FOWLER CHAPTER 10LECTURE 10 CAPACITANCE

CAPACITANCETHE STORING OF ENERGY AS ELECTRICAL CHARGE.

CAPCITORS STORE ELECTRIC CHARGE.THEY ARE MADE FROM 2 CONDUCTIVE PLATESSEPARATED BY A INSULATOR.(DIELECTRIC)

HOW DOES A CAPACITOR WORK? (See figure below)AS BATTERY DISCHARGES, ONE OF THE CAPCITOR PLATES BUILDS UP A NEG. CHARGE WHILE A DIFFICIENCY OF CHARGE BUILDS UP ON THE OTHER PLATE.( POS. CHARGE).WHILE THE CAP IS CHARGING NO ELECTRONS MOVE FROM ONE PLATE TO THE OTHER.WHEN THE CAP IS FULLY CHARGED, ITS VOLTAGE IS EQUAL TO THE BATTERY VOLTAGE THATCHARGED IT.

http://www.youtube.com/watch?v=t9Qwx75eg8wHow a Capacitor Works - by Dr. Oliver Winn

+

-

+

-

+

-

THIS CHARGED CAPACITOR(THE ENERGY SOURCE)CAN BE REMOVED FROM THE CHARGING CIRCUIT

IF A LOAD IS PLACED ACROSS IT, THE CAPACITOR WILL RAPIDLY DISCHARGE.

http://micro.magnet.fsu.edu/electromag/java/capacitor/index.html

Charging And Discharging A Capacitor

MAKE presents: The Capacitor http://www.youtube.com/watch?v=ZYH9dGl4gUE

WHY ARE CAPACITORS NOT USED AS ENERGY SOURCES? 1. THEY HOLD A SMALL AMOUNT OF CHAGRE AS COMPARED TO A BATTERY OF SIMILAR WEIGHT. 2. THEIR VOLTAGE RAPIDLY DECREASES AS THE CAPACITOR IS DISCHARGED THRU A LOAD.

ENERGY IS STORED IN THE DIELECTRIC BY STRESS PLACED ON ELECTRONS IN THEIR ORBITAL PATHS.

VOLTAGE RATING OF CAPACITORS.DCWV: DIRECT CURRENT VOLTAGE RATING, RATED MAXINIUM VOLTAGE THAT A CAPACITOR CAN OPERATOR AT WITHOUT BREAKING DOWN.

YOU TUBE: Capacitor explosion from excessive voltage http://www.youtube.com/watch?v=_WheLp0RdLQ

UNIT OF CAPACITANCE P.247

CAPACITANCE IS MEASURED IN FARADS. (F)

1 FARAD = 1COULOMB/ 1 VOLT = 1C/1VONE FARAD IS THE AMOUNT OF CAPACITANCE THAT STORES 1 COULOMB (Q)OF CHARGE WHEN THE CAP IS CHARGED TO 1 VOLT.

C = Q/V

CAPACITANCE (C) IS USUALLY MEASURED IN MICROFARADS ( uF)

Capacitor Color Code Table

ColorDigit

ADigit

B

MultiplierD

Tolerance

(T) > 10pf

Tolerance

(T) < 10pf

Temperature Coeffic

ient(TC)

Black 0 0 x1 ± 20% ± 2.0pF  

Brown 1 1 x10 ± 1% ± 0.1pF-33x10-

6

Red 2 2 x100 ± 2%±

0.25pF-75x10-

6

Orange 3 3 x1,000 ± 3%  -

150x10-

6

Yellow 4 4x10,00

0± 4%  

-220x10-

6

Green 5 5x100,0

00± 5% ± 0.5pF

-330x10-

6

Blue 6 6x1,000,

000   

-470x10-

6

Violet 7 7      -

750x10-

6

Grey 8 8 x0.01+80%,-

20%   

White 9 9 x0.1 ± 10% ± 1.0pF  

Gold     x0.1 ± 5%    

Silver     x0.01 ± 10%    

Metalized Polyester Capacitors

Disc & Ceramic Capacitors

Capacitor Voltage Color Code Table

Color

Voltage Rating

Type J Type K Type L Type M Type N

Black 4 100   10 10

Brown 6 200 100 1.6  

Red 10 300 250 4 35

Orange 15 400   40  

Yellow 20 500 400 6.3 6

Green 25 600   16 15

Blue 35 700 630   20

Violet 50 800      

Grey   900   25 25

White 3 1000   2.5 3

Gold   2000      

Silver          

Capacitor Voltage Reference•Type J  -  Dipped Tantalum Capacitors. •  •Type K  -  Mica Capacitors. •  •Type L  -  Polyester/Polystyrene Capacitors. •  •Type M  -  Electrolytic 4 Band Capacitors. •  •Type N  -  Electrolytic 3 Band Capacitors.

