EEE

1. Amiraj collage of engineering andAmiraj collage of engineering and
technologytechnology
ELEMENT OF ELECTRICALELEMENT OF ELECTRICAL
ENGINEERINGENGINEERING
TOPIC -series and parallel connection ofTOPIC -series and parallel connection of
capacitercapaciter
YEAR-(2015-2016)YEAR-(2015-2016)
Prepered by-Prepered by-
Bhavya h. sanghaviBhavya h. sanghavi
E.no.-151080106024 Guided by-AnkurE.no.-151080106024 Guided by-Ankur

2. Objectives:Objectives: After completing thisAfter completing this
module, you should be able to:module, you should be able to:
• Calculate the equivalent capacitance of a
number of capacitors connected in series
or in parallel.
• Determine the charge and voltage across
any chosen capacitor in a network when
given capacitances and the externally
applied potential difference.

3. Electrical Circuit SymbolsElectrical Circuit Symbols
Electrical circuitsElectrical circuits often contain two or moreoften contain two or more
capacitors grouped together and attachedcapacitors grouped together and attached
to an energy source, such as a battery.to an energy source, such as a battery.
The following symbols are often used:The following symbols are often used:
+
Capacitor
+
-
-+ - + -
- + - + -
Ground Battery
-+

4. Series CircuitsSeries Circuits
Capacitors or other devices connectedCapacitors or other devices connected
along a single path are said to bealong a single path are said to be
connected inconnected in seriesseries. See circuit below:. See circuit below:
Series
connection of
capacitors. “+ to
– to + …”
Charge inside
dots is induced.
Battery
C1 C2
C3
+
+
-
-
+
+
+
+
-
-
-
-

5. Charge on Capacitors in SeriesCharge on Capacitors in Series
Since inside charge is onlySince inside charge is only inducedinduced, the, the
chargecharge on each capacitor is theon each capacitor is the samesame..
Charge is same:
series connection
of capacitors.
Q = Q1 = Q2 =Q3
Battery
C1 C2
C3
+
+
-
-
+
+
+
+
-
-
-
-
Q1 Q2 Q3

6. Voltage on Capacitors inVoltage on Capacitors in
SeriesSeries
Since theSince the potential differencepotential difference betweenbetween
pointspoints AA andand BB is independent of path, theis independent of path, the
battery voltagebattery voltage VV must equal the sum ofmust equal the sum of
the voltages across each capacitor.the voltages across each capacitor.
Total voltage V
Series connection
Sum of voltages
V = V1 + V2 + V3
Battery
C1 C2
C3
+
+
-
-
+
+
+
+
-
-
-
-
V1 V2 V3
• •A B

7. Equivalent Capacitance:Equivalent Capacitance:
SeriesSeries
V = V1 + V2 + V3
Q1= Q2 = Q3
+
+
-
-
+
+
+
+
-
-
-
-
C1 C2 C3
V1 V2 V3 ;
Q Q
C V
V C
= =
31 2
1 2 3
QQ Q Q
C C C C
= + +
1 2 3
1 1 1 1
eC C C C
= + +
Equivalent CEquivalent Cee
for capacitorsfor capacitors
in series:in series: 1
1 1n
ie iC C=
= ∑

8. Short Cut: Two Series CapacitorsShort Cut: Two Series Capacitors
The equivalent capacitanceThe equivalent capacitance CCee forfor twotwo seriesseries
capacitors is thecapacitors is the product divided by the sumproduct divided by the sum..
1 2
1 1 1
;
eC C C
= + 1 2
1 2
e
C C
C
C C
=
+
3 µF 6 µF
+
+
-
-
+
+
-
-
C1 C2
Example:Example: (3 F)(6 F)
3 F 6 F
eC
µ µ
µ µ
=
+
Ce = 2 µFCe = 2 µF

9. Parallel CircuitsParallel Circuits
Capacitors which are all connected to theCapacitors which are all connected to the
same source of potential are said to besame source of potential are said to be
connected inconnected in parallelparallel. See below:. See below:
Parallel capacitors:
“+ to +; - to -”
C2 C3
C1
+
+
--
+
+
--
+
+
--
Charges:
QT = Q1 + Q2 + Q3
Voltages:
VT = V1 = V2 = V3

10. Equivalent Capacitance: ParallelEquivalent Capacitance: Parallel
Q = Q1 + Q2 + Q3
;
Q
C Q CV
V
= =
Equivalent CEquivalent Cee
for capacitorsfor capacitors
in parallel:in parallel: 1
n
e i
i
C C
=
= ∑
Equal Voltages:Equal Voltages:
CVCV = C= C11VV11 + C+ C22VV22 + C+ C33VV33
Parallel capacitors
in Parallel:
C
2
C
3
C
1
+
+--
+
+
--
+
+
--
CCee = C= C11 + C+ C22 + C+ C33

11. Example 1.Example 1. Find theFind the equivalent capacitanceequivalent capacitance
of the three capacitors connected inof the three capacitors connected in parallelparallel
with a 24-V battery.with a 24-V battery.
CCee forfor
parallel:parallel:
Ce = 12 µFCe = 12 µF
C2
C
3
C
1
2 µF 4 µF 6 µF
24 V
Q = Q1 + Q2 + Q3
VT = V1 = V2 = V3
1
n
e i
i
C C
=
= ∑
CCee = (2 + 4 + 6)= (2 + 4 + 6) µµFF
Note that the equivalent capacitanceNote that the equivalent capacitance CCee forfor
capacitors incapacitors in parallelparallel is alwaysis always greater thangreater than
the largestthe largest in the circuit. (12in the circuit. (12 µF > 6> 6 µF)

12. Example 1 (Cont.)Example 1 (Cont.) Find theFind the totaltotal charge Qcharge QTT
andand chargecharge across each capacitor.across each capacitor.
Ce = 12 µFCe = 12 µF
C2
C
3
C
1
2 µF 4 µF 6 µF
24 V
Q = Q1 + Q2 + Q3
V1 = V2 = V3 = 24 V
;
Q
C Q CV
V
= =
QQ11 == (2(2 µµF)(24 V) =F)(24 V) = 4848 µµCC
QQ11 == (4(4 µµF)(24 V) =F)(24 V) = 9696 µµCC
QQ11 == (6(6 µµF)(24 V) =F)(24 V) = 144144 µµCC
QQTT = C= CeeVV
QQTT = (12= (12 µµF)(24 V)F)(24 V)
QT = 288 µCQT = 288 µC

13. Summary: Series CircuitsSummary: Series Circuits
1
1 1n
ie iC C=
= ∑
Q = Q1 = Q2 = Q3
Q = Q1 = Q2 = Q3
V = V1 + V2 + V3
V = V1 + V2 + V3
1 2
1 2
e
C C
C
C C
=
+
For two capacitors at a time:For two capacitors at a time:

14. Summary: Parallel CircuitsSummary: Parallel Circuits
Q = Q1 + Q2 + Q3
Q = Q1 + Q2 + Q3
V = V1 = V2 =V3
V = V1 = V2 =V3
1
n
e i
i
C C
=
= ∑
For complex circuits, reduce the circuit in steps
using the rules for both series and parallel
connections until you are able to solve problem.
For complex circuits, reduce the circuit in steps
using the rules for both series and parallel
connections until you are able to solve problem.

15. THANK YOUTHANK YOU