The answer is A bc I did the quiz and I got it right
Complete Question
A 10 gauge copper wire carries a current of 20 A. Assuming one free electron per copper atom, calculate the drift velocity of the electrons. (The cross-sectional area of a 10-gauge wire is 5.261 mm2.)
mm/s
Answer:
The drift velocity is ![v = 0.0002808 \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%200.0002808%20%5C%20m%2Fs)
Explanation:
From the question we are told that
The current on the copper is ![I = 20 \ A](https://tex.z-dn.net/?f=I%20%20%3D%2020%20%5C%20A)
The cross-sectional area is
The number of copper atom in the wire is mathematically evaluated
![n = \frac{\rho * N_a}Z}](https://tex.z-dn.net/?f=n%20%20%3D%20%20%5Cfrac%7B%5Crho%20%2A%20%20N_a%7DZ%7D)
Where
is the density of copper with a value ![\rho = 8.93 \ g/m^3](https://tex.z-dn.net/?f=%5Crho%20%3D%20%208.93%20%5C%20g%2Fm%5E3)
is the Avogadro's number with a value ![N_a = 6.02 *10^{23}\ atom/mol](https://tex.z-dn.net/?f=N_a%20%20%3D%206.02%20%2A10%5E%7B23%7D%5C%20atom%2Fmol)
Z is the molar mass of copper with a value ![Z = 63.55 \ g/mol](https://tex.z-dn.net/?f=Z%20%3D%20%2063.55%20%5C%20g%2Fmol)
So
Given the 1 atom is equivalent to 1 free electron then the number of free electron is
![N = 8.46 * 10^{28} \ electrons](https://tex.z-dn.net/?f=N%20%20%3D%208.46%20%2A%2010%5E%7B28%7D%20%20%5C%20%20electrons)
The current through the wire is mathematically represented as
![I = N * e * v * A](https://tex.z-dn.net/?f=I%20%20%3D%20%20N%20%2A%20e%20%2A%20v%20%2A%20A)
substituting values
![20 = 8.46 *10^{28} * (1.60*10^{-19}) * v * 5.261 *10^{-6}](https://tex.z-dn.net/?f=20%20%3D%20%208.46%20%2A10%5E%7B28%7D%20%2A%20%281.60%2A10%5E%7B-19%7D%29%20%2A%20v%20%2A%20%205.261%20%2A10%5E%7B-6%7D)
=> ![v = 0.0002808 \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%200.0002808%20%5C%20m%2Fs)
I think it’s D-decreases the amount of work.
- The mechanic did 5406 Joules of work pushing the car.
That's the energy he put into the car. When he stops pushing, all the energy he put into the car is now the car's kinetic energy.
- Kinetic energy = (1/2) (mass) (speed²)
And there we have it
- The car's mass is 3,600 kg.
- Its speed is 'v' m/s .
- (1/2) (mass) (v²) = 5,406 Joules
(1/2) (3600 kg) (v²) = 5406 joules
1800 kg (v²) = 5406 joules
v² = (5406 joules) / (1800 kg)
v² = (5406/1800) (joules/kg)
= = = = = This section is just to work out the units of the answer:
- v² = (5406/1800) (Newton-meter/kg)
- v² = (5406/1800) (kg-m²/s² / kg)
= = = = =
v = √(5406/1800) m/s
<em>v = 1.733 m/s</em>