Chemistry: A 14-gauge copper wire has a diameter of 1.676 mm. What magnitude current flows in amperes when the drift velocity is 0.500 mm/s? (The density of free electrons in copper is 8.34 ✕ 1028 e−/m3.).)

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A 14-gauge copper wire has a diameter of 1.676 mm. - id1416765172935, tatyananannanana

Ответ:

duhitsmiracle59

19.01.2022

Chemistry

14.7 A

Explanation:

The magnitude current flowing in a conductor is given by

$I=\frac{Q}{t}$

where

Q is the total charge

t is the time interval

The total charge passing through a point in the conductor can be written as

Q=neAd

where

n is the density of free electrons

A is the cross-sectional area of the conductor

$e=1.6\cdot 10^{-19}C$ is the electron charge

d is the length of the conductor

The time interval can be written as

$t=\frac{d}{v_d}$

where

d is the length of the conductor

v_d is the drift velocity of the electrons

Re-arranging the three equations, we get:

$I=\frac{neAd}{d/v_d}=neAv_d$

For the copper wire here we have:

$v_d = 0.500 mm/s = 0.5\cdot 10^{-3} m/s$

$n=8.34\cdot 10^{28} m^{-3}$

The diameter is 1.676 mm, so the area is

$A=\pi (\frac{d}{2})^2=\pi (\frac{1.676\cdot 10^{-3}}{2})^2=2.2\cdot 10^{-6}m^2$

So, the current in the wire is

$I=(8.34\cdot 10^{28})(1.6\cdot 10^{-19})(2.2\cdot 10^{-6})(0.5\cdot 10^{-3})=14.7 A$

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A 14-gauge copper wire has a diameter of 1.676 mm. What magnitude current flows in amperes when the drift velocity is 0.500 mm/s? (The density of free electrons in copper is 8.34 ✕ 1028 e−/m3.).)

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