Lectures 5 to 6
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The Capacitance and dielectrics
Definition and Calculating of Capacitance
Capacitors in series.
Capacitors in parallel.
Energy of a charged capacitor.
Dielectric materials and dielectric constant.
The relation between the induced charge and
dielectric constant.
• Definition and Calculating of Capacitance
• What is the uses of the capacitor?
• A capacitor is a device that stores electric charge.
• Define the capacitor?
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A capacitor consists of two conductors, carrying charges
of equal magnitudes but opposite sign, separated by an
insulator, which could be air or even a vacuum.
• What are the applications of the capacitors?
• Capacitors have many applications:
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Computer RAM memory and keyboards.
Electronic flashes for cameras.
Electric power surge protectors.
Radios and electronic circuits.
Electric power supplies.
Timing circuits.
What are the types of the capacitors?
1- A parallel-plate capacitor consists of
two parallel conducting plates, each of area A,
separated by a distance d.
2- A spherical capacitor consists of an inner sphere of radius
a surrounded by a concentric spherical shell of radius b.
3- A cylindrical capacitor consists of a solid cylindrical
conductor of radius a and length l surrounded by a coaxial
cylindrical shell of radius b.
• Define the of Capacitance
• The capacitance C of a capacitor
• is the ratio of the charge on either conductor to the potential
difference between the conductors:
• The capacitance has SI units of coulombs per volt, 1 F = 1 C/V
• The SI unit of capacitance is the farad (F)
• In practice,
• microfarads F (10-6 F)
• picofarads pF (10-12 F).
• Calculating Capacitance of Parallel-Plate Capacitors
• the capacitance of a parallel-plate capacitor is proportional
to the area of its plates and inversely proportional to the
plate separation d.
Combinations of Capacitors
Capacitors in series
Capacitors in parallel
Combinations of Capacitors
Series Combination
• Two capacitors connected as shown in Figure are known as
a series combination of capacitors.
Combinations of Capacitors
Series Combination
• The equivalent capacitance Ceq can be calculated from
Capacitors in parallel Combination
• The individual potential differences across capacitors
connected in parallel are the same and are equal to the
potential difference applied across the combination.
Parallel Combination
• the equivalent capacitor Ceq
• Energy Stored in a Charged Capacitor
• The work done in charging the capacitor appears as
electric potential energy U stored in the capacitor,
• we can express the potential energy stored in a charged
capacitor in the following forms:
Quations
Dielectric materials and dielectric constant
• A dielectric is a non-conducting material, an electrical insulator, such
as rubber, glass, or waxed paper.
• Dielectrics decrease the field strength between the plates.
• The non-conducing molecules orient themselves such that their
electric dipoles subtract from the field produced by the charged plates.
• Since the field is reduced, the voltage between the plates is reduced.
• Dielectric materials and dielectric constant
• Dielectrics are “fillings” that are inserted between
the plates of a capacitor and increase its
capacitance, or ability to separate charge.
• When a dielectric is inserted between the plates of a
capacitor, the capacitance increases by a dimensionless
factor , which is called the dielectric constant of the
material.
• The dielectric constant is the ratio of the field without
the dielectric (Eo) to the net field (E) with the dielectric:
•  = Eo /E,
 = C / Co
The relation between the induced charge and dielectric constant
if E0 is the electric field without the dielectric, the field in the
presence of a dielectric is
The relation between the induced charge and dielectric constant
The voltages with and without the dielectric are related by
the factor  as follows:
• The dielectric constant  varies from one
material to another.
Problem 1
Problem 2
Problem 3
Problem 3
Problem 4
Problem 4
Problem 5
Problem 5
Problem 6
Problem 6