**Problem Statement:**Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 68.9 A. The resistance per unit length is to be 0.132 Ω/km. The densities of copper and aluminum are 8960 and 2600 kg/m³, respectively. Compute the following:(a) The magnitude \( J \) of the current density for a copper cable.(b) The mass per unit length \( \lambda \) for a copper cable.(c) The magnitude \( J \) of the current density for an aluminum cable.(d) The mass per unit length \( \lambda \) for an aluminum cable.**Inputs for Your Calculations:**(a) \[\text{Number}\]Units [ _select units_ ](b) \[\text{Number}\]Units [ _select units_ ](c) \[\text{Number}\]Units [ _select units_ ](d) \[\text{Number}\]Units [ _select units_ ]**Explanation:**In mathematical terms, the current density \( J \) is given by the formula:\[ J = \frac{I}{A} \]where:- \( I \) is the current (68.9 A in this case).- \( A \) is the cross-sectional area of the cable.Furthermore, the mass per unit length \( \lambda \) is determined by:\[ \lambda = \rho \cdot A \]where:- \( \rho \) is the density of the material.- \( A \) is the cross-sectional area of the cable, which can be derived from the resistance and the electrical properties of the materials, using:\[ R = \frac{\rho_{\text{electrical}} \cdot l}{A} \]where:- \( \rho_{\text{electrical}} \) is the resistivity of the material.- \( l \) is the length of the cable.- \( R \) is the resistance per unit length (0.132 Ω/km).Make sure to use appropriate units and conversion factors in your calculations. **Note:**There are no graphs or diagrams in this image. The problem requires performing a series of calculations with the information provided.

Current in copper and aluminum i=68.9 AResistance per unit length of both material is Density of…

Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 68.9 A. The resistance per unit length is to be 0.132 0/km. The densities of copper and aluminum are 8960 and 2600 kg/m³, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length À for a copper cable and (c) J and (d) À for an aluminum cable. (a) Number i (b) Number i IN (c) Number (d) Number i Units Units Units Units

Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 68.9 A. The resistance per unit length is to be 0.132 0/km. The densities of copper and aluminum are 8960 and 2600 kg/m³, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length À for a copper cable and (c) J and (d) À for an aluminum cable. (a) Number i (b) Number i IN (c) Number (d) Number i Units Units Units Units

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

An iron wire has a cross-sectional area equal to 5.50 x 10-6 m². Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 12.0 A. (a) How many kilograms are there in 1.00 mole of iron? 0.055 kg/mol (b) Starting with the density of iron and the result of part (a), compute the molar density of iron (the number of moles of iron per cubic meter). 1.43163 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. mol/m³ (c) Calculate the number density of iron atoms using Avogadro's number. atoms/m³ (d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom. electrons/m³ (e) Calculate the drift speed of conduction electrons in this wire. m/s Need Help? Read It
In (Figure 1) the battery has emf 45.0 V and negligible internal resistance. R₁ = 7.00 2. The current through R₁ is 1.50 A and the current through R3 = 4.50 A. Figure ww R₁ www R₂ www- R₂ < 1 of 1 ▼ What is the resistance R₂? Express your answer with the appropriate units. R₂: Submit Part B R3 11 .0 Submit μA Value What is the resistance R3 ? Express your answer with the appropriate units. Request Answer HÅ Value Units Request Answer Units ?
A copper wire has a circular cross section with a radius of 1.66 mm. HINT (a) If the wire carries a current of 3.18 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 x 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 x 1029 electrons/m³. m/s
A copper wire of cross-sectional area 2.40 x 10-6 m² and length 4.00 m has a current of 2.60 A uniformly distributed across that area. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 25.0 min? (a) Number (b) Number i Units Units
Cell membranes contain channels that allow ions to cross the phospholipid bilayer. Suppose that a particular potassium channel carries a current of 2.1 pA2.1 pA. How many potassium ions (K+K+) pass through it in 1.0 ms1.0 ms?
A 190-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,230 A. If the conductor is copper with a free charge density of 8.50 × 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (Use 3.156 × 107 for the number of seconds in a year.) yr
An electric utility company supplies a customer's house from the main power lines (120 V) with two copper wires, each of which is 46.0 m long and has a resistance of 0.109 2 per 300 m. (a) Find the potential difference at the customer's house for a load current of 102 A. V (b) For this load current, find the power delivered to the customer. kW
An aluminum wire having a cross-sectional area equal to 3.10 x 10-6 m² carries a current of 6.00 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/s
A power transmission line is hung from metal towers with glass insulators having a resistance of 1.00× 109 ΩWhat current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)
Problem 1. A 50.0 m long Aluminum wire has a diameter of 0.50 mm and is at 20.0°C. If it carries a current of 0.50 mA, (a) calculate the power delivered to it? (b) If the temperature is increased to 340°C and the potential difference across the wire remains constant, what is the power delivered?
Whale and Kanmuro are two islands located in the Chimera archipelago. These two are separated by a distance of 20 miles. A power link is to be established between them. The power link delivers a maximum power of 600 MW at full capacity with an operating voltage of 500 kV. Solve for the resistivity of the cable, assuming a conductor diameter of 1.5 cm. Express your answer in p0-m.
A high-voltage copper transmission line with a diameter of 2.60 cm and a length of 100 km carries a steady current of 8.50 x 10² A. If copper has a free charge density of 8.46 x 1028 electrons/m³, over what time interval does one electron travel the full length of the line? yr