Capacitors

• Whenever an electric voltage exists between two separated conductors, an electric field is present within the space between those conductors
• Fields


  interactions that can be spread across empty space; don't have mass and don't need to exist within matter at all
• The interaction of magnets is described in terms of the magnetic field in the space between them
• Whenever a voltage exists between two points, there will be an electric field manifested in the space between
• Field Force


  amount of "push" that a field exerts over a certain distance
• Field Flux


  the total quantity, or effect, of the field through space
• Force and flux are analogous to voltage (push) and current (flow) through a conductor, although, field flux can exist in totally empty space (without motion of particles like electrons) whereas current can only take place where there are free electrons to move
• The amount of field flux that will develop in space is proportional to the amount of field force applied divided by the amount of opposition to field flux
• The type of insulating material separating two conductors dictates the specific opposition to field flux. The number of extra free electrons added to the conductor (or free electrons taken away) is directly proportional to the amount of field flux between the two conductors
• Capacitors


  take advantage of the "squeezing" of extra electrons into a conductor by placing two conductive plates (usually metal) in close proximity with each other
• In a capacitor, wires attach to the respective plates for connection to other components
• When a voltage is applied across the two plates of a capacitor, a concentrated field flux is created between them, allowing a significant difference of free electrons (a charge) to develop between the two plates
• What happens as the electric field is established by the applied voltage?


  extra free electrons are forced to collect on the negative conductor, while free electrons are "robbed" from the positive conductor. This differential charge equates to a storage of energy in the capacitor, representing the potential charge of the electrons between the two plates
• The greater the difference of electrons on opposing plates of a capacitor, the greater the field flux, and the greater "charge of energy" the capacitor will store
• Energy storage in a capacitor is a function of the voltage between the plates
• Capacitors tend to resist changes in voltage drop. When voltage across a capacitor is increased or decreased, the capacitor "resists" the change by drawing current from or supply current to the source of the voltage change, in opposition to the change
• To store more energy in a capacitor, the voltage across it must be increased (add more electrons to the negative plate and take more away from the positive plate, necessitating a current in that direction)
• Capacitor's tendency to oppose changes in voltage


  "A charged capacitor tends to stay charged; a discharged capacitor tends to stay discharged"; a capacitor left untouched will indefinitely maintain whatever state of voltage charge it has been left in
• Capacitors will eventually lose their stored voltage charges due to internal leakage paths for electrons to flow from one plate to the other.
• Charging Capacitor


  the voltage across a capacitor is increased, so it draws current from the rest of the circuit (acts as a power load); there is an increasing amount of energy stored in its electric field
• Discharging Capacitor


  the voltage across a capacitor is decreased, so the capacitor supplies current to the rest of the circuit (acts as power source); store of energy decreases as energy is released to the rest of the circuit
• If a voltage source is applied to an uncharged capacitor (sudden increase of voltage), the capacitor draws current from that source, absorbing energy from it, until the capacitor's voltage equals that of the source
• If a load resistance is connected to a charged capacitor, the capacitor will supply current to the load until it has released all its stored energy, and its voltage decays to zero. Once the capacitor voltage reaches this final (discharged) state, its current decays to zero
• B/c of the role of insulating material in affecting field flux, it has the special name: dielectric
• Permittivity


  extent to which materials inhibit or encourage the formation of electric field flux
• Capacitance


  measure of a capacitor's ability to store energy for a given amount of voltage drop; measure of the intensity of opposition to changes in voltage
• Ohm's Law for a Capacitor


  i = C dv/dt

  i = instantaneous current through capacitor

  C = capacitance in Farads

  dv/dt = instantaneous rate of voltage change (volts/second)
• instantaneous current


  amount of current at a specific point in time
• constant current


  average current over an unspecified period of time
• dv/dt


  rate of change of voltage (v/sec increase or decrease) at a specific point of time, the same specific point that instantaneous current is referenced at
• In a capacitor, time is an essential variable b/c current is related to how rapidly voltage changes over time
• For a slow, steady voltage increase rate, there must be a slow, steady rate of charge building in the capacitor, which equates to a slow, steady flow rate of electrons, or current
• Three basic factors of capacitor construction determining the amount of capacitance created:


  plate area, plate spacing, dielectric material
• Plate Area


  all other factors being equal, greater plate area gives greater capacitance; less plate area gives less capacitance

  • b/c larger plate area results in more field flux (charge collected on plates) for a given field force (voltage across plates)
• Plate Spacing


  all other factors being equal, further plate spacing gives less capacitance; closer plate spacing gives greater capacitance

  • b/c closer spacing results in greater field force (voltage across capacitor divided by distance between plates), which results in greater field flux (charge collected on plates) for any given voltage applied across the plates
• Dielectric Material


  all other factors being equal, greater permittivity of the dielectric gives greater capacitance; less permittivity of the dielectric gives less capacitance

  • materials with greater permittivity allow for more field flux (less opposition), and thus a greater collected charge, for any given amount of field force (applied voltage)
• "Relative" Permittivity


  permittivity of a material, relative to that of a pure vacuum; the greater the number, the greater the permittivity of the material
• Capacitance Formula


  C = EA / d

  C = capacitance in Farads

  E = permittivity of dielectric

  A = area of plate overlap in m^2

  d = distance between plates in meters
• When capacitors are connected in series, the total capacitance is less than any one of the series capacitors' individual capacitances

  • if two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors
• Formula for Series Capacitance


  C total = [C1^-1 + C2^-1 + ... + Cn^-1]^-1