Chapter 24 Capacitance

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Chapter 24Capacitance
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Topics

• Capacitance
• Storage of Electrical Energy
• Capacitors, Batteries and Circuits
• Dielectrics

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Capacitance
The capacitance of a device is defined by
Q is the charge stored V is the potential
difference within the system
The unit is the farad (F) Coulomb/Volt But
since the farad is such a huge unit we usually
use mF 10-6 F or pF 10-12 F
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Capacitance Spherical Conductor
The potential on the surface of a spherical
conductor of radius R is
Therefore, its capacitance is
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Capacitance Capacitors
A capacitor is a device that stores charge Q on
one conductor and charge Q on the other
conductor
The stored charge creates an electric field, and
therefore, a potential difference between the
conductors
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Capacitance Parallel Plate Capacitors
If two conducting plates of area A are separated
by a small distance d the electric field
between them will be approximately constant and
of magnitude
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Capacitance Parallel Plate Capacitors
Since the electric field is constant, the
potential difference between the plates is
simply
so the capacitance is
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Capacitance Cylindrical Capacitors
A coaxial cable of length L is an example of a
cylindrical capacitor
R2
R1
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Storage of Electrical Energy
Work must be done to move positive charge from a
negatively charged conductor to one that is
positively charged. Or to move negative charge
in the reverse direction.
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Storage of Electrical Energy
In moving charge dq, the electrical potential
energy of the capacitor is increased by
Therefore,
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Energy Density of Electric Field
Electric field
Electric potential
Potential energy
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Energy Density of Electric Field
The energy density ue
This expression holds true for any electric field
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Capacitors, Batteries and Circuits
The potential is the same throughout a conductor
when it is in electrostatic equilibrium that is,
when the charge has stopped moving
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Capacitors in Parallel
At equilibrium, the potential across
each capacitor is the same, namely, 12 V
same potential
same potential
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The two capacitors are equivalent to a single
capacitor with capacitance
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Capacitors in Series
At equilibrium, the sum of the potentials
across both capacitors will be equal to 12 V
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The potential across C1 that across C2 is equal
to the potential difference between points a
and b
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Dielectrics
A non-conducting material is called a dielectric
Michael Faraday 1791 1867
Michael Faraday discovered that the capacitance
increases when the space between conductors is
replaced by a dielectric
wikimedia
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Dielectrics
Electric field strength in the presence of a
dielectric is
where k (kappa) is called the dielectric constant
of the inserted material
E0 is the field before the dielectric is
inserted.
is called the permittivity
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Maximum electric field strength
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Molecular View of Dielectric
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Molecular View of Dielectric
-sb
sb
The polarized molecules of the dielectric tend
to align themselves parallel to the electric
field due to the charges on the conductors
- - - - - - - -

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Molecular View of Dielectric
The bound charge sb induced on the surface of
the dielectric creates an electric field
opposed to the electric field of the free
charge sf on the conductors, thereby reducing
the field between them
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Summary

• Capacitance C Q / V (farad)
• Capacitors
• In parallel C C1 C2
• In series 1/C 1/C1 1/C2
• Stored energy U ½ QV
• Energy density ue ½ e0 E2
• Effect of dielectric E E0 / k