A 3-meter long copper wire has 1.5 amps of current in it. The radius of the wire

Question

A 3-meter long copper wire has 1.5 amps of current in it. The radius of the wire is 0.5 mm. (Use values of resistivity from Table 27.2 in the textbook by Serway.)

from the table --( copper 1.7 x10^-8)

3.9 x10^-3temp coefficient

A 3-meter long copper wire has 1.5 amps of current in it. The radius of the wire is 0.5 mm. (Use values of resistivity from Table 27.2 in the textbook by Serway.) (a) Find the magnitude of the electric field inside the wire N/C (b) How much energy is stored in the wire (i.e. in its electric field)? (c) Find the rate of conversion of electrical energy to thermal energy.

Explanation / Answer

R = rho L / A

R = (1.7 x 10^-8)(3) / (pi (0.5 x 10^-3)^2)

R = 0.065 Ohm

V = I R = 0.0974 Volt

(A) E = V / L = 0.0325 N/C

(B) energy density = e0 E^2 / 2

= (8.854 x 10^-12)(0.0325^2)/2

= 4.667 x 10^-15 J/m^3

Energy = (4.667 x 10^-15) (3 x pi x (0.5 x 10^-3)^2)

= 1.10 x 10^-20 J

(C) P = I^2 R = 1.5^2 (0.065)

P =0.146 Watt

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