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Multiple Choice
Typical household wiring in the United States is 14-gauge copper wire. 14-gauge wire has a radius of . What is the electron drift speed if a current is carried in a 14-gauge wire?
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E
Verified step by step guidance
1
First, understand that the electron drift speed (v_d) can be calculated using the formula: v_d = I / (n * A * e), where I is the current, n is the number of charge carriers per unit volume, A is the cross-sectional area of the wire, and e is the elementary charge.
Calculate the cross-sectional area (A) of the wire using the formula for the area of a circle: A = π * r^2. Here, r is the radius of the wire, which is given as 0.815 mm. Convert this radius to meters before substituting into the formula.
Determine the number of charge carriers per unit volume (n) for copper. This is typically around 8.5 x 10^28 electrons per cubic meter for copper.
Use the elementary charge (e), which is approximately 1.6 x 10^-19 C (coulombs), in the formula for drift speed.
Substitute the values for I (10 A), n, A, and e into the drift speed formula to solve for v_d. This will give you the electron drift speed in meters per second, which you can then convert to millimeters per second if needed.