CAPACITORS

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WHAT IS A CAPACITOR? A capacitor is an electronic device for storing electric charges. It consists of two conductors [metal plates]carrying opposite charges. The plates are separated by an insulating material known as dielectric .

Basic schematic diagram of a parallel plate capacitor. | Download Scientific Diagram

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PRACTICAL FORMS OF CAPACITORS

1.Variable air capacitors 2.Paper capacitors 3.Electrolytic capacitor

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Capacitance,C of a capacitor is defined as the ratio of charge Q on either plates to the potential difference V between them. Capacitance is also the ability of a capacitor to store charges. C = Q/V ………….formula1 The unit of capacitance is Farads

CAPACITANCE,C

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WORKED EXAMPLE

A capacitor of charge 5 x 10 -8 Coulomb has a potential of 100 V. What is the capacitance of the capacitor? SOLUTION C = Q/V = 5 x 10 -8 /100 = 5 x 10 -10 F

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FACTORS AFFECTING CAPACITANCE 1.The distance, d between the plates The closer the plates, the greater the capacitance. 2.The area, A of the plate The larger the area of the plates the greater the capacitance.

Basic schematic diagram of a parallel plate capacitor. | Download Scientific Diagram

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3. The nature [or dielectric constant or permittivity, ɛ ] of the dielectric The greater the dielectric constant,the greater the capacitance. C= ɛ A/d ………… formula 2 A= area of the plate ɛ = permittivity/dielectric constant of the material d = distance between the plates

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M ateria I Vac uun-m Fused quartz Neoprene rubber Nylon Paper Polystyrene Pyrex glass Dielectric Constant ( 1.00000 1.00059 3.78 6.7 3.7 2-56 5.6

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Relative permittivity, ɛ r Relative permittivity, ɛ r is the ratio of the permittivty ɛ of a material to the permittivty of free space/vacuum, ɛ 0 relative permittivity= permittivity of the material permittivity of free space ɛ r = ɛ / ɛ o [ɛ o = 8.854 x 10 -12 F/m] ɛ = ɛ r ɛ o ………………… eq 2 1

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C = ɛ r ɛ o A/d ……….formula 3

From formula 2 C= ɛ A/d [ ɛ = ɛ r ɛ o ]

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WORKED EXAMPLE A parallel plate capacitor has an area 10 cm 2 a plate of separation 2 cm is charged initially to 100 V in a vacuum. Calculate: a.Capacitance of the capacitor b.Charge on the plates c.Capacitance of the capacitor if the space between the plates is filled with mica wire, ɛ r = 5

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To find the capacitance C= ɛ r ɛ o A/d = 1x 8.854 x 10 -12 x 10 x 10 -4 / 2 x 10 -2 = 4.43 x 10 -13 F To find the charge on the plates Q= CV= 4.43 x 10 -13 X 100 =4.43 x 10 -13 Coulombs

SOLUTION

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To find the Capacitance of the capacitor if the space between the plates is filled with mica wire, ɛ r = 5

C = ɛ r ɛ o A/d = 5 x 8.854 x 10 -12 x 10 x 10 -4 / 2 x 10 -2 = 2 .21 x 10 -12 F

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CAPACITORS IN SERIES

Capacitors in series and capacitors in parallel: Equivalent of combination

3 capacitaors of equal capacitane ,when connected in series have net capacitance - Physics - Electrostatic Potential And Capacitance - 9086869 | Meritnation.com

TOTAL CAPACITANCE

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RESISTORS IN PARALLEL

Capacitor Series and Parallel Circuit Capacitance Calculator

TOTAL CAPACITANCE

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APPLICATIONS OF CAPACITORS Capacitors are used in: 1.radio circuits for tuning 2.ignition system of motor vehicles 3.elimination of sparks when a circuit containing inductance is suddenly opened e.g , in induction coils.

4.smoothening rectified current from d.c . power supply. 5.blocking noise in a.c.amp lifiers

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ENERGY STORED IN CAPACITOR

W= ½ CV 2 or W= ½ Q 2 /C or W= QV W is in Joules,Q is in Coulombs,V is in volts and C in Farads WORKED EXAMPLE A capacitor of capacitance 5 µF is subjected to a potential difference of 1000 V across its terminals. Calculate the energy stored in the capacitor.

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SOLUTION

W = ½ CV 2 = ½ x 5 x 10 -6 x 1000 2 = 2.5 Joules