Capacitance

1
Capacitance

• Batteries are devices which store energy based on
  a chemical reaction
• It would be useful to have a device for
  short-term energy storage
• Capacitors are just such devices
• They store separated charges for later use

2
Capacitance

• Capacitors are very useful guys
• They store energy to power the flash bulb in your
  camera and the bits in computer memory
• They protect equipment from voltage surges

3
Capacitance
A capacitor is just two parallel conducting
plates separated by an air gap, or by placing
some insulating material between the plates. The
symbol for a capacitor is If we connect a
battery to the plates, we separate a charge Q
where Q CV. C is a proportionality constant
called the Capacitance and is measured in Farads.
4
Capacitance

• One Farad is a HUGE capacitance. Most electronic
  equipment has capacitors with values in the pico-
  to micro-farad range.
• The capacitance is a constant for a given set of
  plates
• We can calculate the value of the capacitance
  from the geometry of the plates

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Capacitance
6
Dielectrics

• Capacitors are usually constructed with an
  insulating material between the plates
• This helps prevent a breakdown or arcing between
  the plates at higher voltages
• The plates can be placed closer together without
  danger of touching reducing d
• The capacitance is increased by a factor K

7
Dielectrics

• K is called the dielectric constant
• The formula for capacitance is now
• Now the trick is to figure out why the placement
  of the insulator increases the capacitance

8
Dielectrics
We place a charge Q on a capacitor. The potential
difference between the plates is just V0 where Q
C0V0. We assume there is only air between the
plates.
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Dielectrics
We now insert an insulator. If the molecules in
the insulator are polar, they will orient as
shown. If they are not polar, the electron cloud
will be displaced as shown. One sees a net
negative charge on the dielectric next to the
positive plate and a net positive charge next to
the negative plate. The electric field between
the plates is reduced by a factor K. The force
felt by a test charge is thus reduced by K.
10
Dielectrics
The work to move a test charge from the negative
to the positive plate is reduced by K. So, the
potential energy and thus the electric potential
is reduced by K.
11
Energy Storage in Capacitors

• The energy stored in a capacitor is just the work
  necessary to separate the charges in the first
  place.
• As you keep moving charges, you have a greater
  force to overcome because the potential keeps
  increasing
• The total work is just the total charge times the
  average voltage or W QV/2.

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Energy Storage in Capacitors
13
Energy Storage in Capacitors

• We can consider the energy to be stored in the
  electric field between the plates

14
Heart Muscle Cells

• The cell wall acts as a capacitor since charges
  are separated on the interior and exterior
  surfaces. The voltage is in the millivolt range.

Molecules in the cell wall are polarized. The
charge on the outside of the wall is on the order
of 10-8 Coulomb.
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Heart Muscle Cells
When the heart beats, the wall depolarizes in a
wave as shown in this picture. Here the wave
proceeds from left to right. After
depolarization is complete, the cell wall
repolarizes.
This cycle gives rise to an electrical signal
that can be detected externally with an EKG
machine.
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EKG Tracing
The P wave is contraction of the upper chambers
or atria. The QRS is the ventricles. The wave
proceeds from left to right and toward the front,
then down to the left and toward the rear of the
heart. The T wave is the re-polarization of the
muscle in preparation for the next beat. Heart
defects show up as variations in the wave pattern.