Capacitor Tolerance Letter Codes Table

  Letter B C D F G J K M Z

Tolerance

C <10pF ±pF 0.10.25

0.5 1 2        

C >10pF ±%     0.5 1 2 5 10 20+80-20

Consider the capacitor below:

           

               

The capacitor on the left is of a ceramic disc type capacitor that has the code 473J printed onto its body. Then the 4 = 1st digit, the 7 = 2nd digit,the 3 is the multiplier in pico-Farads, pF and the letter J is the tolerance and this translates to:

   47pF * 1,000 (3 zero's) = 47,000 pF , 47nF or 0.047 uF   the J indicates a tolerance of +/- 5%

CAP CODES SEE APPENDIX H

FACTORS THAT DETERMINE THE CAPACITANCE OF A CAPACITOR

What factors determine the capacitance of a capacitor?

1. Area of the plates

2. Distance between the plates

3. Type of dielectric

4. Temperature.

1. AREA OF THE PLATES: CAPACITANCE IS DIRECTLY PROPORTIONAL TO THE AREA OF THE PLATES. DOUBLE THE AREA , DOUBLES THE CAPACITANCE. WHY? THE AREA OF DIELECTRIC. IS DOUBLED.

2. DISTANCE BETWEEN PLATES: CAPACITANCE IS INVERSELY PROPORTIONAL TO THE DISTANCE BETWEEN THE PLATES. AS DISTANCE INCREASES, CAPACITANCE DECREASES.

3. TYPE OF DIELECTRIC: AIR, PAPER, MICA. DEPENDS ON VALUE OF K THE DIELECTRIC CONSTANT (K) : IS ABILITY OF A DIELECTRIC MATERIAL TO DISTORT AND STORE ENERGY. ALSO CAN BE EXPRESSED AS K HAS NO UNITS. THE LARGER K IS, THE LARGER THE CAPACITANCE. K FOR SOME COMMONLY USED MATERIALS; AIR = 1 MICA ≈ 5 CERAMICS ≈ 4000

4. TEMPERATURE, LEAST INPORTANT FACTOR, CRITICAL IN APPLICATIONS SUCH AS OSCILLATOR CIRCUITS.

SOME + OR – TEMPERATURE COEFFICIENTS CAN INCREASE CAPACITANCE. + TEMP. COEFFICIENTS (P) CAUSES K TO INCREASE AS TEMP. INCREASES.

- TEMP. COEFFICIENTS (N) CAUSES K TO INCREASE AS TEMP. DECREASES. 0 TEMP. COEFFICIENTS (NPO) TEMP. HAS NO EFFECT ON K. TEMP. COEFFICIENTS ARE GIVEN IN PPM/Cº CAPACITORS ARE RATED AT 25º C.

R

TYPES OF CAPACITORS P.250

ELECTROLYTIC CAPACITORS

ELECTROLYTIC (RADIAL LEAD)

ELECTROLYTIC (AXIAL LEAD)

http://www.youtube.com/watch?v=YCSNWi3UHf4Capacitor Replacement Tutorial

ELECTROLYTIC CAPACITORS ARE MADE FROM ALTERNATING + AND – ALUMINIUM PLATES SEPARATED BY AN ELECTROLYTE AND DIELECTRIC. LARGE PLATE AREA AND THIN DIELECTRIC MAKE THE CAPACITANCE OF ELECTROLYTIC CAPACITORS HIGH FOR THEIR SIZE AND WEIGHT.A SMALL LEAKAGE CURRENT OCCURS FROM ONE PLATE TO THE OTHER THRU THE DIELECTRIC.ELECTROLYTIC CAPACITORS ARE USED IN DC CIRCUITS ONLY.

