Capacitor Engr. Faheemullah Shaikh Lecturer, Department of Electrical Engineering.

Topic Outline Definition of Capacitance Calculating Capacitance Combinations of Capacitors Energy Stored in a Charged Capacitor Capacitors with Dielectrics An Atomic Description of a Dielectric

Capacitance and Dielectric Capacitors: Device that store electric charge A capacitor consists of two conductors separated by an insulator. Capacitance: Depends on its geometry and on the material, called a dielectric, that separates the conductors.

Definition of Capacitance Pictures from Serway & Beichner A capacitor consists of two conductors (known as plates) carrying charges of equal magnitude but opposite sign. A potential difference  V exists between the conductors due to the presence of the charges. What is the capacity of the device for storing charge at particular value of  V?

Definition of Capacitance Experiments show the quantity of electric charge Q on a capacitor is linearly proportional to the potential difference between the conductors, that is Q ~  V. Or we write Q = C  V The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them: C = Q VV SI Unit: farad (F), 1F = 1 C/V Typical device have capacitances ranging from microfarad to picofarad.

Parallel-Plate Capacitors Pictures from Serway & Beichner (a)The electric field between the plates of a parallel-plate capacitor is uniform near the center but non uniform near the edges. (b)Electric field pattern of two oppositely charged conducting parallel plates.

Parallel - Plate Capacitors A parallel-plate capacitor consists of two parallel conducting plates, each of area A, separated by a distance d. When the capacitor is charged, the plates carry equal amounts of charge. One plate carries positive charge, and the other carries negative charge. The plates are charged by connection to a battery. Describe the process by which the plates get charged up.

Capacitors Storing a charge between the plates Electrons on the left plate are attracted toward the positive terminal of the voltage source This leaves an excess of positively charged holes The electrons are pushed toward the right plate Excess electrons leave a negative charge _ + _

Parallel-Plate Capacitors Two parallel metallic plates of equal area A separated by a distance d as shown. One plate carries a charge Q and the other carries a charge –Q. And surface charge density of each plate is  = Q/A. A d If plates are large, then charges can distribute themselves over a substantial area, and the amount of charge that can be stored on a plate for a given potential diff increases as A is increased. Thus we expect C to be proportional to A  C ~ A Variation with A

Parallel-Plate Capacitors Variation with d A d Potential difference ∆V constant across, E field increases as d decreases. There is a potential difference of V volts between the plates, therefore the work in transferring 1 C of charge between the plates is V joules. ∆V = Ed

Air tank Analogy to Charging a Capacitor

Capacitors Applications Types of capacitors The dielectric material determines the type of capacitor Common types of capacitors are: ◦ Mica ◦ Ceramic ◦ Plastic film

Capacitors Applications Some capacitors are polarised, they can only be connected one way around Electrolytic capacitors are polarised

Capacitors Applications Variable capacitors are used in communication equipment, radios, televisions and VCRs They can be adjusted by consumers by tuning controls Trimmers are internal adjusted capacitors that a consumer cannot adjust

Capacitors Applications These variable capacitors would be difficult to squeeze into your mobile phone and iPod Current technology uses semi- conductor variable capacitors called varactors (varicaps)

Combinations of Capacitors

Parallel Combination The individual potential differences across capacitors connected in parallel are all the same and are equal to the potential difference applied across the combination.

Parallel Combination Combinations of Capacitors When the capacitors are first connected, electrons transfer between wires and plates. Leave left plates positively charged and right plates negatively charged. Energy source for this charge transfer is internal chemical energy stored in the battery. Flow of charges ceases when the voltage across the capacitors is equal to that across the battery terminals. Capacitors reach their maximum charge when the flow of charges ceases.

Parallel Combination Combinations of Capacitors Let the maximum charges on the two capacitors Q1 and Q2. Total charge Q stored by two capacitors is Q = Q1+Q2. Voltage across are the same  Q1=C1  V, Q2=C2  V Define an equivalent capacitor having C eq s.t. Q = C eq  V We have C eq  V = C1  V + C2  V And hence C eq = C1 + C2 (for parallel combination) In general C eq = C1 + C2+ C3+ ………….. (for parallel combination)

Combinations of Capacitors Series Combination Voltage  V across battery terminals is split between two capacitors.  V =  V1 +  V2 Where  V1 and  V2 are potential diff across capacitors C1 and C2. Suppose we have equivalent capacitor C eq = Q/  V For each capacitor, we have  V1 = Q/C1 and  V2=Q/C2  Q/C eq = Q/C1 + Q/C2  1/C eq = 1/C1 + 1/C2 (series combination) In general 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ….. (series combination)

Example: Equivalent Capacitance In parallel use C=C1+C2 In series use 1/C=1/C1+1/C  F  F 2.50  F 8.50  F  F In series use 1/C=1/C1+1/C  F

Example: Equivalent Capacitance In parallel use C=C1+C2 In series use 1/C=1/C1+1/C2

Example: Equivalent Capacitance In series use 1/C B =1/C+1/C+1/C In series use 1/C A =1/C+1/CC C/2 C/3 In parallel use C eq =C+C/2+C/3

Charging & Discharging of Capacitor

Charging a capacitor Current flow Initially ◦ High Finally ◦ Zero Exponential model Charging factors ◦ Capacitance ◦ Resistance I t

Charging of Capacitor

Time Constant

Discharging of Capacitor Current flow Initially ◦ High ◦ Opposite to charging Finally ◦ Zero Exponential model Discharging factors ◦ Capacitance ◦ Resistance I t

Discharging of Capacitor

Energy Stored in Capacitor

Current Voltage Relationship in Capacitor

Capacitors with Dielectrics A dielectric is a non conducting material, such as rubber, glass, or waxed paper. When a dielectric is inserted between the plates of a capacitor, the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance increases by a factor , which is called the dielectric constant. Dielectric constant is a property of a material and varies from one material to another.

Dielectric Strength For any given separation d, the maximum voltage that can be applied to a capacitor without causing a discharge depends on the dielectric strength (maximum electric field) of the dielectric. If magnitude of the electric field in the dielectric exceeds the dielectric strength, then the insulating properties break down and the dielectric begins to conduct.

Dielectric Constant and Dielectric Strength of Various Materials at Room Temperature Material Dielectric Constant  Dielectric Strength (V/m) Air (dry) x 10 6 Bakelite4.924 x 10 6 Fused quartz3.788 x 10 6 Neoprene rubber6.712 x 10 6 Nylon3.414 x 10 6 Paper3.716 x 10 6 Polystyrene x 10 6 Polyvinyl Chloride3.440 x 10 6 Porcelain612 x 10 6 Pyrex Glass5.614 x 10 6 Silicone Oil2.515 x 10 6 Strontium Titanate2338 x 10 6 Teflon2.160 x 10 6 Vacuum Water80-

Capacitors with Dielectric Material What are the advantages of dielectric material in a capacitor? Increase the capacitance Possible mechanical support between the plates, which allows the plates to be close together without touching, thereby decreasing d and increasing C.

Case Study Problems

Already we have calculated while deriving the mathematical relationship of capacitor