series and parallel connection of capacitor

EEE

1. Amiraj collage of engineering and Amiraj collage of engineering and
technologytechnology
ELEMENT OF ELECTRICAL ELEMENT OF ELECTRICAL
ENGINEERINGENGINEERING
TOPIC -series and parallel connection of TOPIC -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-Ankur E.no.-151080106024 Guided by-Ankur
sirsir

2. Objectives: Objectives: After completing this After 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 more often contain two or more
capacitors grouped together and attached capacitors 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 connected Capacitors or other devices connected
along a single path are said to be along a single path are said to be
connected in connected in seriesseries. See circuit below:. See circuit below:
Series
connection of
capacitors. “+ to
– to + …”
Charge inside
dots is induced.
Battery
C
1 C
2
C
3
+
+
-
-
+
+
+
+
-
-
-
-

5. Charge on Capacitors in SeriesCharge on Capacitors in Series
Since inside charge is only Since inside charge is only inducedinduced, the , the
chargecharge on each capacitor is the on each capacitor is the samesame..
Charge is same:
series connection
of capacitors.
Q = Q
1
= Q
2
=Q
3
Battery
C
1 C
2
C
3
+
+
-
-
+
+
+
+
-
-
-
-
Q
1
Q
2
Q
3

6. Voltage on Capacitors in Voltage on Capacitors in
SeriesSeries
Since the Since the potential differencepotential difference between between
points points AA and and BB is independent of path, the is independent of path, the
battery voltage battery voltage V V must equal the sum of must equal the sum of
the voltages across each capacitor.the voltages across each capacitor.
Total voltage V
Series connection
Sum of voltages
V = V
1
+ V
2
+ V
3
Battery
C
1 C
2
C
3
+
+
-
-
+
+
+
+
-
-
-
-
V
1
V
2
V
3
• •
A B

7. Equivalent Capacitance: Equivalent Capacitance:
SeriesSeries
V = V
1
+ V
2
+ V
3
Q
1
= Q
2
= Q
3
+
+
-
-
+
+
+
+
-
-
-
-
C
1
C
2
C
3
V
1
V
2
V
3 ;
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 C
e e
for capacitors for capacitors
in series:in series:
1
1 1
n
ie iC C
=
=å

8. Short Cut: Two Series CapacitorsShort Cut: Two Series Capacitors
The equivalent capacitance The equivalent capacitance CC
ee for for twotwo series series
capacitors is the capacitors is the product divided by the sumproduct divided by the sum..
1 2
1 1 1
;
e
C C C
= +
1 2
1 2
e
CC
C
C C
=
+
3 mF6 mF
+
+
-
-
+
+
-
-
C
1
C
2
Example:Example: (3 F)(6 F)
3 F 6 F
e
C
m m
m m
=
+
C
e
= 2 mF C
e
= 2 mF

9. Parallel CircuitsParallel Circuits
Capacitors which are all connected to the Capacitors which are all connected to the
same source of potential are said to be same source of potential are said to be
connected in connected in parallelparallel. See below:. See below:
Parallel capacitors:
“+ to +; - to -”
C
2C
3
C
1 ++
--
++
--
++
--
Charges:
Q
T
= Q
1
+ Q
2
+ Q
3
Voltages:
V
T
= V
1
= V
2
= V
3

10. Equivalent Capacitance: ParallelEquivalent Capacitance: Parallel
Q = Q
1
+ Q
2
+ Q
3
;
Q
C Q CV
V
= =
Equivalent CEquivalent C
e e
for capacitors for capacitors
in parallel:in parallel:
1
n
e i
i
C C
=
=å
Equal Voltages: Equal Voltages:
CVCV
= C= C
11VV
11 + C + C
22VV
22 + C + C
33VV
33
Parallel capacitors
in Parallel:
C
2
C
3
C
1
++
--
++
--
++
--
CC
ee = C = C
11 + C + C
22 + C + C
33

11. Example 1.Example 1. Find the Find the equivalent capacitanceequivalent capacitance
of the three capacitors connected in of the three capacitors connected in parallelparallel
with a 24-V battery.with a 24-V battery.
CC
ee for for
parallel:parallel:
C
e
= 12 mFC
e
= 12 mF
C
2
C
3
C
1
2 mF4 mF6 mF
24 V
Q = Q
1
+ Q
2
+ Q
3
V
T
= V
1
= V
2
= V
3
1
n
e i
i
C C
=
=å
CC
ee = (2 + 4 + 6) = (2 + 4 + 6) mmFF
Note that the equivalent capacitance Note that the equivalent capacitance CC
ee for for
capacitors in capacitors in parallelparallel is always is always greater than greater than
the largestthe largest in the circuit. (12 in the circuit. (12 mF > 6 > 6 mF)

12. Example 1 (Cont.)Example 1 (Cont.) Find the Find the totaltotal charge Qcharge Q
TT
and and chargecharge across each capacitor. across each capacitor.
C
e
= 12 mFC
e
= 12 mF
C
2
C
3
C
1
2 mF4 mF6 mF
24 V
Q = Q
1
+ Q
2
+ Q
3
V
1
= V
2
= V
3
= 24 V
;
Q
C Q CV
V
= =
QQ
11 = = (2 (2 mmF)(24 V) = F)(24 V) = 48 48 mmCC
QQ
11 = = (4 (4 mmF)(24 V) = F)(24 V) = 96 96 mmCC
QQ
11 = = (6 (6 mmF)(24 V) = F)(24 V) = 144 144 mmCC
QQ
TT = C = C
eeVV
QQ
TT = (12 = (12 mmF)(24 V) F)(24 V)
Q
T
= 288 mC Q
T
= 288 mC

13. Summary: Series CircuitsSummary: Series Circuits
1
1 1
n
ie iC C
=
=å
Q = Q
1
= Q
2
= Q
3
Q = Q
1
= Q
2
= Q
3
V = V
1
+ V
2
+ V
3
V = V
1
+ V
2
+ V
3
1 2
1 2
e
CC
C
C C
=
+
For two capacitors at a time:For two capacitors at a time:

14. Summary: Parallel CircuitsSummary: Parallel Circuits
Q = Q
1
+ Q
2
+ Q
3
Q = Q
1
+ Q
2
+ Q
3
V = V
1
= V
2
=V
3
V = V
1
= V
2
=V
3
1
n
e i
i
C C
=
=å
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