ELECTROLYTIC CAPACITOR CONSTRUCTION

NONPOLARIZED CAPS: USED IN AC CIRCUITS, ARE MADE FROM TWO BACK TO BACK CAPACITORS OF OPPOSITE POLARITY.

TANTALUM, ALUMINUM CAPSALUMINUM ARE THE MOST COMMON, TANTALUM MORE EXPENSIVE, SMALLER, MORE STABLE AND RELIABLE, HAVE LESS LEAKAGE CURRENT.

http://www.youtube.com/watch?v=_ZBYbANWfWI&list=UU2bkHVIDjXS7sgrgjFtzOXQTantalum: Nutmeg of the West

FILM AND PAPER CAPSUSE PAPER OR PLASTIC FILM AS DIELECTRIC.CONSTRUCTED USING ROLLS OF FOIL AND DIELECTRIC. COVERED WITH INSULATION. RANGE UP TO SEVERAL 100 Uf.RATED IN VA OR DCWV. MOLDED CAPS : INSULATION MOLDED AROUND CAP.

DIPPED CAPS: DIPPED IN PLASTIC INSULATION

TUBULAR CAPS: CAPS PLACED INSIDE A TUBE, WHICH IS INSULATED AND SEALED.

MICA CAPS: MICA USED AS DIELECTRIC. MOST COMMON STYLE IS DISC.

CERAMIC CAPS: MADE OF 2 PLATES SEPARATED BY A CERAMIC DISC. CAPACITANCE < 0.1uF

CAPACITORS CAN BE CLASSIFIED BY FUNCTION

VARIABLE CAPS : PADDERS TRIMMERS USED IN TUNING CIRCUITS SUCH AS RADIO,TV TUNING

OLD SCHOOL TUNING CAPACITORS

VARIOUS STYLES OF TRIMMERS

FEED THRU CAPACITORSUSED AS BYPASS FILTER CAPACITORS. ALLOWS D/C THRU, RADIO FREQUENCIES ARE BYPASSED TO GROUND.

STAND OFF CAPCITORS: SIMILAR TO FEEDTHROUGH CAPS, SAME FUNCTION.

SMD( SURFACE MOUNT DEVICE) CAPCITORSABOUT THE SAME SIZE AS CHIP RESISTORS.AVAILABLE AS CERAMIC, TANTALUM AND ELECTROLYTIC CAPS.

FILTER CAPSMOST ARE ELECTROLYTIC, CAN BE USED AS FILTERS IN POWER SUPPLIES TO FLATTEN OUT PULSES.

http://www.youtube.com/watch?v=TsKYWFr7VCwCapacitor Replacement

ENERGY STORAGE CAPCITORSSTORE ENERGY FOR VARIOUS USES, CAN PRODUCE LARGE AMOUNTS OF POWER WHEN DISCHARGED IN A SHORT TIME PERIOD. THESE CAPS MUST BE BUILT TO WITHSTAND LARGE ENERGY DISCHARGES.ARE RATED BY CURRENT AND ENERGY CAPACITITES.

ENERGY STORED IN A CAP IS FOUND BY;

W =0.5CV² = 0.5 XCAPACITANCE X VOLTAGE X VOLTAGEW : IS IN JOULES

EXAMPLE 10-3 P.255HOW MUCH ENERGY CAN A CAP STORE RATED AT 300uF WITH 450V APPILED TO IT.

W = .5CV²W = .5(300uF)X(450V)²W = 30.4J NOT A LOT OF ENERGY PRODUCED.BUT IF THIS CAP IS DISCHARGED IN A SHORT TIME PERIOD. SAY 2ms

(REMEMBER P = W/t =JOULE/ SEC = WATT)

P = W/t = 30.4J/0.002SEC = 15,200 W = 15.2KW!!!!!!

HIGH CURRENT CAPACITOR

YOU TUBE: High voltage capacitor bank vs. watermelon http://www.youtube.com/watch?v=gj1pkyCL75E

Example of a improved capacitors able to store twice as much energy as conventional devices. This improved capacitors could be used in consumer devices such as cellular telephones – and in defense applications requiring both high energy storage and rapid current discharge.

