Electrical Energy and Capacitance

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Electrical Energy and Capacitance
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• Potential difference and electrical potential
• Work and potential energy
• Potential energy is a scalar quantity with charge
  to the negative of the work done by the
  conservative force
• ?PEPef-Pei - Wf
• Coulomb force is conservative
• If imagine a small charge placed in a uniform
  electric field E. As the charge moves from A to
  B, the work done on the charge by the electric
  field
• WFx?x q Ex (xf-xi)

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• Work energy theorem
• Wq Ex ?x ?KE
• But the work done by a conservative force can be
  reinterpreted as the negative of the charge in a
  potential energy associated with that force
• ?PE of a system consisting on an object of charge
  q through a displacement ?x in a constant
  electric field E is given by
• ?PE -WAB -q Ex ?x
• SI unit J (Joule)

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• ? KE ?PE el ?KE (0-?q? E d 0
• ?KE ?q? E d
• Similarly , KE equal in magnitude to the loss of
  gravitational potential energy
• ?KE ?PEg ?KE (0 mgd) 0
• ?KEmgd

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• Electric Potential
• F qE
• The electric potential difference between points
  A and B is the charge in electric potential
  energy as a charge q moves from A to B, divided
  by the charge q ?V VA-VB ?PE/q
• SI unit J/C or V (Joule/Coulomb or Volt)
• Electric potential is a scalar quantity

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• Electric potential and potential energy due to
  point charges
• The electric field of a point charge extends
  throughout space, so its electrical potential
  also
• Electric potential created by a point charge
  Vke q/r
• The electric potential of two or more charges is
  obtained by applying the superposition principle
  the total electric potential at some point P due
  to several point charges is the algebraic sum of
  the V due to the individual charges

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• Potentials and charged conductors
• The electric potential at all points on a charged
  conductor
• W -?PE -q( VB-VA)
• No net work is required to move a charge between
  two points that are at the same electric
  potential
• All points on the surface of a charged conductor
  in electrostatic equilibrium are at the same
  potential

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• The electric potential is a constant everywhere
  on the surface of a charged conductor
• The electric potential is constant everywhere
  inside a conductor and equal to the same value at
  the surface
• The electron volt is defined as KE that an
  electron gains when accelerated through a
  potential difference of 1V
• 1eV 1.6x 10-19 C V 1.6x10-19 J

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• Equipotential surface is a surface on which all
  points are at the same potential
• The electric field at every point of an
  equipotential surface is perpendicular to the
  surface.

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• Capacitance
• A capacitor- is a device used in variety of
  electric circuits
• The capacitance C of a capacitor is the ratio of
  the magnitude of the charge on either conductor
  (plate) to the manitude

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