Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 25, Problem 3P
To determine
Wire which has higher number density (number per unit volume) of charge carriers.
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A copper wire is dCu = 0.0500 cm in diameter, 3.00 m long, and has a charge carrier density of 8.50x10^28 electrons/m3. The copper wire is attached to an equal length of aluminum wire with diameter dAl = 0.0100 cm and charge carrier density of 6.02x10^28 electrons/m3. A current of 0.400 A flows through the copper wire.
a. The ratio of current densities in the two wires, JCu/JAl is:___.
b. The ratio of drift velocities in the two wires, vd–Cu/vd–Al is:____.
A copper wire has a circular cross-section with a radius of1.25 mm. (a) If the wire carries a current of 3.70 A, findthe drift speed of electrons in the wire. (Take the density ofmobile charge carriers in copper to be n= 1.10 x 1029 electrons/m3.) (b) For the same wire size and current, find thedrift speed of electrons if the wire is made of aluminum withn= 2.11 x 1029 electrons/m3.
When a current flows in an aluminum wire of diameter 2.83 mm, the drift speed of the conduction electrons is 0.000147 m/s.How many electrons are flowing past a given point each second? The conduction electron density in aluminum is 6.00×1028 m−3.
Chapter 25 Solutions
Physics for Scientists and Engineers
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- An 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_forwardConsider a wire of a circular cross-section with a radius of R = 3.00mm. The magnitude of the currentdensity is modeled as J=cr2=5.00106Am4r2 . Whatis the current through the inner section of the wire from the center to r = 0.5R?arrow_forwardFigure P21.6 represents a section of a conductor of nonuniform diameter carrying a current of I = 5.00 A. The radius of cross-section A1 is r1 = 0.400 cm. (a) What is the magnitude of the current density across A1? The radius r2 at A2 is larger than the radius r1 at A1. (b) Is the current at A2 larger, smaller, or the same? (c) Is the current density at A2 larger, smaller, or the same? Assume A2 = 4A1. Specify the (d) radius, (e) current, and (f) current density at A2. Figure P21.6arrow_forward
- 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_forwardThree equally long meter-long copper wires with diameters of 1 mm, 2 mm and 3 mm are connected in series and connected to a voltage of 12 V. How much current flows through the wires (I)? What are the stresses on the individual sections (U1, U2, U3)? (specific resistance of copper is 0.017 Vmm2/ Am)arrow_forwardThe conduction electrons in a cylindrical, current-carrying wire have a drift velocity of 0.35 mm/s. The wire has a radius of 1.0 mm and contains 8.6 x 1028 conduction electrons per m3. What is the current in the wire? (The magnitude of the charge of an electron is 1.602 x 10-19 C.) a. 3.0 A b. 6.0 A c. 9.0 A d. 12 A e. 15 Aarrow_forward
- Two pieces of copper wire have the same length, but wire A has square cross section of side s, whereas wire B has circular cross section of diameter s. Which of the following is TRUE? A. The resistivity of both wires is the same B. The resistance of both wires is the same C. The resistance of wire A is greater than B D. The resistance of wire B is greater than Aarrow_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_forwardA 10-gauge copper wire has a cross-sectional area A = 5.26 mm2 and carries a current of I = 5.00 A . The density of copper is ρ = 89.50 g/cm3 . One mole of copper atoms (6.02 × 1023 atoms) has a mass of approximately 63.50 g. What is the magnitude of the drift velocity of the electrons, assuming that each copper atom contributes one free electron to the current?arrow_forward
- A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is 8.5 x1028/m3 Find the magnitudes of (a) the current density in the wire (b) the electric field in the wire (c) How much time is required for an electron to travel the length of the wire? For copper: p = 1.72 x10-82. m n = 8.5 x1028/m3arrow_forwardIf R1 = R2 = R3 = R4 = R5 = R6= 14 Ω, and V = 15 V, what is the current (in A) through R2? If R1 = R2 = R3 = R4 = R5 = R6= 14 Ω, and V = 15 V, what is the current (in A) through R4?arrow_forwardHow long does it take electrons to get from a car battery to the starting motor? Assume the current is 310 A and the electrons travel through a copper wire with cross-sectional area 0.160 cm2 and length 0.930 m. The number of charge carriers per unit volume is 8.49 × 1028 m-3.arrow_forward
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