When a current flows in an aluminum wire of diameter 4.41 mm. the drift speed of the conduction electrons is 1.01 x 10 -4 m/s. What is the electron current in the wire? The conduction electron density in aluminum is 6.00 x 1028 m-3

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Question:

When a current flows in an aluminum wire of diameter 4.41 mm. the drift speed of the conduction electrons is 1.01 x 10 -4 m/s. What is the electron current in the wire? The conduction electron density in aluminum is 6.00 x 1028 m-3

Answer:14.5AExplanation:The following data are givenDiameter,D=4.41mm=0.00441m,Hence the area can be calculated as [tex]Arae=\pi \frac{d^{2}}{4}\\ Arae=\pi \frac{0.00441^{2}}{4}\\Area=1.53*10^{-5}m^{2}[/tex]also the speed of the electron which we refer to as the drift speed is given as 1.01*10^-4m/sand lastly the conduction electron density, n =6.00*10^28From the formula connecting the drift velocity to the current which is [tex]I=qnAv\\i=current,\\q=charge\\A=area \\v=drift speed[/tex]if we insert values we arrive at [tex]I=1.6*10^{-19}*6*10^{28}*1.5*10^{-5}*1.01*10^{-4}\\I=14.5*10^{-19+28-5-4}\\I=14.5A[/tex]Hence the electron current in the wire is 14.5A

answer from olasunkanmilesanmi

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Answers #2

Answer:The electron current in the wire is 14.976A in the direction opposite the motion of the charges.Explanation:The current (I) flowing through a wire of cross-sectional area (A), made of a material with free charge density (n), is related to the carriers of the current each of charge Q, and the drift velocity v at which the carriers move, as follows;I = n x Q x A x v -------------------------(i)From the question;The wire is made of aluminium and hasdiameter d, = 4.41mm = 0.00441mA = [tex]\frac{\pi d^2}{4}[/tex] Take [tex]\pi[/tex] = 3.142=> A = [tex]\frac{3.142 * 0.00441^2}{4}[/tex]=> A = 1.5 x 10⁻⁵m²drift speed, v = 1.01 x 10⁻⁴m/selectron charge density, n = 6.00 x 10²⁸ m⁻³Q = charge on an electron = -1.6 x 10⁻¹⁹CSubstitute these values into equation (i) to get the current through the wire as follows;I = 6.00 x 10²⁸ x (-1.6 x 10⁻¹⁹) x 1.5 x 10⁻⁵ x 1.01 x 10⁻⁴Solve for I;I = -14.976AThe negative sign indicates that the direction of conventional current is opposite that of the motion of the negative charges.Therefore, the electron current in the wire is 14.976A in the direction opposite the motion of the charges.

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