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Unformatted text preview: Drift Velocity  If we apply an electric field to a wire, and can monitor the velocity of a single electron, how fast does it travel over the length of the cylinder?  Possible answers: 3 x 10 8 m/sec. (speed of light in a vacuum) Somewhat less than 3 x 10 8 m/sec. since it’s traveling in a conductor Slower than running water in your home. Let’s calculate the drift velocity u (it helps to draw pictures) Volume of cylinder = AL, the cross sectional area times the length Number of free electrons in cylinder = nAL where n = the density of free electrons per cubic meter Charge carried by electrons in cylinder = nALq e where q = charge on an electron Length of cylinder = ut = L (so we can substitute this for L above) where u = drift velocity of the electrons in m/s t = time in seconds Charge carried by electrons in cylinder = nALq e = nAutq e Current = charge/time = i = nAuq e or u = i/(nAq e ) where i = current in Amperes and u is the speed of e 1 L Crosssectional Area A Drift velocity v Drift Velocity  Assume we have a current of 5 A in a copper wire of crosssectional area 2 mm 2 (~14 gauge wire).  n = 8.5 x 10 28 electrons/m 3 for copper, q = 1.6 x 1019 C  Solving, u = 5/(8.5 x 10 28 x 2 x 106 x 1.6 x 1019 ) = 0.18 x 10 3 m/s = 0.18 mm/s  Two Observations: Closing a switch results in electrical effects occurring at the speed of light in a conductor. The drift velocity for an electron is much different. •Assuming the distance from the electric meter on your house to your room is 15 m, our electron will take 15/(1.8 x 104 ) = 8.3 x 10 4 seconds = 23 hours or about a day to travel this distance, slower than running water. Questions? 2 Vs. Voltage  Energy is expended to move the charges in an electric circuit  Voltage is the energy per unit of charge associated with the motion of charge between two points ....
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This note was uploaded on 04/04/2008 for the course EE 302 taught by Professor Mccann during the Spring '06 term at University of Texas.
 Spring '06
 MCCANN

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