An 18-gauge copper wire (the size usually used for lamp cords) has a nominal dia

Question

An 18-gauge copper wire (the size usually used for lamp cords) has a nominal diameter of 1.02 mm . Consider a situation in which this wire is carrying a constant current of 4.10 A to an electric lamp. Copper has 8.5×10^28free electrons per cubic meter.

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Part A

What length of the conducting wire would be needed to contain 23 mm^3 of free electrons?

------------------------mm

Part B

What is the drift speed of the free electrons in this current-carrying copper wire?

----------------------mm/s

Part C

Each drifting free electron will have some contribution to its kinetic energy due to its drifting speed. What is the total kinetic energy of 23 mm3of free electrons in this current-carrying copper wire?

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Part D

In Part A, you have already calculated the length of this copper wire which contains 23 mm^3 of free electrons. What is the resistance of this length of wire? The resistivity of copper is 1.72×108 m .

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Part E

In Part A, you have already calculated the length of this copper wire which contains 23 mm^3 of free electrons. What is the voltage drop over this length of 18-gauge copper wire when it is carrying a current of 4.10 A ?

--------------------------V

Part F

In Part A, you have already calculated the length of this copper wire which contains 23 mm3 of free electrons. What is the absolute value of the change in electrical potential energy for the 23 mm3 of free electrons when they have passed through this length of wire?

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PLEASE DO ALL PARTS

Explanation / Answer

here,

diameter of wire, d = 1.02 mm

radius r = 0.51 mm

r = 0.51 * 10^-3 m

current in the wire , I = 4.1 A

density of electron , d = 8.5 * 10^28 electrons per cubic meter

(a)

lenth of wire be L

volume = 23 mm

pi * r^2 * L = 23

pi* 0.51^2 * L = 23

L = 28.16 mm

length of the conducting wire would be needed to contain 23 mm^3 of free electrons is 28.16 mm

(b)

n = 8.5 *10^28 /m^3

drift speed , Vd = I/(n * A * q)

Vd = 4.1 /(8.5 *10^28 * pi * 0.51^2 * 10^-6 * 1.6 * 10^-19)

Vd = 3.69 * 10^-4 m/s

Vd = 0.368 mm/s

the drift speed of the free electrons in this current-carrying copper wire is 0.368 mm/s

(c)

number of electrons , N = n * volume

N = 8.5 *10^28 * 23 *10^-9

N = 195.5 * 10^19

totak kinetic energy ,KE = 0.5 * me*Vd^2 * N

KE = 0.5 * 9.1 * 10^-31 * 3.69^2 * 10^-8 * 195.5 * 10^19

KE = 1.21 * 10^-16 J

the total kinetic energy of 23 mm3of free electrons in this current-carrying copper wire is 1.21 * 10^-16 J

(d)

resistivity , p = 1.72 * 10^-8 ohm m

L = 28.16 * 10^-3 m

resistance , R = p * L/Area

R = 1.72 * 10^-8 * 28.16 * 10^-3 /(pi * 0.51^2 * 10^-6 )

R = 5.93 * 10^-4 ohm

the resistance of this length of wire is 5.93 * 10^-4 ohm

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