[continued from previous message]   
      
   kind of like how a comedian put it, "Why is it 'corn on the cob' and   
   'corn'?  Instead, it should be 'corn' and 'corn off the cob'."  Of   
   course, one could use the short-form "work" to indicate either   
   "general work", "effective work" or "productive work" by its use in   
   context.   
   ---------   
      
   -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-   
   -|-|-| (4) ELECTRICITY |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-   
   -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-   
      
   Now, I am going to apply work using prescotts on an electrical   
   circuit.   
      
   ***************************   
   Let's find the average drift velocity:   
     -------------------------   
     A is the cross-section of the wire  (m²)   
     n is "free" electrons per unit volume  (electrons/m³)   
     e is the magnitude of charge of an electron   
          (1.602 * 10^(-19) C/electron)   
     v is the average drift velocity of the electrons  (m/s)   
     I is the current in the wire  (C/s)   
     dq is an infinitesimal amount of charge  (C)   
     dt is an infinitesimal amount of time  (s)   
     dN is an infinitesimal number of electrons  (electrons)   
     -------------------------   
    (1)               dq = e*dN   
      
                      dN = nAv*dt   
    (2)               dt = dN/(nAv)   
      
    (1)/(2)        dq/dt = e*dN/(dN/nAv)   
                       I = enAv   
                       v = I/(enA)   
      
   ***************************   
   Let's find force:   
     -------------------------   
     W_j is the Work in Joules  (N*m)   
     f is the force  (N)   
     s is the distance  (m)   
     V is the voltage  (N*m/C)   
     -------------------------   
                      W_j = F*s   
                     dW_j = F*v*dt   
                  dW_j/dt = F*v   
                      V*I = F*v   
      
                             V*I   
                        F = -----   
                              v   
      
                          = VenA   
      
     -------------------------   
     P is pressure  (Pa)   
     -------------------------   
                             F   
                        V = ---   
                            enA   
      
                            P   
                          = --   
                            en   
      
   So we can say that "voltage is the electromagnetic-pressure (created   
   by an EMF source) per density of charge."   
      
   Notice that the pressure supplied by an EMF has nothing to do with the   
   length of the circuit.  A battery hooked to a 1-meter circuit of 1cm²   
   wire uses the same pressure to start a current as a similar battery   
   hooked to a 10000-meter circuit of similar wire!   
      
   ***************************   
     -------------------------   
     W_i is the Initial Work (in Prescotts)  (N*s)   
         (the work done to start the electrical circuit)   
     t is a duration of time  (s)   
     m_e is the mass of an electron  (9.109 * 10^(-31) kg/electron)   
     -------------------------   
                      W_i = F*t   
                          = VenA*t   
      
   Notice that in this case "W_i" does not equal "m_e*v".  This is   
   because over the period of time "t", which is greater than the average   
   change in time between electron collisions, the acceleration of the   
   electron is hindered when the electron loses its energy during a   
   collision.   
      
      
   ***************************   
     -------------------------   
     U is Initial Work (in Prescotts) per Coulomb  (N*s/C)   
     Q is an amount of charge  (C)   
     p is the resistivity of the wire  (ohm*m)   
     l is the length of the wire  (m)   
     -------------------------   
                        U = W_i/Q   
                          = F/I   
                          = (VenA)/(V/R)   
                          = enAR   
                          = enA*(p*l/A)   
                          = enpl   
      
   Thus, we can say that "U" is a constant for any given circuit.  So,   
   given any circuit, a constant amount of work is done to move a coulomb   
   along the circuit.   
      
      
   ***************************   
     -------------------------   
     µ is Initial Work (in Prescotts) per Coulomb*meter  (N*s/(C*m))   
     -------------------------   
                        µ = dU/dl   
                          = enp   
      
   So, the rate at which work is done per unit distance depends on the   
   material.   
      
   ***************************   
     -------------------------   
     t_c is the change in time between electron collisions  (s)   
     -------------------------   
      
   Each electron gains "m_e*v" of energy before it makes a collision and   
   losses it's energy.  The collision will take place in "t_c" seconds.   
   "U" is the amount of work to move a coulomb "l" meters along the wire.   
    And, in "l" meters, there will be "l/(v*t_c)" number of collisions.   
   So,   
      
              l     m_e*v   
            ----- * ----- = U   
            v*t_c     e   
      
                   l*m_e   
                  ------- = enpl   
                   t_c*e   
      
                             m_e   
                     t_c  =  ----   
                             e²np   
      
      
   which is correct.   
      
   -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-   
   -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-   
      
   by Raheman Velji   
   November 7, 2004   
      
   you can also view this (and updated versions) at...   
   ...http://www.angelfire.com/un/rv   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)