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Concept explainers
(a)
The resistivity of the aluminum at a temperature of
(a)
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Answer to Problem 9P
The resistivity of the aluminum wire at a temperature of
Explanation of Solution
Write the expression for the resistivity.
Here,
Conclusion:
Substitute
Therefore, the resistivity of the aluminum at a temperature of
(b)
The current density in the wire.
(b)
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Answer to Problem 9P
The current density in the wire is
Explanation of Solution
Write the expression for the current density.
Here,
Write the expression for the current.
Here,
Use equation (III) in (II) to solve for
Conclusion:
Substitute
Therefore, the current density in the wire is
(c)
The total current in the wire.
(c)
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Answer to Problem 9P
The total current in the wire is
Explanation of Solution
Use equation (II) to solve for
Write the expression for the
Here,
Use equation (VI) in (V) to solve for
Conclusion:
Substitute
Therefore, the total current in the wire is
(d)
The drift speed of the
(d)
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Answer to Problem 9P
The drift speed of the conduction electrons is
Explanation of Solution
Write the expression for the charge density.
Here,
Write the expression for
Here,
Use equation (IX) to solve for
Conclusion:
Substitute
Substitute
Therefore, the drift speed of the conduction electrons is
(e)
The potential difference exists between the ends of a
(e)
![Check Mark](/static/check-mark.png)
Answer to Problem 9P
The potential difference exists between the ends of a
Explanation of Solution
Write the expression for the potential difference.
Here,
Conclusion:
Substitute
Therefore, the potential difference exists between the ends of a
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Chapter 21 Solutions
Principles of Physics: A Calculus-Based Text
- 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 potential difference of 12 V is found to produce a current of 0.40 A in a 3.2 m length of wire with a uniform diameter of 0.80 cm. a) What is the value of the resistivity of the wire, and b) the resistance of the wire?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_forward
- A thin copper wire with a diameter 2.5 mm is connected to a 1.2-V potential difference, a current of 2.0 amps flows through the wire. The resistivity of copper is 1.72 × 10-8 Ω ∙ m. What is the length of the wire?arrow_forwardAn aluminum wire with a diameter of 0.085 mm has a uniform electric field of 0.285 V/m imposed along its entire length. The temperature of the wire is 55.0 degrees Celsius. 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 of a 1.70 m length of the wire to produce the states electric field?arrow_forwardA copper wire of radius a = 0.273 mm has an aluminum jacket of outer radius b = 0.399 mm. There is a current i = 2.82 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 × 10-80-m and 2.75 × 10-8Q-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 17.0 V between the ends maintains the current, what is the length in meters of the composite wire?arrow_forward
- 3.0 A battery has an emf of 12 V and an internal resistance of 0.05000. What is the terminal voltage when the current drawn from the battery is 8.0 A? The terminal voltage is = V. (1) If a current of 40 mA exists in a metal wire, how many electrons flow past a given cross section of the wire in 6 min? Number of electrons flow past a given cross section of the wire = Part B 4. (a) An object is pushed a distance 4.2 m along a frictionless horizontal table by a constant applied force of magnitude 3D22.0N directed at an angle of 23.0° below the horizontal as shown in Figure. If the mass (m) of the object is 2.00 kg calculate the work done by the applied force and power if it takes 3 minutes. Paarrow_forwardA copper wire of radius a = 0.330 mm has an aluminum jacket of outer radius b = 0.476 mm. There is a current i = 1.50 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 x 1080-m and 2.75 x 1080-m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 18.0 V between the ends maintains the current, what is the length in meters of the composite wire? (a) Number i (b) Number (c) Number i Units Units Unitsarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
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