Transcript 16.6 Capacitance A capacitor is a device used in a variety of electric circuits  The capacitance, C, of a capacitor is defined as.

16.6 Capacitance
A capacitor is a device used in a variety
of electric circuits
 The capacitance, C, of a capacitor is
defined as the ratio of the magnitude of
the charge on either conductor (plate)
to the magnitude of the potential
difference between the conductors
(plates)

Lectures are at:
http://kottan-labs.bgsu.edu/202/
Capacitance, cont


Q  Q  V=V and means
C  
 voltage drop
V  V 
Units: Farad (F)
1F=1C/V
 A Farad is very large


Often will see µF or pF
16.7 Parallel-Plate Capacitor
The capacitance of a device depends on
the geometric arrangement of the
conductors
 For a parallel-plate capacitor whose
plates are separated by air:

A
C  o
d
Permittivity of the free space
Applications of Capacitors –
Camera Flash

The flash attachment on a camera uses
a capacitor
A battery is used to charge the capacitor
 The energy stored in the capacitor is
released when the button is pushed to take
a picture
 The charge is delivered very quickly,
illuminating the subject when more light is
needed

Applications of Capacitors -Computers

Computers use
capacitors in many
ways



Some keyboards use
capacitors at the bases of
the keys
When the key is pressed,
the capacitor spacing
decreases and the
capacitance increases
The key is recognized by
the change in
capacitance
16.8 Capacitors in Circuits
Q1=C1Vab, Q2=C2Vab
The total charge supplied by
the source:
Qtotal=Q1+Q2=Vab(C1+C2)
Equivalent capacitance Ceq
Ceq=C1+C2
Q1 and Q2 are not
necessarily equal but
Vab is the same.
Capacitors in Parallel

The total charge is
equal to the sum of the
charges on the
capacitors


Qtotal = Q1 + Q2
The potential
difference across the
capacitors is the same

And each is equal to the
voltage of the battery
Capacitors in Parallel, final
 Ceq
= C1 + C2
 The equivalent capacitance of a
parallel combination of capacitors is
greater than any of the individual
capacitors
V1=Q/C1, V2=Q/C2
 1
1 
V=V1+V2= Q  
 C1 C2 
1
1
1


Ceq C1 C 2
In a series connection
the magnitude of
charge on all plates is
the same!
Equivalent capacitance Ceq
More About Capacitors in
Series
An equivalent
capacitor can be
found that performs
the same function as
the series
combination
 The potential
differences add up
to the battery
voltage

Capacitors in Series, cont
V  V1  V2
1
1
1


Ceq C1 C2

The equivalent capacitance of a series
combination is always less than any
individual capacitor in the combination
Problem-Solving Strategy
Be careful with the choice of units
 When two or more unequal capacitors are
connected in series, they carry the same
charge, but the potential differences across
them are not the same
 The capacitances add as reciprocals
and the equivalent capacitance is
always less than the smallest
individual capacitor

Problem-Solving Strategy, cont

When two or more capacitors are
connected in parallel, the potential
differences across them are the same

The charge on each capacitor is
proportional to its capacitance
 The
capacitors add directly to
give the equivalent capacitance
Problem-Solving Strategy, final

A complicated circuit can often be reduced to
one equivalent capacitor



Replace capacitors in series or parallel with their
equivalent
Redraw the circuit and continue
To find the charge on, or the potential
difference across, one of the capacitors, start
with your final equivalent capacitor and work
back through the circuit reductions
Example:
Step 1
Step 2
Step 1:
Cp=C1+C2
Cp=0.10 mF+0.20 mF
Cp =0.30 mF
Step 2:
1/Cs=1/C3+1/Cp
0.60mF  mF
Cs 

 0.20mF
C3  Cp 0.60mF  mF
C3 C p
16.9 Energy Stored in a
Capacitor
Average voltage during charging:
0
Vfinal  Vinitial Vfinal
Va 

2
2
Since Vfinal is the applied voltage, we write Va=V/2.
Energy stored (=work done by the battery):
1
1
2
W  QVa  QV  CV
2
2
V
A plot of voltage vs.
charge of a capacitor
is a straight line with
slope 1/C. The area
under the line equals
QV/2=Energy stored.
Applications

Defibrillators



When fibrillation occurs, the heart produces a
rapid, irregular pattern of beats
A fast discharge of electrical energy through the
heart can return the organ to its normal beat
pattern
In general, capacitors act as energy
reservoirs that can slowly charged and then
discharged quickly to provide large amounts
of energy in a short pulse
16.10 Capacitors with
Dielectrics

A dielectric is an insulating material
that, when placed between the plates
of a capacitor, increases the capacitance


Dielectrics include rubber, plastic, or waxed
paper
C = κCo = κεo(A/d)

The capacitance is multiplied by the factor
κ when the dielectric completely fills the
region between the plates
Reasoning:
E0
-Q0
+Q0
Electric field lines inside an
empty capacitor
(b) The electric field produces
polarization
(c) The resulting positive and
negative surface charges
on the dielectric reduce the
electric field within the
dielectric
(a)
Dielectric constant
E=E0/k or V=V0/k
Capacitance in presence of a
dielectric:
Q0
Q0
kQ0
C


 kC0
V V0 /k
V
A
C  k 0
d
Since k>1, the dielectric
enhances the capacitance of
the capacitor!
Capacitors with Dielectrics
The value of k depends on the nature of the
dielectric material, as the table below indicates:
(at 300 K)
Dielectric Strength
For any given plate separation, there is
a maximum electric field that can be
produced in the dielectric before it
breaks down and begins to conduct
 This maximum electric field is called the

dielectric strength
Capacitors Designs
Paper capacitor
(b) High-voltage oil capacitor
(c) Electrolytic capacitor
(a)