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Lectures 5 to 6. 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.
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Lectures 5 to 6 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.
What is the uses of the capacitor? • A capacitor is a device that stores electric charge. • Define the capacitor? • 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: • 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 CapacitorsCapacitors in seriesCapacitors 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 capacitanceCeq 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:
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.