High voltage capacitor bank: Used with power  factor correction equipments, where large blocks of three phase voltage are required.

In ultracapacitors, the electrode is based on a carbon technology, which allows for a very large surface area. The combination of this surface area along with a very small charge separation gives the ultracapacitors the high energy density they possess. Most ultracapacitors are rated in farads and typically can be found in the 1F to 5,000F

ULTRACAPACITORS

Fun with ultracapacitors!! http://www.youtube.com/watch?v=EoWMF3VkI6U

SUPER CAPCITORS CAN STORE ENERGY UP T0 1000’S OF FARADS.

Supercapacitors store more energy than ordinary capacitors by creating a double layer of separated charges between two plates made from porous, typically carbon-based materials. The plates create the double-layer by polarizing the electrolyte (yellow) in between them.

Since supercapacitors work electrostatically, rather than through reversible chemical reactions, they can theoretically be charged and discharged any number of times (perhaps a million times). They have little or no internal resistance, which means they store and release energy without using much energy—and work at very close to 100 percent efficiency (97-98 percent is typical).

Supercapacitors can sometimes used as a direct replacement for batteries. Here's a cordless drill powered by a bank of supercapacitors for use in space, developed by NASA. The big advantage over a normal drill is that it can be charged up in seconds rather than hours.

The ultimate electronic energy-storage device would store plenty of energy but also charge up rapidly and provide powerful bursts when needed. Sadly, today’s devices can only do one or the other: capacitors provide high power, while batteries offer high storage.

Now researchers at the University of Maryland have developed a kind of capacitor that brings these qualities together. The research is in its early stages, and the device will have to be scaled up to be practical, but initial results show that it can store 100 times more energy than previous devices of its kind. Ultimately, such devices could store surges of energy from renewable sources, like wind, and feed that energy to the electrical grid when needed. They could also power electric cars that recharge in the amount of time that it takes to fill a gas tank, instead of the six to eight hours that it takes them to recharge today.

NANOCAPACITORS

nanowires

The nanocapacitor takes advantage of self-assembly. It also uses self-alignment. The nanocapacitor can only take advantage of these physical properties because the individual components are so small and placed so close together. Pores 50 nanometers in diameter and 30 nanometers deep are etched into a glass plate covered with aluminum with 25 nanometer spacing

SCHEMATIC SYMBOLS

FIXED NONPOLARIZED FIXED,POLARIZED

CURVED LINE SHOWS NEGETIVE PLATE

CAPACITORS IN DC CIRCUITS

WHEN THE SWITCH IS CLOSED, A SURGE OF CURRENT OCCURS, CHARGINGTHE CAPACITOR, THIS OCCURS IN A SHORT TIME PERIOD.AS THE CAPACITOR CHARGES I DECREASES, VOLTAGE INCREASES.

RC TIME CONSTANT (T)

T = PRODUCE OF RESISTANCE X CAPACITANCE IS CALLED THE TIME CONSTANT.

T =RCRC = OHMS X FARADSRC = VOLT/AMPS X COULUMBS/VOLT =COULUMB/AMPERE = COULUMB/COULUMB/SEC = SEC : THE UNIT FOR RC TIME CONSTANT IS SECONDS.

WHEN A CAP IS CHARGING T IS THE TIME UNTIL CAP REACHES 63.2% OF ITS SOURCE VOLTAGE, ITS FIRST TIME CONSTANT.

RC Charging Circuit

RC Charging Curves

RC Discharging Circuit

                                    

                      

RC Discharging Curves

WHEN A CAP IS DISCHARGING T IS THE TIME UNTIL 63.2% OF CAPCITANCE IS LOST.

Time constants0 1 2 3 4 5

After 2 T, the capacitor is 86.5 % charged.

After 3 T, the capacitor is 95.0 % charged.After 4 T, the capacitor is 98.2 % charged.

After 5 T, the capacitor is 99.3 % charged.

RC Time Constant -- Charge100

0

% o

f so

urc

e vo

ltag

e

The capacitor is essentially charged after 5 T.

After 1 T, the capacitor is 63.2 % discharged. After 2 T, the capacitor is 86.5 % discharged.

