A copper wire has a square cross section 3.32 mm on a side. The wire is 4.55 m l

ID: 306157 • Letter: A

Question

A copper wire has a square cross section 3.32 mm on a side. The wire is 4.55 m long and carries a current of 3.98 A .

The density of free electrons is 8.5×1028m?3.

Part A
Find the magnitude of the current density in the wire.
Express your answer using three significant figures.

Part B
Find the magnitude of the electric field in the wire.
Express your answer using three significant figures.

Part C
How much time is required for an electron to travel the length of the wire?
Express your answer using three significant figures.

Part D
What is the resistance of this wire?
Express your answer using three significant figures.

Solution:

a) J = I / A

=> J = 3.98 / (3.32 * 10^-3)^2

=> J = 3.61 * 10^5 A/m^2

b) E = p * J ( where p is density of resistivity of copper)

=> E = 1.72 * 10^-8 * 3.61 * 10^5

=> E = 6.21 * 10^-3 N/C

c) t = d / v

=> t = d * n * e A / I

=> t = 4.55 * 8.5 * 10^28 * 1.6 * 10^-19 * (3.32 * 10^-3)^2 / 3.98

=> t = 171.37 * 10^3 s

=> t = 1.71 * 10^5 seconds

d) R = p * l / A

=> R = 1.72 * 10^-8 * 4.55 / (3.32 * 10^-3)^2

=> R = 0.71 * 10^-2

=> R = 7.10 * 10^-3 ohm

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