How long does it take an electron to travel from the outlet to the lamp?

A table lamp is connected to an electric outlet by a copper wire of diameter .20 cm and length 2.0m. Assume that the current through the lamp is 1.5A, and that this current is steady. How long does it take an electron to travel from the outlet to the lamp?How long does it take an electron to travel from the outlet to the lamp?Use J=n*e*v_d, where J is the current density, n is the free charge concentration, e is the charge of an electron, and v_d is the drift velocity.



J = current/area=1.5/(π*(0.001)^2)=4.77E5 A/m^2



It is conventional to assume one free electron per copper atom. n = # electrons/m^3 = NA*ρ/M, where NA = Avogadro's number, ρ is the density of copper and M is the molar mass of copper. n = 6.022E23*8960/0.06354 = 8.49E28 m^-3.



Drift velocity is therefore 4.77E5/8.49E28/1.6E-19 = 3.51E-5 m/s.



Total time for an electron to travel 2.0 m is 2/3.51E-5 = 15.8 hours



Of course you don't have to wait until electrons from the outlet reach the lamp; free electrons in the copper wire leave the wire and are replaced by electrons from the outlet. The signal travels at nearly the speed of light, even though the drift speed of an electron is only 13 cm/hour.

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Check out http://en.wikipedia.org/wiki/Drift_veloc… and you will see how slow drift velocities typically are for electrons in copper wires.How long does it take an electron to travel from the outlet to the lamp?like .oo1 secondHow long does it take an electron to travel from the outlet to the lamp?Only the outermost electrons actually move.



A mol of copper contains Avogadro's number of atoms and occupies about 7.15 ml = 7150 mm3. (EDIT: Earlier I had transposed digits and got the wrong number for this part.) The wire cross section is 3.1416 mm2, so a Coulomb of mobile electrons occupy 7150 mm3 / 3.1416 mm2 = 2.276 m of wire.



A Coulomb contains Avogadro's number of electrons. If one electron per atom is mobile (big assumption), then the average mobile electron is moving at 1.5 x 2.276 = 3.414 m/s.



It takes about 2 / 3.414 = 0.586 sec.



Of course, this assumes the lamp is powered by D/C current. A/C just moves back and forth about 30 millimeters.How long does it take an electron to travel from the outlet to the lamp?
The current is defined as the number of coulombs per second passing by a certain point.



We can figure out the resistance of the copper wire using the equation...



R = p (l/A) where p(rho) is the resistivity, which of copper is...1.68x10^-8 (ohm meters)



l is the length of wire, 2.0m, and A is the cross sectional area which is given by pi(r^2) where r is the radius of wire, .10cm = .001m



Using this resistance get the voltage, V = IR



This voltage due to the conservation of energy gives us the equation



eV = 1/2mv^2 where e is the electronic charge, solve for velocity v



v = sqrt(2eV/m)



Using this velocity, solve for how long it takes the electron to travel 2m.