Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 28, Problem 69PQ
To determine
The expression for drift velocity.
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Consider a copper wire with a diameter of 2.75 mm.
A. What is the drift speed of the electrons in the copper wire when a current of 13.0 A flows through it? Assume that each copper atom contributes one free electron to the metal. The density of copper is 8.92 g/cm3.
B. How does this drift speed compare to the random rms speed of an electron at 20.0°C? To make this comparison, determine the random rms speed of an electron at 20.0°C using the ideal gas model and find the ratio of the two speeds.
An iron wire has a cross - sectional area of 5.00 x 10-6 m2.Carry out steps (a) through (e) to compute the drift speed ofthe conduction electrons in the wire. (a) How many kilogramsare there in 1 mole of iron? (b) Starting with the density of ironand the result of part (a), compute the molar density of iron(the number of moles of iron per cubic meter). (c) Calculatethe number density of iron atoms using Avogadro’s number.(d) Obtain the number density of conduction electrons giventhat there are two conduction electrons per iron atom. (e) Ifthe wire carries a current of 30.0 A, calculate the drift speed ofconduction electrons.
A copper (resistivity = 1.72 EXP-8 Ω.m) conductor with a square cross section, 1.0 mm on a side is 100 m long and is initially 20oC.
1. If the temperature coefficient (a) of copper is 0.00393 per degree Celsius, what is the change in resistance of the copper conductor if the temperature is increased to 100 degrees Celsius?
2. What is the resistance of this conductor?
Chapter 28 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 28.1 - Prob. 28.1CECh. 28.2 - Prob. 28.2CECh. 28.3 - Prob. 28.3CECh. 28.5 - When a lightbulb burns out, its filament breaks so...Ch. 28.6 - A battery with terminal potential is connected to...Ch. 28.7 - A battery of terminal potential is connected to a...Ch. 28 - Prob. 1PQCh. 28 - Prob. 2PQCh. 28 - Prob. 3PQCh. 28 - Prob. 4PQ
Ch. 28 - Prob. 5PQCh. 28 - Prob. 6PQCh. 28 - Prob. 7PQCh. 28 - Prob. 8PQCh. 28 - Prob. 9PQCh. 28 - Prob. 10PQCh. 28 - Prob. 11PQCh. 28 - Prob. 12PQCh. 28 - Prob. 13PQCh. 28 - Prob. 14PQCh. 28 - The current in a wire varies with time (measured...Ch. 28 - Prob. 16PQCh. 28 - The amount of charge that flows through a copper...Ch. 28 - Prob. 18PQCh. 28 - Prob. 19PQCh. 28 - Prob. 20PQCh. 28 - Prob. 21PQCh. 28 - Prob. 22PQCh. 28 - A copper wire that is 2.00 mm in radius with...Ch. 28 - Prob. 24PQCh. 28 - Prob. 25PQCh. 28 - Prob. 26PQCh. 28 - What is the electric field in an aluminum wire if...Ch. 28 - Prob. 28PQCh. 28 - Prob. 29PQCh. 28 - Prob. 30PQCh. 28 - Prob. 31PQCh. 28 - Prob. 32PQCh. 28 - Two concentric, metal spherical shells of radii a...Ch. 28 - Prob. 34PQCh. 28 - Prob. 35PQCh. 28 - Prob. 36PQCh. 28 - Prob. 37PQCh. 28 - A lightbulb is connected to a variable power...Ch. 28 - Prob. 39PQCh. 28 - Prob. 40PQCh. 28 - Prob. 41PQCh. 28 - Prob. 42PQCh. 28 - Prob. 43PQCh. 28 - A Two wires with different resistivities, 1 and 2,...Ch. 28 - A copper and a gold wire are supposed to have the...Ch. 28 - Gold bricks are formed with the dimensions 7358134...Ch. 28 - Prob. 47PQCh. 28 - Prob. 48PQCh. 28 - Prob. 49PQCh. 28 - Prob. 50PQCh. 28 - Prob. 51PQCh. 28 - Prob. 52PQCh. 28 - Prob. 53PQCh. 28 - Prob. 54PQCh. 28 - A two-slice bread toaster consumes 850.0 W of...Ch. 28 - Prob. 56PQCh. 28 - Prob. 57PQCh. 28 - Prob. 58PQCh. 28 - Prob. 59PQCh. 28 - Prob. 60PQCh. 28 - Prob. 61PQCh. 28 - Prob. 62PQCh. 28 - Prob. 63PQCh. 28 - Prob. 64PQCh. 28 - Prob. 65PQCh. 28 - Prob. 66PQCh. 28 - Prob. 67PQCh. 28 - Prob. 68PQCh. 28 - Prob. 69PQCh. 28 - Prob. 70PQCh. 28 - Prob. 71PQCh. 28 - Prob. 72PQCh. 28 - Prob. 73PQCh. 28 - Prob. 74PQCh. 28 - Review When a metal rod is heated, its resistance...Ch. 28 - Prob. 76PQCh. 28 - Prob. 77PQCh. 28 - Prob. 78PQCh. 28 - Prob. 79PQCh. 28 - Prob. 80PQCh. 28 - Prob. 81PQCh. 28 - A conducting material with resistivity is shaped...