After 3 T, the capacitor is 95.0 % discharged.After 4 T, the capacitor is 98.2 % discharged.

After 5 T, the capacitor is 99.3 % discharged.

Time constants0 1 2 3 4 5

100

0

% o

f ca

pac

itor

vol

tage

36.8%

13.5%5.0% 1.8% 0.7%

The capacitor is essentially discharged after 5 T.

RC Time Constant -- Discharge

Q

WHEN A CAP IS CHARGING T = TIME UNTIL CAP REACHES 63.2% OF SOURCE VWHEN A CAP IS DISCHARGING T = TIME UNTIL 63.2% OF CAPACITOR V IS LOST.

EXAMPLE F 10-21 P.259 WHAT IS T FOR THE CAP CHARGING IN THIS CIRCUIT?

T = RC = 2MΩ X 4uF = 8 SECIF THE SOURCE VOLTAGE IS 10V THEN;AFTER 1T VOLTAGE CHARGE ON THE CAP WOULD BE 10V X 63.2% = 6.32VAFTER 2T VOLTAGE CHARGE ON THE CAP WOULD BE 10V X 86.5% = 8.65V( DATA FROM GRAPH ON PREVIOUS SLIDE)

2MΩ

4uF

6.32V

8.65V

10V

200V 4uF 2MΩ

DISCHARGING OF A CAPACITORWHEN SWITCH IS CLOSED CAPCITOR IS CHARGED TO 200VWHEN SWITCH IS OPENED CAPACITOR IS DISCHARGED THRU THE RESISTOR.TC IS STLL 8 SEC. USE SAME VALUES FOR R AND C FROM PERVIOUS EXAMPLE.

AFTER 1TC CAP. IS DISCHARGED TO 63.2% OF 200V.632 X 200V = 126.4VAFTER 2TC CAP. IS DISCHARGED TO 63.2% OF 200V.632 X (200-126.4) =46.5V

CAPACITORS IN AC CIRCUITS

CAPACITIVE REACTANCEIS THE CAPACITORS OPPOSITION TO A/C, SOMETHING LIKE RESISTANCE.SYMBOL: Xc, UNIT IS THE OHM.

REACTANCE DOES NOT CONVERT ELECTRICAL ENERGY INTO HEAT.Xc IS CONTROLLED BY 2 FACTORS.1.FREQUENCY OF THE CURRENT2.THE AMOUNT OF CAPACITANCE

Xc IS INVERSAL PROPORTIONAL TO CURRENT AND CAPACITANCE.

Xc = 1/ 2пfC = 1/6.28fC

OHM’S LAW FOR Xc: Vc =IcXc

REACTANCE CAN’T BE MEASURED WITH A OHMMETER.

http://www.youtube.com/watch?v=jeTUWIUQAXo

QUALITY OF CAPACITORS P.263IDEALLY CAPACITORS PROVIDE REACTANCE SO CURRENT CAN BE CONTROLLED W/O CONVERTING ELECTRICAL ENERGY INTO HEAT.QUALITY IS THE ABILITY OF A CAPACITOR TO PRODUCE REACTANCE WITH AS LITTLE RESISTANCE AS POSSIBLE.

Q = Xc/R, THIS IS A PURE NUMBER, Q HAS NO UNITS.

IN A CIRCUIT WITH ONLY CAPACITANCE.1. I AND V ARE 90º OUT OF PHASE.2. CIRCUIT USES NO NET ENERGY OR POWER.

ENERGY LOSSES IN CAPACITORS.

OCCURS FROM 3 SOURCES P.264,F. 10-28

PLATE AND LEAD RESISTANCE

DIELECTRIC RESISTANCE

DIELECTRIC FIELD LOSS

THESE 3 LOSSES COMBINED IS CALLED SERIES EQUIVALENT RESISTANCE (ESR)CAPACITORS WITH LOW ESR HAVE LESS ENERGY LOST.THESE RESISTANCE’S CONVERT ELECTRIC ENERGY INTO HEAT ENERGY.

CAPACITORS IN SERIES

WHEN CAPACITORS ARE IN SERIES, TOTAL CAPACITANCE IS ALWAYS LESS THEN THECAPACITANCE OF THE SMALLEST CAPACITOR. WHY?

