FOWLER CHAPTER 10 LECTURE 10 CAPACITANCE

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FOWLER CHAPTER 10LECTURE 10 CAPACITANCE
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CAPACITANCE THE STORING OF ENERGY AS ELECTRICAL
CHARGE.
CAPCITORS STORE ELECTRIC CHARGE. THEY ARE MADE
FROM 2 CONDUCTIVE PLATES SEPARATED BY A
INSULATOR.(DIELECTRIC)
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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 THAT CHARGED IT.
http//www.youtube.com/watch?vt9Qwx75eg8w
How a Capacitor Works - by Dr. Oliver Winn
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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.

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Charging And Discharging A Capacitor
http//micro.magnet.fsu.edu/electromag/java/capaci
tor/index.html
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MAKE presents The Capacitor
http//www.youtube.com/watch?vZYH9dGl4gUE
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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.
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ENERGY IS STORED IN THE DIELECTRIC BY STRESS
PLACED ON ELECTRONS IN THEIR ORBITAL PATHS.
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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
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UNIT OF CAPACITANCE P.247 CAPACITANCE IS
MEASURED IN FARADS. (F) 1 FARAD 1COULOMB/ 1
VOLT 1C/1V ONE 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)
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Capacitor Color Code Table
Color DigitA DigitB MultiplierD Tolerance(T) gt 10pf Tolerance(T) lt 10pf Temperature Coefficient(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 4 x10,000 4   -220x10-6
Green 5 5 x100,000 5 0.5pF -330x10-6
Blue 6 6 x1,000,000     -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
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Capacitor Voltage Color Code Table
Color Voltage Rating Voltage Rating Voltage Rating Voltage Rating Voltage Rating
Color 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.
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• Type L  -  Polyester/Polystyrene Capacitors.
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• Type M  -  Electrolytic 4 Band Capacitors.
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• Type N  -  Electrolytic 3 Band Capacitors.

