Electric field ohm s law_ etc.ppt

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  • 1. Electric Current, Ohm’s Law, and Electric Circuits ISAT 241 Fall 2002 David J. Lawrence
  • 2. Electric Current
    • Consider a bar of material in which positive charges are moving from left to right:
    • Electric current is the rate at which charge
    • passes through the surface, I avg =  Q/  t ,
    • and the instantaneous current is I = dQ/dt .
    imaginary surface I
  • 3. Electric Current
    • SI unit of charge: Coulomb (C)
    • SI unit of current: Ampere (1A= 1C/s)
    • A current of 1 ampere is equivalent to 1 Coulomb of charge passing through the surface each second.
  • 4. Electric Current
    • By definition , the direction of the current is in the direction that positive charges would tend to move if free to do so, i.e., to the right in this example.
    • In ionic solutions (e.g., salt water) positive charges (Na + ions) really do move. In metals the moving charges are negative , so their motion is opposite to the conventional current.
    • In either case, the direction of the current is in the direction of the electric field.
  • 5. Electric Current
    • Na + ions moving through salt water
    • Electrons moving through copper wire
    E I E I
  • 6.  
  • 7. Electric Current
    • The electric current in a conductor is given by
    • where
    • n = number of mobile charged particles
    • (“carriers”) per unit volume
    • q = charge on each carrier
    • v d = “drift speed” (average speed) of
    • each carrier
    • A = cross-sectional area of conductor
    • In a metal, the carriers have charge q  e.
  • 8.  
  • 9. Electric Current
    • The average velocity of electrons moving through a wire is ordinarily very small ~ 10 -4 m/s.
    • It takes over one hour for an electron to travel 1 m!!!
    E I
  • 10.  
  • 11. Ohm’s Law
    • For metals, when a voltage (potential difference) V ba is applied across the ends of a bar, the current through the bar is frequently proportional to the voltage.
    • The voltage across the bar is denoted:
    • V ba = V b  V a .
    area A V b V a E I
  • 12. Ohm’s Law
    • This relationship is called Ohm’s Law.
    • The quantity R is called the resistance of the conductor.
    • R has SI units of volts per ampere. One volt per ampere is defined as the Ohm (  . 1  =1V/A.
    • Ohm’s Law is not always valid!!
  • 13.  
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  • 17. Ohm’s Law
    • The resistance can be expressed as
    • where
      •  is the length of the bar (m)
      • A is the cross-sectional area of the bar (m 2 )
      •  , “Rho”, is a property of the material called the
      • resistivity. SI units of ohm-meters (  -m).
     area A V b V a E I
  • 18. Ohm’s Law
    • The inverse of resistivity is called conductivity :
    • So we can write
  • 19. Resistance and Temperature
    • The resistivity of a conductor varies with temperature (approximately linearly) as
    • where
        •  resistivity at temperature T ( o C)
        •  o  resistivity at some reference temperature T o (usually 20 o C)
        •  “ temperature coefficient of resistivity”.
    • Variation of resistance with T is given by
  • 20.  
  • 21. Electrical Power
    • The power transferred to any device carrying current I (amperes) and having a voltage (potential difference) V (volts) across it is
    • P = VI
    • Recall that power is the rate at which energy is transferred or the rate at which work is done.
    • Units: W (Watt) = J/s
  • 22.  
  • 23.  
  • 24. Electrical Power
    • Since a resistor obeys Ohm’s Law
    • V = IR , we can express the power dissipated in a resistor in several alternative ways:
  • 25.  
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