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- If the current carried by a conductor is doubled, what happens to (a) the charge carrier density, (b) the current density, (c) the electron drift velocity, and (d) the average time interval between collisions?arrow_forwardA conductor carries a current that is decreasing exponentially with time. The current is modeled as I=I0et/ , where I0= 3.00 A is the current at timet = 0.00 s and =0.50 s is the time constant. How much charge flows through the conductor between t = 0.00 s and =3 ?arrow_forwardAn aluminum wire 1.628 mm in diameter (14-gauge) carries a current of 3.00 amps, (a) What is the absolute value of the charge density in the wire? (b) What is the drift velocity of the electrons? (c) What would be the drift velocity if the same gauge copper were used instead of aluminum? The density of copper is 8.96 g/cm3 and thedensity of aluminum is 2.70 g/cm3. The molar mass ofaluminum is 26.98 g/mol and the molar mass of copper is 63.5 g/mol. Assume each atom of metal contributes one free electron.arrow_forward
- Consider a power plant is located 60 km away from a residential area uses Q-gauge (A=42.40mm2) wire ofcopper to transmit power at a current of I = 100.00 A.How much more power is dissipated in the copper wires than it would be in superconducting wires?arrow_forwardA copper wire of cross-sectional area 3.00x10^-6 m2 carries a current of 10.0 A. (a) Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electrons in this wire. (b) Use the ideal gas model to compare the drift speed with the random rms speed an electron would have at 20.0°C. The density of copper is 8.92 g/cm3, and its atomic mass is 63.5 uarrow_forwardConsider a hollow spherical conductor of inner radius a and outer radius 3a. The conductivity (sigma) is a function of r, measured from the center of the sphere: sigma = c / r, where a < r < 3a and c is a constant. a) If we apply a potential difference V between it's inner and outer surfaces, with the inner surface at a higher potential, find the resulting current density j and the electric field E as a function of r. b) Find the resistance R of the spherical resistorarrow_forward
- The vector current density of a 3m long and 3mm diameter conductor is given as 155630 A/m^2. Determine the curent on the conductor, its free electron density, the drift velocity of the charges and the number of electrons passing through the conductor for 3 seconds.arrow_forwardA current of I = 7.3 A is passing through a conductor with cross sectional area A = 6.5 × 10-4 m2. The charge carriers in the conductor, electrons, have a number density n = 2.1 x 1027 m-3. Calculate the numerical value of the drift velocity, v, in m/s. vd =arrow_forwardConsider a resistor of resistivity 4.12 × 10-8 Ω • m. If an electric field of 19 V/m is applied across the resistor and the electron volume concetration in the conductor is 5.82 × 1028 per m3, determine the drift velocity, in mm/s, of the free electron constituting the current.arrow_forward
- Wire section(1) of cross sectional area A1=3mm2 and wire section(2) of cross sectional area A2=7mm2 are connected by a tapered section as shown in the figure. The number density of conduction electrons in the wire is 1030 m-3 ,and resistivity of the wire p=2*10-6 ohm.m . Assume that the current is uniformaly distributed across any cross-section area through the wire's width. Magnitude of electric field in wire section (2) is 6 V/m. A) What is the current flowing in the wire? B) What is the drift speed of conduction electrons in wire section (1)?arrow_forwardA cylindrical, ohmic, uniform conductor is placed in a uniform electric field that points from bottom to top along the axis of the conductor, which is aligned with the z-axis. Which of the following statements is correct (select all that apply)? Group of answer choices A)The current density does not depend on r or φ B)The current density is proportional to the conductivity C)The current density is proportional to the cube of the conductor's radius D)The current density is inversely proportional to the cross-sectional area of the conductorarrow_forwardA copper wire has a circular cross section with a radius of 2.36 mm. (a)If the wire carries a current of 3.68 A, find the drift speed (in m/s) of electrons in the wire. (Take the density of mobile charge carriers in copper to be n = 1.10 ✕ 1029 electrons/m3.) m/s (b)For the same wire size and current, find the drift speed (in m/s) of electrons if the wire is made of aluminum with n = 2.11 ✕ 1029 electrons/m3. m/sarrow_forward
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