Capacitors Capacitors Series Parallel Capacitors by jalal

2. Electrical Engineering Department
CECOS University of I.T & Emerging Sciences Hayatabad, Peshawar
Capacitors----------------------------------------------
PREPARED BY :
JALAL AHMED

3. Capacitors
• Capacitors
• Series and Parallel Capacitors

4. Capacitors
A device used to store an electric charge,
consisting of one or more pairs of conductors
separated by an insulator.
Anode
Cathode

5. Capacitors formula
Where
C = Capacitors
V = Voltage
Q = Charge

6. By rearranging the terms C=Q/V, we can obtain two other
formulas.
Q= CV
V= Q /C
Capacitors Symbol

7. Capacitors Unit
The farad (F) is the basic unit of capacitance.
One Farad
One farad is the amount of capacitance
when one coulomb (C) of charge is
stored with one volt across the plates.

8. Example 1
(a) Calculate the charge stored on a 3-pF capacitor with 20V across it.
(b) Find the energy stored in the capacitor.

9. Example 1
Solution:
(a) Since
(b) The energy stored is
pC6020103 12
 
q
pJ600400103
2
1
2
1 122
 
Cvw
,Cvq

10. Example2
(a) What is the charge stored when the voltage across a 50
μF capacitor is 9 V?
• Solution:
• (a) Since
V =
Q
=
50 μC
= 5.55 μC
C 9 V

11. • (b) What is the capacitance of a capacitor that stores 12 μC of charge
when connected to a 6 V battery?
• Solution:
• (b) Since
C =
Q
=
12 μC
= 2 V
V 6V

12. • (c) Calculate the energy stored in a capacitor with a charge of 200
μC and 9 V across its plates.
• Solution:
• (c) Since
W = ½ QV =
200 μC × 9 V
= 0.9 mJ
2
1.

13. Series Capacitors
Neq CCCCC
1
...
1111
321


14. Series Capacitors
• The equivalent capacitance of series-connected capacitors is
the reciprocal of the sum of the reciprocals of the individual
capacitances.
21
111
CCCeq

21
21
CC
CC
Ceq


According to KVL
VT = V1 + V2 + V3 + V4 + V5 +…+ Vn
QT/CT = Q1/C1 + Q2/C2 + Q3/C3 + Q4/C4 + Q5/C5 +…+ Qn/Cn
Since the charges on all the capacitors are equal, the Q terms can be
factors and cancelled, resulting in
1/CT = 1/C1 + 1/C2 + 1/C3 + 1/C4 + 1/C5 +…+ 1/Cn

15. Parallel Capacitors
Neq CCCCC  ....321

16. Parallel Capacitors
• The equivalent capacitance of N parallel-connected capacitors
is the sum of the individual capacitance.
According to KCL
IT = I1 + I2 + I3 + I4 + I5 +…+ In
This implies that
QT = Q1 + Q2 + Q3 + Q4 + Q5 +…+ Qn
Since the elements are connected in parallel, VT = V1 = V2 = V3 …Vn ,
the voltages can be factored and cancelled, giving
CT = C1 + C2 + C3 + C4 + C5 +…+ Cn

17. Example
• Find the equivalent capacitance seen between terminals a and b of
the circuit in the Fig.

18. Example
Solution:
F4
520
520




F302064 
F20F
6030
6030
 


eqC
:seriesinarecapacitorsF5andF20  
F6with theparalleliniscapacitorF4  
:capacitorsF20and 
withseriesiniscapacitorF30 
capacitor.F60the 