IF 2 CAPS ARE IN SERIES, THEIR COMBINED DIELECTRIC MATERIAL INCREASESTHE DISTANCE BETWEEN THE PLATES WHICH DECREASES THE CAPACITANCEOF THE TWO.

FIRST CAPACITOR

SECOND CAPACITOR

CAPACITORS IN SERIESCt= 1/(1/C1 + 1/C2 + 1/C3+ …..+ 1/Cn )

C1

C2

C3

~

FOR 2 CAPACITORS IN SERIESCt = C1 X C2/ (C1 + C2)

FOR n EQUAL CAPS IN SERIES

SAME FORMUALS AS RESISTORS IN PARALLEL.

OHM’S LAW FOR CAPACITORS Vc = IT X Xc

TOTAL CURRENT :

SEE EX 10-6 AND 10-8 p.266

IN SERIES CIRCUITS, THE LARGEST CAPACITOR DROPS THE LEAST VOLTAGE.CAPACITORS CAN BE USED AS AC VOLTAGE DIVIDERS.WHY USE CAPS INSTEAD OF RESISTORS? CAPACITORS USE ZERO POWER.

321 CCCC IIIIT

n

CCN

NT CCCCC XXXXX 321

TOTAL CAPREACTANCE

VOLTAGE DISTRIBUTION WITH CAPCITORS

100V

2uF

1uF

V

V

33.3V

66.7V

-

-

+

+

HOW DO YOU SOLVE FOR VOLTAGE DROPS WITH CAPACITORS IN SERIES CIRCUITS.

REMEMBER C = Q/V OR V =Q/C, AS C INCREASES, V DECREASES.

VC IS INVERSLY PROPORTIONAL C.

FOR THESE 2 CAPS IN SERIES

VC1 = C2/(C1 + C2) X VT

= 1uF/(1uF+ 2uF) X100V = 66.7V

VC1 = C1/(C1 + C2) X VT

= 2uF/(1uF+ 2uF) X100V = 33.3V

CAPACITORS IN PARALLEL P.267FOR CAPACITORS IN PARALLEL CAPACITANCE IS ADDITIVE. WHY?THE EFFECTIVE AREA OF TWO CAPACITORS IN PARALLEL ADD TOGETHER AND INCREASETHE SURFACE AND DIELECTRIC AREA OF THE PLATES.

FIRST CAPACITOR

SECOND CAPACITOR

COMBINED CAPACITORS

The total reactance of two capacitors in parallel can also be found by applying the product-over-sum formula: 

TOTAL CAPACITIVE REACTANCE

FOR n EQUAL REACTANCES

TOTAL REACTANCE CAN ALSO BE FOUND FROM :

XcT = 1/6.28fCT OR OHM’S LAW XcT = VT/ ITEX. 10-9

~C1 C2 C3

N

T

CCCC

C

XXXX

X1111

1

321

21

21

CC

CCC XX

XXX

T

n

XX CCT

"It's not the volts that kill you, it's the amps" http://www.youtube.com/watch?v=8xONZcBJh5A

CAPACITORS IN SERIESC1

C2

C3

~FOR 2 CAPS IN SERIES

FOR n EQUAL CAPS IN SERIES

SAME FORMUALS AS RESISTORS IN PARALLEL.

OHM’S LAW FOR CAPACITORS

IN SERIES CIRCUITS, THE LARGEST CAPACITOR DROPS THE LEAST VOLTAGE.

N

T

CCCC

C1111

1

321

21

21

CC

CCCT

n

CCN

TOTAL CAPACITIVE REACTANCENT CCCCC XXXXX

321

CTC XIV

321 CCCC IIIIT

TOTAL CURRENT

CAPACITORS IN PARALLEL nT CCCCC 321

TOTAL CAPACITIVE REACTANCE

N

T

CCCC

C

XXXX

X1111

1

321

21

21

CC

CCC XX

XXX

T

FOR 2 CAPACITORS

FOR n EQUAL CAPACITIVE REACTANCES IN PARALLEL

n

XX CCT

CfX

TC

28.6

1OR

C1 C2 C3~

V

V

NT CCCCC IIIII 321

_____________________________________________________________________________________________