A current of 1.00mA is through a 1.00cm long, 1.00mm, cylindrical wire. The dens

Question

A current of 1.00mA is through a 1.00cm long, 1.00mm, cylindrical wire. The density of copper is D_Cu = 8.96 g/cm^3 = 8.96 times 10^3 kg/m^3. The molar mass of copper is M_Cu = 63.55 g/mol = 6.355 times 1^0-2 kg/mol. Each atom of copper has one conducting electron (free electron) and the resistivity of copper is given by, rho_Cu = 1.68 times 10^-8 Ohm m. Avogadro's Number, N_A = 6.022 times 10^23 atoms/mol. (I) Find the volume of copper of the wire. Find the mass of copper of the wire. (II) Find the number of copper atoms in the wire. Find the total free charge of the wire. (III) Find the time it takes for the charge to move the length of the wire, using the current and the total free charge of the wire. (IV) The average speed of electrons in the wire is equal to the length of the wire divided by the time it takes electrons to move through the whole length of wire. Find the average speed of electrons in the wire. (V) Find the resistance of the copper wire. (VI) Find the average power dissipated by the wine.

Explanation / Answer

I) Volume of copper wire , V= volume of cylinder = 3.14*r2*L

                                                                 = 3.14*(0.5*10-3)2*1*10-2 = 7.85*10-9 m3

Mass of wire, m = density*V = 8.96*103*7.85*10-9 =7.03*10-5 kg

II) No. of Cu atom in wire, n = (NA/MCu)*m = (6.022*1023/(6.355*10-2))*7.03*10-5 = 6.66*1020

III) Current, I = q/t =1.00 mA

Total free charge, q = e*n = 1.6*10-19*6.66*1020 = 106.6 C

Time for the charge to move the length of the wire, t = q/I = 106.6/10-3 = 106600 s = 106600/3600 hr = 29.61 hr

IV) average speed of the electron , v = L/t = 1*10-2/106600 = 9.38*10-8 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.