A 5.30 m length of 2.1 mm -diameter wire carries a 790 mA current when 18.0 mV i

ID: 1428408 • Letter: A

Question

A 5.30 m length of 2.1 mm -diameter wire carries a 790 mA current when 18.0 mV is applied to its ends. The drift velocity is 2.1×105 m/s .

a)Determine the resistance R of the wire

b)Determine the resistivity

c) determine the current dencity

d) determine the electic field inside the wire

e) determine the number n of free electons per unit voulme

Given

length l = 5.3 m

diameter d = 2.1mm , radiur r = d/2 = 1.05 mm = 1.05 * 10^-3 m

current I = 0.79 A

voltage V = 0.018 V

drift velocity vd = 2.1 * 10^-5 m/s

a) resistance

R = V / I = 0.018/0.79

R = 0.023 ohm

b) resistivity

rho = R * A / l

rho = 0.23 * 3.14 * sqr( 1.05 * 10^-3) / 5.3

rho = 1.5 * 10^-5 ohm-m

current density J = I / A

J = 0.79/3.14*sqr(1.05 * 10^-3)

J = 2.28 * 10^5 A / m^2

electric field E = V/d = 0.018 / 5.3

E = 3.3 * 10 ^-3 V/m

n = J / e * A

n = 2.28 * 10^5 / 1.6 * 10^-19 * 3.14 * sqr(1.05 * 10^-3)

n = 0.4116 * 10^30 electrons

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