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Capacitor Tolerance Letter Codes Table
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
  Letter B C D F G J K M Z
Tolerance C lt10pF pF 0.1 0.25 0.5 1 2        
Tolerance C gt10pF     0.5 1 2 5 10 20 80-20
CAP CODES SEE APPENDIX H
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FACTORS THAT DETERMINE THE CAPACITANCE OF A
CAPACITOR
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What factors determine the capacitance of a
capacitor?
1. Area of the plates
2. Distance between the plates
3. Type of dielectric
4. Temperature.
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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.
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TYPES OF CAPACITORS P.250
ELECTROLYTIC CAPACITORS
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ELECTROLYTIC (RADIAL LEAD)
ELECTROLYTIC (AXIAL LEAD)
http//www.youtube.com/watch?vYCSNWi3UHf4
Capacitor Replacement Tutorial
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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. ELECTROL
YTIC CAPACITORS ARE USED IN DC CIRCUITS ONLY.
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ELECTROLYTIC CAPACITOR CONSTRUCTION
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NONPOLARIZED CAPS USED IN AC CIRCUITS, ARE MADE
FROM TWO BACK TO BACK CAPACITORS OF OPPOSITE
POLARITY.
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TANTALUM, ALUMINUM CAPS ALUMINUM ARE THE MOST
COMMON, TANTALUM MORE EXPENSIVE, SMALLER, MORE
STABLE AND RELIABLE, HAVE LESS LEAKAGE CURRENT.
http//www.youtube.com/watch?v_ZBYbANWfWIlistUU
2bkHVIDjXS7sgrgjFtzOXQ
Tantalum Nutmeg of the West
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FILM AND PAPER CAPS USE 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
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TUBULAR CAPS CAPS PLACED INSIDE A TUBE, WHICH IS
INSULATED AND SEALED.
MICA CAPS MICA USED AS DIELECTRIC.
MOST COMMON STYLE IS DISC.
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CERAMIC CAPS MADE OF 2 PLATES SEPARATED BY A
CERAMIC DISC.
CAPACITANCE lt 0.1uF
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CAPACITORS CAN BE CLASSIFIED BY FUNCTION
VARIABLE CAPS PADDERS
TRIMMERS USED IN TUNING CIRCUITS
SUCH AS RADIO,TV
TUNING
OLD SCHOOL TUNING CAPACITORS
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VARIOUS STYLES OF TRIMMERS
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FEED THRU CAPACITORS USED AS BYPASS FILTER
CAPACITORS. ALLOWS D/C THRU, RADIO FREQUENCIES
ARE BYPASSED TO GROUND.
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STAND OFF CAPCITORS SIMILAR TO FEEDTHROUGH CAPS,
SAME FUNCTION.
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SMD( SURFACE MOUNT DEVICE) CAPCITORS ABOUT THE
SAME SIZE AS CHIP RESISTORS. AVAILABLE AS
CERAMIC, TANTALUM AND ELECTROLYTIC CAPS.
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FILTER CAPS MOST ARE ELECTROLYTIC, CAN BE USED AS
FILTERS IN POWER SUPPLIES TO FLATTEN OUT PULSES.
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http//www.youtube.com/watch?vTsKYWFr7VCw
Capacitor Replacement
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ENERGY STORAGE CAPCITORS STORE 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
VOLTAGE W IS IN JOULES EXAMPLE 10-3
P.255 HOW MUCH ENERGY CAN A CAP STORE RATED AT
300uF WITH 450V APPILED TO IT. W .5CV² W
.5(300uF)X(450V)² W 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!!!!!!
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HIGH CURRENT CAPACITOR
YOU TUBE High voltage capacitor bank vs.
watermelon
http//www.youtube.com/watch?vgj1pkyCL75E
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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.
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High voltage capacitor bank Used with
power  factor correction equipments, where large
blocks of three phase voltage are required.
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ULTRACAPACITORS
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
Fun with ultracapacitors!!
http//www.youtube.com/watch?vEoWMF3VkI6U
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SUPER CAPCITORS CAN STORE ENERGY UP T0 1000S 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 energyand work at very
close to 100 percent efficiency (97-98 percent is
typical).
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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.
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NANOCAPACITORS
The ultimate electronic energy-storage device
would store plenty of energy but also charge up
rapidly and provide powerful bursts when needed.
Sadly, todays 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.
nanowires
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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
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SCHEMATIC SYMBOLS
FIXED,POLARIZED
FIXED NONPOLARIZED
CURVED LINE SHOWS NEGETIVE PLATE
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CAPACITORS IN DC CIRCUITS WHEN THE SWITCH IS
CLOSED, A SURGE OF CURRENT OCCURS, CHARGING THE
CAPACITOR, THIS OCCURS IN A SHORT TIME PERIOD. AS
THE CAPACITOR CHARGES I DECREASES, VOLTAGE
INCREASES.
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RC TIME CONSTANT (T) T PRODUCE OF RESISTANCE X
CAPACITANCE IS CALLED THE TIME CONSTANT. T
RC RC OHMS X FARADS RC VOLT/AMPS X
COULUMBS/VOLT COULUMB/AMPERE
COULUMB/COULUMB/SEC SEC THE UNIT FOR
RC TIME CONSTANT IS SECONDS.
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RC Charging Circuit
WHEN A CAP IS CHARGING T IS THE TIME UNTIL CAP
REACHES 63.2 OF ITS SOURCE VOLTAGE, ITS FIRST
TIME CONSTANT.
RC Charging Curves
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RC Discharging Curves
RC Discharging Circuit
                                                          
WHEN A CAP IS DISCHARGING T IS THE TIME UNTIL
63.2 OF CAPCITANCE IS LOST.
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RC Time Constant -- Charge
100
of source voltage
0
0
1
2
5
3
4
Time constants
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.
The capacitor is essentially charged after 5 T.
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RC Time Constant -- Discharge
100
of capacitor voltage
36.8
13.5
5.0
1.8
0.7
0
0
1
2
5
3
4
Time constants
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.
The capacitor is essentially discharged after 5 T.
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Q
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WHEN A CAP IS CHARGING T TIME UNTIL CAP REACHES
63.2 OF SOURCE V WHEN 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 2MO X 4uF 8
SEC IF THE SOURCE VOLTAGE IS 10V THEN AFTER 1T
VOLTAGE CHARGE ON THE CAP WOULD BE 10V X 63.2
6.32V AFTER 2T VOLTAGE CHARGE ON THE CAP WOULD BE
10V X 86.5 8.65V ( DATA FROM GRAPH ON PREVIOUS
SLIDE)
8.65V
6.32V
2MO
10V
4uF
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DISCHARGING OF A CAPACITOR WHEN SWITCH IS CLOSED
CAPCITOR IS CHARGED TO 200V WHEN 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 126.4V AFTER 2TC
CAP. IS DISCHARGED TO 63.2 OF 200V .632 X
(200-126.4) 46.5V
200V
4uF
2MO
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CAPACITORS IN AC CIRCUITS
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CAPACITIVE REACTANCE IS 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 CURRENT 2.THE
AMOUNT OF CAPACITANCE Xc IS INVERSAL
PROPORTIONAL TO CURRENT AND CAPACITANCE. Xc 1/
2?fC 1/6.28fC OHMS LAW FOR Xc Vc IcXc
REACTANCE CANT BE MEASURED WITH A OHMMETER.
http//www.youtube.com/watch?vjeTUWIUQAXo
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QUALITY OF CAPACITORS P.263 IDEALLY 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.
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ENERGY LOSSES IN CAPACITORS. OCCURS FROM 3
SOURCES P.264,F. 10-28
DIELECTRIC RESISTANCE
DIELECTRIC FIELD LOSS
PLATE AND LEAD RESISTANCE
THESE 3 LOSSES COMBINED IS CALLED SERIES
EQUIVALENT RESISTANCE (ESR) CAPACITORS WITH LOW
ESR HAVE LESS ENERGY LOST. THESE RESISTANCES
CONVERT ELECTRIC ENERGY INTO HEAT ENERGY.
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CAPACITORS IN SERIES
WHEN CAPACITORS ARE IN SERIES, TOTAL CAPACITANCE
IS ALWAYS LESS THEN THE CAPACITANCE OF THE
SMALLEST CAPACITOR. WHY?
FIRST CAPACITOR
SECOND CAPACITOR
IF 2 CAPS ARE IN SERIES, THEIR COMBINED
DIELECTRIC MATERIAL INCREASES THE DISTANCE
BETWEEN THE PLATES WHICH DECREASES THE
CAPACITANCE OF THE TWO.
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CAPACITORS IN SERIES Ct 1/(1/C1 1/C2 1/C3
.. 1/Cn )
FOR 2 CAPACITORS IN SERIES Ct C1 X C2/ (C1 C2)
C1
SAME FORMUALS AS RESISTORS IN PARALLEL.
FOR n EQUAL CAPS IN SERIES

C2
TOTAL CAP REACTANCE
C3
OHMS LAW FOR CAPACITORS Vc IT X Xc
TOTAL CURRENT
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.
SEE EX 10-6 AND 10-8 p.266
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VOLTAGE DISTRIBUTION WITH CAPCITORS
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
2uF
V
33.3V

VC1 C2/(C1 C2) X VT 1uF/(1uF 2uF)
X100V 66.7V
100V
-
1uF
66.7V
V

VC1 C1/(C1 C2) X VT 2uF/(1uF 2uF)
X100V 33.3V
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CAPACITORS IN PARALLEL P.267 FOR CAPACITORS IN
PARALLEL CAPACITANCE IS ADDITIVE. WHY? THE
EFFECTIVE AREA OF TWO CAPACITORS IN PARALLEL ADD
TOGETHER AND INCREASE THE SURFACE AND DIELECTRIC
AREA OF THE PLATES.
FIRST CAPACITOR
COMBINED CAPACITORS
SECOND CAPACITOR
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C1
C2
C3

TOTAL CAPACITIVE REACTANCE
The total reactance of two capacitors in parallel
can also be found by applying the
product-over-sum formula 
FOR n EQUAL REACTANCES
TOTAL REACTANCE CAN ALSO BE FOUND FROM XcT
1/6.28fCT OR OHMS LAW XcT VT/ IT EX. 10-9
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http//www.youtube.com/watch?v8xONZcBJh5A
"It's not the volts that kill you, it's the amps"
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FOR n EQUAL CAPS IN SERIES
CAPACITORS IN SERIES
C1
FOR 2 CAPS IN SERIES

V
C2
SAME FORMUALS AS RESISTORS IN PARALLEL.
TOTAL CAPACITIVE REACTANCE
C3
OHMS LAW FOR CAPACITORS
TOTAL CURRENT
IN SERIES CIRCUITS, THE LARGEST CAPACITOR DROPS
THE LEAST VOLTAGE.
__________________________________________________
___________________________________________
CAPACITORS IN PARALLEL
TOTAL CAPACITIVE REACTANCE
FOR 2 CAPACITORS
V
C1
C2
C3

FOR n EQUAL CAPACITIVE REACTANCES IN PARALLEL
OR