Capacitors
A capacitor is a device that
has the ability “capacity” to
store electric charge and
energy.
Capacitors
In a circuit diagram a capacitor is
represented by two parallel lines of
equal length
Capacitors
Capacitance is defined as
Q
C
Q  the charge on the plates
V
V  electric potential across the plates
coulomb
Unit :
 farad : F
volt
Figure 20-13
A Parallel-Plate Capacitor
Capacitors
Permitivity of free space  o
o 
1
4 k
=8.85 1012
C2
k  Coulomb's constant
2
N m
Capacitors
Capacitance of a parallel plate capacitor
C
o A
d
d= distance between plates
A= area of the plates
Capacitors
A dielectric material is an
insulator that increases the
capacitance of a capacitor when
placed between the plates.
Each material has a dielectric
constant k not to be confused
with k.(p 665)
Figure 20-15
The Effect of a Dielectric on the Electric Field of a Capacitor
Capacitors
Capacitance of a parallel plate capacitor filled with
a dielectric
C
k o A
d
d= distance between plates
A= area of the plates
k  dielectric constant
Capacitors
Energy stored in a capacitor
2
1
1
Q
2
U  QV  CV 
2
2
2C
Capacitors
Capacitors connected in parallel
have an equivalent capacity
equal to the sum of the
individual capacities.
Capacitors
The charge on individual
capacitors will be equal to
Q  C  CV
Capacitors
The total charge in the circuit
will be equal to
Q   C1  C2  C3  ... 
Capacitors
Capacitors connected in series
have an equivalent capacity
whose reciprocal is equal to the
sum of the reciprocals of the
capacities of the individual
capacitors.
Capacitors
1
1
1
1
 
  ...
Ceq C1 C2 C3
Capacitors
Capacitors connected in series
all have the same charge Q
Figure 21-17
Capacitors in Series
Capacitors
Voltage drops across capacitors
connected in a series
Q
V1 
C1
Q
V2 
C2
Q
V3 
C3
Capacitors
Voltage drops across capacitors
connected in a series
Vtotal
Q

Ceq
Capacitors
Capacitors connected in parallel
have an equivalent capacitance
which is equal to the sum of the
capacitances of the individual
capacitors.
Figure 21-16
Capacitors in Parallel
Capacitors
Ceq  C1  C2  C3  ...
Capacitors
Charges on capacitors
connected in parallel are
calculated by multiplying the
voltage drop by individual
capacitances.
Capacitors
Qeq  Q1  Q2  Q3  ...
 V (C1  C2  C3  ...)
Figure 21-16
Capacitors in Parallel
Example 21-8
Energy in Parallel
Figure 21-17
Capacitors in Series
Active Example 21-3
Find the Equivalent Capacitance and the Stored Energy
Figure 21-18
A Typical RC Circuit
Figure 21-19
Charge Versus Time for an RC Circuit
Figure 21-20
Current Versus Time in an RC Circuit
Example 21-9
Charging a Capacitor
Figure 21-21
Discharging a Capacitor
Figure 21-39
Problems 21-53 and 21-55
Figure 21-43
Problems 21-67 and 21-87
Figure 21-45
Problem 21-78
Capacitors
Solve problems 53-58 on pages
711 and 712.