Concept explainers
(a)
The resistivity of the aluminum at a temperature of
(a)
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)
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)
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)
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)
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
Want to see more full solutions like this?
Chapter 21 Solutions
Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, 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 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_forwardA copper wire has a circular cross section with a radius of 1.06 mm. (a) If the wire carries a current of 3.38 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
- A cylindrical resistor of radius 5.0 mm and length 2.0 cm is made of material that has a resistivity of 3.5 * 10-5 ohm m.What are (a) the magnitude of the current density and (b) the potential difference when the energy dissipation rate in the resistor is 1.0W?arrow_forwardA 1.30 m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0∘C) the ammeter reads 18.8 A, while at 92.0∘C it reads 16.6 A. You can ignore any thermal expansion of the rod. (A) Find the resistivity for the material of the rod at 20∘C Express your answer with the appropriate units. (B) Find the temperature coefficient of resistivity at 20∘C for the material of the rod. Express your answer in inverse degrees Celsius.arrow_forwardA copper wire of radius a = 0.256 mm has an aluminum jacket of outer radius b = 0.337 mm. There is a current i = 1.59 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 × 10-8Ω·m and 2.75 × 10-8Ω·m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 15.0 V between the ends maintains the current, what is the length in meters of the composite wire?arrow_forward
- An aluminum wire with a diameter of 0.125 mm has a uniform electric field of 0.255 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. ρ = Ω · m (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 1.90 m length of the wire to produce the stated electric field? ΔV = Varrow_forwardAs part of a class project you are given 0.900 g of copper and asked to fabricate a wire with uniform cross-section. You use up 95% of the copper and make a wire with a resistance of 0.893 Ω. The resistivity of copper is 1.72 10-8 Ω · m and its density is 8.92 103 kg/m3. What length of wire do you end up with? What is the diameter of the wire?arrow_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_forward
- What is the current in a wire in which 3.62x1020 electrons pass a single point every 8.79 seconds? Report your answer with three significant digits. (e = 1.602x10-19 C)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_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_forward