrical resistivity, also known as specific resistance, depends o…

Question

Chapter 22, Problem 63GP

To determine

To choose: The length and diameter of the required copper wire.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 22, Problem 62GP

Chapter 22, Problem 64GP

Students have asked these similar questions

Four capacitors are connected as shown in the figure below. (Let C = 12.0 µF.) A circuit consists of four capacitors. It begins at point a before the wire splits in two directions. On the upper split, there is a capacitor C followed by a 3.00 µF capacitor. On the lower split, there is a 6.00 µF capacitor. The two splits reconnect and are followed by a 20.0 µF capacitor, which is then followed by point b. (a) Find the equivalent capacitance between points a and b. µF(b) Calculate the charge on each capacitor, taking ΔVab = 16.0 V. 20.0 µF capacitor µC 6.00 µF capacitor µC 3.00 µF capacitor µC capacitor C µC

Two conductors having net charges of +14.0 µC and -14.0 µC have a potential difference of 14.0 V between them. (a) Determine the capacitance of the system. F (b) What is the potential difference between the two conductors if the charges on each are increased to +196.0 µC and -196.0 µC? V

Please see the attached image and answer the set of questions with proof.

Chapter 22 Solutions

College Physics: A Strategic Approach (3rd Edition)

Ch. 22 - What causes electrons to move through a wire as a...Ch. 22 - All wires in Figure Q22.519 are made of the same...Ch. 22 - A wire carries a 4 A current. What is the current...Ch. 22 - Prob. 7CQ Ch. 22 - Cells in the nervous system have a potential...Ch. 22 - a. Which directionclockwise or...Ch. 22 - Prob. 10CQ Ch. 22 - The wires in Figure Q22.11 are all made of the...Ch. 22 - The two circuits in Figure Q22.12 use identical...Ch. 22 - The two circuits in Figure Q22.13 use identical...

Ch. 22 - Rank in order, from largest to smallest, the...Ch. 22 - The circuit in Figure Q22.16 has three batteries...Ch. 22 - When lightning strikes the ground, it generates a...Ch. 22 - One way to find out if a wire has corroded is to...Ch. 22 - Over time, atoms boil off the hot filament in an...Ch. 22 - Rank in order, from largest to smallest, the...Ch. 22 - A 100 W lightbulb is brighter than a 60 W...Ch. 22 - Lightbulbs are typically rated by their power...Ch. 22 - Lightbulbs are typically rated by their power...Ch. 22 - A copper wire is stretched so that its length...Ch. 22 - The potential difference across a length of wire...Ch. 22 - A stereo amplifier creates a 5.0 V potential...Ch. 22 - A resistor connected to a 3.0 V battery dissipates...Ch. 22 - If a 1.5 V battery stores 5.0 kJ of energy (a...Ch. 22 - Figure Q22.29 shows a side view of a wire of...Ch. 22 - A person gains weight by adding fatand therefore...Ch. 22 - The current in an electric hair dryer is 10 A. How...Ch. 22 - 2.0 1013 electrons flow through a transistor in...Ch. 22 - Three wires meet at a junction. Wire 1 has a...Ch. 22 - When a nerve cell depolarizes, charge is...Ch. 22 - A wire carries a 15 A current. How many electrons...Ch. 22 - In a typical lightning strike, 2.5 C flows from...Ch. 22 - A capacitor is charged to 6.0 104 C, then...Ch. 22 - In an ionic solution, 5.0 1015 positive ions with...Ch. 22 - The starter motor of a car engine draws a current...Ch. 22 - A car battery is rated at 90 A h, meaning that it...Ch. 22 - What are the values of currents IB and IC in...Ch. 22 - The currents through several segments of a wire...Ch. 22 - How much electric potential energy does 1.0 C of...Ch. 22 - What is the emf of a battery that increases the...Ch. 22 - A 9.0 V battery supplies a 2.5 mA current to a...Ch. 22 - An individual hydrogen-oxygen fuel cell has an...Ch. 22 - An electric catfish can generate a significant...Ch. 22 - A Wire with resistance R is connected to the...Ch. 22 - Wires 1 and 2 are made of the same metal. Wire 2...Ch. 22 - Prob. 20P Ch. 22 - Resistivity measurements on the leaves of corn...Ch. 22 - What is the resistance of a. A 1.0-m-long copper...Ch. 22 - A motorcyclist is making an electric vest that,...Ch. 22 - Prob. 24P Ch. 22 - A 3.0 V potential difference is applied between...Ch. 22 - Prob. 26P Ch. 22 - Prob. 27P Ch. 22 - The aluminum wire in a high-voltage transmission...Ch. 22 - Figure P22.29 shows the...Ch. 22 - Figure P22.30 is a...Ch. 22 - In Example 22.6 the length of a 60 W, 240 ...Ch. 22 - The electric field inside a 30-cm-long copper wire...Ch. 22 - A copper wire is 1.0 mm in diameter and carries a...Ch. 22 - Two identical lightbulbs are connected in series...Ch. 22 - A 1.5 V battery moves 2000 C of charge around a...Ch. 22 - a. What is the resistance of a 1500 W (120 V) hair...Ch. 22 - Every second, a battery increases the electric...Ch. 22 - A 70 W electric blanket runs at 18 V. a. What is...Ch. 22 - A 60-cm-long heating wire is connected to a 120 V...Ch. 22 - An electric eel develops a potential difference of...Ch. 22 - The total charge a household battery can supply is...Ch. 22 - A 3.0 V battery powers a flashlight bulb that has...Ch. 22 - A heating element in a toaster dissipates 900 W...Ch. 22 - Older freezers developed a coating of ice inside...Ch. 22 - The hot dog cooker described in the chapter heats...Ch. 22 - Air isnt a perfect electric insulator, but it has...Ch. 22 - The biochemistry that takes place inside cells...Ch. 22 - High-resolution measurements have shown that an...Ch. 22 - When an ion channel opens in a cell wall (see...Ch. 22 - The total charge a battery can supply is rated in...Ch. 22 - A 1.5 V D-cell battery is rated at 15,000 mA h...Ch. 22 - The heating element of a simple heater consists of...Ch. 22 - Variations in the resistivity of blood can give...Ch. 22 - A 40 W (120 V) lightbulb has a tungsten filament...Ch. 22 - Wires arent really ideal. The voltage drop across...Ch. 22 - When the starter motor on a car is engaged, there...Ch. 22 - The electron beam inside a television picture tube...Ch. 22 - The two segments of the wire in Figure P22.59 have...Ch. 22 - A long wire used as a heating element carries a...Ch. 22 - Prob. 61GP Ch. 22 - Prob. 62GP Ch. 22 - Prob. 63GP Ch. 22 - If resistors 1 and 2 are connected to identical...Ch. 22 - An immersion heater used to boil water for a...Ch. 22 - The graph in Figure P22.66 shows the current...Ch. 22 - Its possible to estimate the percentage of fat in...Ch. 22 - If you touch the two terminals of a power supply...Ch. 22 - The average resistivity of the human body (apart...Ch. 22 - MCAT-Style Passage Problems Lightbulb Failure...Ch. 22 - MCAT-Style Passage Problems Lightbulb Failure...Ch. 22 - MCAT-Style Passage Problems Lightbulb Failure...Ch. 22 - MCAT-Style Passage Problems Lightbulb Failure...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

To choose: The length and diameter of the required copper wire.

Solution Summary: The author explains how to choose the length and diameter of the required copper wire.

Concept explainers

To choose: The length and diameter of the required copper wire.

Want to see the full answer?

Chapter 22 Solutions