Concept explainers
(a)
The amount of iron in
(a)
Answer to Problem 16P
Explanation of Solution
Given Info: The cross-sectional area of iron wire is
Amount of iron in one mole is given as,
It is the standard value for iron wire.
Convert the amount of iron into
Thus,
Conclusion:
Therefore,
(b)
The molar density of iron.
(b)
Answer to Problem 16P
The molar density of iron is
Explanation of Solution
Given Info: The cross-sectional area of iron wire is
The formula for the molar density is,
Here,
Substitute
Thus, the molar density of iron is
Conclusion:
Therefore, the molar density of iron is
(c)
The number density of iron atoms.
(c)
Answer to Problem 16P
The number density of iron atoms is
Explanation of Solution
Given Info: The cross-sectional area of iron wire is
The formula for the number density is,
Here,
Substitute
Thus, the number density of iron atoms is
Conclusion:
Therefore, the number density of iron atoms is
(d)
The number density of two
(d)
Answer to Problem 16P
The number density of two conduction iron atoms is
Explanation of Solution
Given Info: The cross-sectional area of iron wire is
The formula for the number density of two conduction atoms is,
Here,
Substitute
Thus, the number density of two conduction iron atoms is
Conclusion:
Therefore, the number density of two conduction iron atoms is
(e)
The drift speed of the conduction electrons.
(e)
Answer to Problem 16P
The drift speed of the conduction electrons is.
Explanation of Solution
Given Info: The cross-sectional area of iron wire is
Formula to calculate the drift speed is,
Substitute
Conclusion:
Therefore, the total drift speed of the conduction electrons is.
Want to see more full solutions like this?
Chapter 21 Solutions
Principles of Physics
- 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_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_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
- Taking R = 1.00 k and = 250 V in Figure P21.49, determine the direction and magnitude of the current in the horizontal wire between a and e. Figure P21.49arrow_forwardA 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.arrow_forwardAn aluminum wire of radius 1.00 mm carries a current of 1.00 mA. The density of aluminum is 2.70x103kg/m3, and 1 mole of aluminum has a mass of 26.98g. There is one conduction electron per aluminum atom. a. The current density in the wire is:___ A/m2 b. The drift velocity of the electrons carrying this current is:___ x10-8m/s c. The distance traveled by an electron in 10 hours is:___mm.arrow_forward
- If a metallic wire of cross sectional area 4.0 x 10-6 m2 carries a current of 6.0 A and has a mobile charge density of 4.24 x 1028 carriers/m3, what is the average drift velocity of the mobile charge carriers? (charge value = 1.6 x 10-19 C)arrow_forwardA current of 14 A is traveling through a cylindrical metallic wire with a radius of 1.5 mm. The number density of free electron charge carriers in the wire is 8.0 x 1028 electrons/m3. What is the drift velocity of the electrons in the current? a. 0.95 mm/s b. 0.35 mm/s c. 0.15 mm/s d. 0.55 mm/s e. 0.75 mm/sarrow_forwardA cylindrical conducting wire which is 342.57cm long, 85.39mm thick and resistivity of 3.13Ω.m, (a) has the resistance of R = ? If current I = 12.9A is generated by flowing of 217 electrons/m3 via a conductor, Then the electrons through this conductor (b) have a density J = ?and (c) are drifting at a speed of VD = ?arrow_forward
- A 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_forwardA high-voltage copper transmission line with a diameter of 1.40 cm and a length of 120 km carries a steady current of 8.25 102 A. If copper has a free charge density of 8.46 1028 electrons/m3, over what time interval does one electron travel the full length of the line?arrow_forwardA copper wire is carrying 5.0 A of current. Given that the electric field between the ends of the cable has a value of 0.75 V/m. (a) find the current density in the wire. (b) the drift speed of the mobile charges. (c) If a potential difference of 20.0 V is applied. Find the resistance, length and cross-sectional area of the cable. Note: the density of copper D=8960 kg/m3, and the molar mass of the copper is m=0.063 kg/mol. Assume each atom of contributes with one electron.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning