Concept explainers
(a)
The resistivity of the aluminum at
(a)
Answer to Problem 33P
The resistivity of the aluminum is
Explanation of Solution
Write the expression to obtain the resistivity of the aluminum at
Here,
Conclusion:
Substitute
Therefore, the resistivity of the aluminum is
(b)
The current density in the wire.
(b)
Answer to Problem 33P
The current density in the wire is
Explanation of Solution
Write the expression to obtain the current density in the wire.
Here,
Conclusion:
Substitute
Therefore, the current density in the wire is
(c)
The current in the wire.
(c)
Answer to Problem 33P
The current in the wire is
Explanation of Solution
Write the expression to obtain the current in the wire.
Here,
Substitute
Here,
Conclusion:
Calculate the radius of the wire.
Substitute
Therefore, the current in the wire is
(d)
The drift velocity of the
(d)
Answer to Problem 33P
The drift velocity of the conduction electron is
Explanation of Solution
Write the expression to obtain the electron density.
Here,
Write the expression to obtain the drift velocity.
Here,
Conclusion:
Substitute
Substitute
Therefore, the drift velocity of the electron is
(e)
The applied voltage.
(e)
Answer to Problem 33P
The applied voltage is
Explanation of Solution
Write the expression to obtain the applied voltage.
Here,
Conclusion:
Substitute
Therefore, the applied voltage is
Want to see more full solutions like this?
Chapter 27 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- 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_forwardA 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?arrow_forwardTaking 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_forward
- Consider 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_forwardA 0.68-mm-diameter copper wire carries a tiny current of 2.5 μA. The molar mass of copper is 63.5 g/mole and its density is 8900 kg/m^3. NA=6.02×10^23 Estimate the electron drift velocity. Assume one free electron per atom. Express your answer to two significant figures and include the appropriate units. vd=arrow_forwardAn aluminum wire with a diameter of 0.125 mm has a uniform electric field of 0.195 V/m imposed along its entire length. The temperature of the wire is 35.0°C. Assume one free electron per atom. (a) Use the information in this Table of Resistivities and Temperature Coefficients to determine the resistivity (in Ω · m) of aluminum at this temperature. (b) What is the current density (in MA/m2) in the wire? J =----- MA/m2 (c) What is the total current (in mA) in the wire? I =--------- mA (d) What is the drift speed of the conduction electrons? vd = ------µm/s (e) What potential difference must exist between the ends of a 1.70 m length of the wire to produce the stated electric field? ΔV = --------- Varrow_forward
- temperature of the hot filament. 19. An aluminum wire with a diameter of 0.100 mm has a uni- form electric field of 0.200 V/m imposed along its entire length. The temperature of the wire is 50.0"C. Assume one free electron per atom. (a) Use the information in Table 26.2 to determine the resistivity of aluminum at this temperature. (b) What is the current density in the wire? (c) What is the total current in the wire? (d) What is the drift speed of the conduction electrons? (e) What potential difference must exist between the ends ofa 2.00-m length of the wire to produce the stated electric ficld?arrow_forwardA copper wire of radius a = 0.172 mm has an aluminum jacket of outer radius b = 0.231 mm. There is a current i = 1.58 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 × 10*Q-m and 2.75 × 10-°2-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 10.4 V between the ends maintains the current, what is the length in meters of the composite wire? (a) Number i Units (b) Number i Units (c) Number i Unitsarrow_forwardA strip of doped silicon 260.0 um wide contains 8.80 x 10-2 conduction electrons per cubic meter and an insignificant number of holes. When the strip carries a current of 102 µA, the drift speed of the electrons is 59.6 cm/s. What is the thickness of the strip? Umarrow_forward
- An aluminum wire (ρ = 2.82x10-8Ωm at 20 °C and α = 3.9x10-3°C-1)with a diameter of 0.085 mm has a uniform electric field of 0.185 V/m imposed along its entire length. The temperature of the wire is 35.0° C. Assume one free electron per atom. Determine the resistivity of aluminum at this temperature? What is the current density in the wire? What is the total current in the wire? What is the drift speed of the conduction electrons? What potential difference must exist between the ends of a 2.50-m length of the wire to produce the stated electric field?arrow_forwardAn aluminum wire with a diameter of 0.125 mm has a uniform electric field of 0.215 V/m imposed along its entire length. The temperature of the wire is 45.0°C. Assume one free electron per atom. (a) Use the information in this Table of Resistivities and Temperature Coefficients to determine the resistivity (in 2· m) of aluminum at this temperature. (b) What is the current density (in MA/m²) in the wire? J = MA/m2 (c) What is the total current (in mA) in the wire? I = mA (d) What is the drift speed of the conduction electrons? um/s (e) What potential difference must exist between the ends of a 2.50 m length of the wire to produce the stated electric field? AV = Varrow_forwardAn aluminum wire has a length of 1.50 m and a cross sectional area of 0.460 mm2. If the resistivity of aluminum is 2.82 x 10-8 0. m and a potential difference of 0.700 V is maintained across its length, determine the current in the wire (in A).arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning