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FOWLER CHAPTER 10
LECTURE 10 CAPACITANCE
CAPACITANCE
THE STORING OF ENERGY AS ELECTRICAL CHARGE.
CAPCITORS STORE ELECTRIC CHARGE.
THEY ARE MADE FROM 2 CONDUCTIVE PLATES
SEPARATED 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 THAT
CHARGED IT.
How a Capacitor Works - by Dr. Oliver Winn
http://www.youtube.com/watch?v=t9Qwx75eg8w
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.
+
-
Charging And Discharging A Capacitor
http://micro.magnet.fsu.edu/electromag/java/capacitor/index.html
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/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)
Capacitor Color Code Table
Metalized Polyester Capacitors
Tolera
nce
(T) > 1
0pf
Tolera
nce
(T) < 1
0pf
Tempe
rature
Coeffic
ient
(TC)
Color
Digit
A
Digit
B
Multipli
er
D
Black
0
0
x1
± 20%
± 2.0pF
Brown
1
1
x10
± 1%
± 0.1pF
-33x10-
Red
2
2
x100
± 2%
±
0.25pF
-75x10-
Orange
3
3
x1,000
± 3%
6
6
150x10
-6
Disc & Ceramic Capacitors
Yellow
Green
Blue
Violet
4
5
6
7
4
5
6
x10,00
0
± 4%
x100,0
00
± 5%
220x10
-6
± 0.5pF
330x10
-6
470x10
x1,000,
000
-6
750x10
7
-6
Grey
8
8
x0.01
+80%,20%
White
9
9
x0.1
± 10%
Gold
x0.1
± 5%
Silver
x0.01
± 10%
± 1.0pF
Capacitor Voltage Color Code Table
Voltage Rating
Color
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.
Type J
Type K
Black
4
100
Brown
6
200
100
1.6
Red
10
300
250
4
Orange
15
400
Yellow
20
500
Green
25
600
Blue
35
700
Violet
50
800
Grey
White
Gold
Silver
3
Type L
Type M
Type N
10
10
35
40
400
6.3
6
16
15
630
20
900
25
25
1000
2.5
3
2000
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
C <10pF ±pF
0.1
0.2
5
0.5
1
2
0.5
1
2
Tolerance
C >10pF ±%
CAP CODES SEE APPENDIX H
J
K
M
Z
5
10
20
+8020
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
R
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.
TYPES OF CAPACITORS P.250
ELECTROLYTIC CAPACITORS
ELECTROLYTIC (RADIAL LEAD)
ELECTROLYTIC (AXIAL LEAD)
Capacitor Replacement Tutorial
http://www.youtube.com/watch?v=YCSNWi3UHf4
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 CAPS
ALUMINUM ARE THE MOST COMMON, TANTALUM MORE EXPENSIVE, SMALLER, MORE
STABLE AND RELIABLE, HAVE LESS LEAKAGE CURRENT.
Tantalum: Nutmeg of the West
http://www.youtube.com/watch?v=_ZBYbANWfWI&list=UU2bkHVIDjXS7sgrgjFtzOXQ
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
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
TUNING
USED IN TUNING CIRCUITS SUCH AS RADIO,TV
OLD SCHOOL TUNING CAPACITORS
VARIOUS STYLES OF TRIMMERS
FEED THRU CAPACITORS
USED 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) CAPCITORS
ABOUT THE SAME SIZE AS CHIP RESISTORS.
AVAILABLE AS CERAMIC, TANTALUM AND ELECTROLYTIC CAPS.
FILTER CAPS
MOST ARE ELECTROLYTIC, CAN BE USED AS FILTERS IN
POWER SUPPLIES TO FLATTEN OUT PULSES.
Capacitor Replacement
http://www.youtube.com/watch?v=TsKYWFr7VCw
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!!!!!!
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.
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?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.
NANOCAPACITORS
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.
nanowires
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.
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, CHARGING
THE 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 =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.
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
RC Discharging Curves
RC Discharging Circuit
WHEN A CAP IS DISCHARGING T IS THE
TIME UNTIL 63.2% OF CAPCITANCE IS LOST.
RC Time Constant -- Charge
% of source voltage
100
0
0
1
2
3
Time constants
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.
The capacitor is essentially charged after 5 T.
RC Time Constant -- Discharge
% of capacitor voltage
100
0
36.8%
13.5%
0
1
5.0%
2
3
Time constants
1.8%
4
0.7%
5
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.
Q
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 = 2MΩ 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
2MΩ
10V
4uF
6.32V
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
2MΩ
CAPACITORS IN AC CIRCUITS
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/ 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.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.
ENERGY LOSSES IN CAPACITORS.
OCCURS FROM 3 SOURCES P.264,F. 10-28
DIELECTRIC RESISTANCE
PLATE AND LEAD 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 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.
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
TOTAL CAP
REACTANCE
CN 
C
n
X CT  X C1  X C2  X C3  X C N
OHM’S LAW FOR CAPACITORS
TOTAL CURRENT :
~
Vc = IT X Xc
I CT  I C1  I C2  I C3
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
C2
C3
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.
2uF
V
+
FOR THESE 2 CAPS IN SERIES
33.3V
VC1 = C2/(C1 + C2) X VT
= 1uF/(1uF+ 2uF) X100V = 66.7V
100V
1uF
V
+
66.7V
VC1 = C1/(C1 + C2) X VT
= 2uF/(1uF+ 2uF) X100V = 33.3V
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
C1
~
TOTAL CAPACITIVE REACTANCE
X CT 
1
1
1
1
1



X C1 X C2 X C 3 X C N
The total reactance of two capacitors in parallel can also be
found by applying the product-over-sum formula:
X CT 
X C1  X C2
X C1  X C2
FOR n EQUAL REACTANCES
X CT
XC

n
TOTAL REACTANCE CAN ALSO BE FOUND FROM :
XcT = 1/6.28fCT OR OHM’S LAW XcT = VT/ IT
EX. 10-9
C2
C3
"It's not the volts that kill you, it's the amps"
http://www.youtube.com/watch?v=8xONZcBJh5A
CT 
CAPACITORS IN SERIES
FOR 2 CAPS IN SERIES
1
1
1
1
1



C1 C2 C3 C N
FOR n EQUAL CAPS IN SERIES
C1  C2
C1  C2
CT 
C1
C
CN 
n
V
SAME FORMUALS AS RESISTORS IN PARALLEL.
X CT  X C1  X C2  X C3  X C N
TOTAL CAPACITIVE REACTANCE
C2
C3
VC  IT  X C
OHM’S LAW FOR CAPACITORS
TOTAL CURRENT
~
I CT  I C1  I C2  I C3
IN SERIES CIRCUITS, THE LARGEST CAPACITOR DROPS THE LEAST VOLTAGE.
_____________________________________________________________________________________________
CT  C1  C2  C3  Cn
CAPACITORS IN PARALLEL
TOTAL CAPACITIVE REACTANCE
FOR 2 CAPACITORS
X CT 
FOR n EQUAL CAPACITIVE
REACTANCES IN PARALLEL
OR
X CT 
X C1  X C2
1
1
1
1



X C1 X C2 X C 3 X C N
X C1  X C2
X CT 
X CT 
I CT  I C1  I C2  I C3  I C N
1
XC
n
1
6.28  f  C
V
~
C1
C2
C3