Resitivity A 10m length of copper wire (r = 1mm) carries 10 Amps.What is the pot

Question

Resitivity A 10m length of copper wire (r = 1mm) carries 10 Amps.What is the potential difference between the ends of the wire? How much power will be dissapated by the wire as heat? What is the average drift velocity upsilon _d of the electrons in the wire? Tapered Wire A 10m length of tapered copper wire (r_o = 1mm, r_1= 2 mm) carries 10 Amps. What is the potential difference between the ends of the wire? How much power will be dissapated by the wire as heat? What is the average drift velocity epsilon_d of the electrons in the wire?

Explanation / Answer

I will answer the first question. Post the second in another question thread:

a) to do this, we need to calculate first the electric field in V/m so:

Let's calculate Area first:

A = 3.1416 * (0.001)2 = 3.1416x10-6 m2

The reported resistivity of copper is 1.72x10-8 ohm m so:

E = 1.72x10-8 * 10 / 3.1416x10-6 = 0.0547 V/m

Then potential difference is:

V = 0.0547 * 10 = 0.547 V

To get the power, we need to know the potential which is:

P = I*V = 0.547 * 10 = 5.47 J

In cal: 5.47 * 0.239= 1.3073 cal.

Finally to get the drift velocity Vd:

Copper has a density of 8.94 g/cm3, and an atomic weight of 63.546 g/mol, so there are 140685.5 mol/m3. In one mole of any element there are 6.02×1023 atoms (Avogadro's constant). Therefore in 1 m3 of copper there are about 8.5×1028 atoms (6.02×1023 × 140685.5 mol/m3).

vd = 10 / (8.5x1028 * 1.6x10-19 * 3.1416x10-6)

vd = 2.34x10-4 m/s

Hope this helps

vd =

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