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A 14-gauge copper wire has a diameter of 1. 628 mm. What magnitude current flows when the drift velocity is 1. 00 mm/s?

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Answer: 7.47 milliamperes (mA).

Explanation:The drift velocity of electrons in a wire is related to the current flowing through the wire by the equation:

I = nAevd

where I is the current, n is the number density of electrons, A is the cross-sectional area of the wire, e is the charge of an electron, and vd is the drift velocity.

The number density of electrons in copper is approximately 8.5 x 10^28 electrons per cubic meter.

The cross-sectional area of the wire is given by the formula for the area of a circle:

A = πr^2

where r is the radius of the wire. The diameter of the wire is given as 1.628 mm, so the radius is half of this value:

r = 0.814 mm = 0.814 x 10^-3 m

Therefore, the cross-sectional area of the wire is:

A = π(0.814 x 10^-3 m)^2 = 5.21 x 10^-7 m^2

The charge of an electron is -1.6 x 10^-19 C.

The drift velocity is given as 1.00 mm/s = 1.00 x 10^-3 m/s.

Substituting these values into the equation for the current, we get:

I = (8.5 x 10^28 electrons/m^3) x (5.21 x 10^-7 m^2) x (-1.6 x 10^-19 C) x (1.00 x 10^-3 m/s)

I = -7.47 x 10^-3 A

The magnitude of the current is:

|I| = 7.47 x 10^-3 A

Therefore, the magnitude of the current flowing through the wire is 7.47 milliamperes (mA).

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