Download Chapter 26: Capacitance and Dielectrics

Chapter 26:Capacitance and
Dielectrics
Capacitors
 A capacitor is made up of 2 conductors carrying charges of
equal magnitude and opposite sign.
The Capacitance (C) of a capacitor is defined as:
Q
C
V
where Q is the charge on either conductor and ∆V is the
potential difference between them
 The SI unit of
conductance is the farad (F).
 1 F = 1 coulomb per volt (C/V)
-
Parallel-Plate Capacitors
 Two metallic plates of equal area “A” are separated by a
distance “d”. One plate carries a + charge while the other
carries a – charge.
 The surface density of each plate is
Q

A
 The electric field between the plates is


Q

E

o A o
Parallel-Plate Capacitors
 Since the field between the plates is uniform and points
directly from one plate to the other, the magnitude of the
potential difference between the two equals Ed
Qd
V  Ed 
o A
 Therefore the capacitance is given by:


C
Q o A

V
d
Combinations of Capacitors
 Capacitors can be combined in electric circuits.
 When studying circuits a circuit diagram can be used and
specific circuit symbols are given to designate a capacitor,
battery, and switch.
Capacitor
Symbol
Battery Symbol
Switch Symbol
Various Combinations
 Parallel Combination
 ∆V1=∆V2=∆V
 Q total=Q1+Q2
 Equivalent capacitor
 Q total = Cequiv(∆V)
 Cequiv = C1+C2+C3…
 Series Combination
 ∆Vtotal=∆V1+∆V2
 Q1=Q2=Q
 Equivalent capacitance
 1/Cequiv = 1/C1 + 1/C2 + 1/C3…
Energy Stored in Charged
Capacitor
 Electric potential energy is stored in the system
 Energy stored in a charged capacitor
Q2 1
U
 C(V ) 2
2C 2
 The energy in a capacitor is stored in the electric field
betweenthe two plates as the capacitor is charged.
 The electric field is proportional to the charge on the
capacitor
Capacitors with Dielectrics
 A Dielectric is a non-conducting material like rubber or glass.
 The Dielectric constant (κ) varies from from one material to
the next.
 The capacitance of a capacitor containing a dielectric is:
C  CO
 With the addition of the dielectric the charge remains the
same, the potential difference decreases, and the capacitance
increases.

 The capacitance
increases by the factor “κ” when the dielectric
is filling the space between the plates.
Electric Dipole in an Electric Field
 The Electric dipole moment has a magnitude of p=2aq
 2a is the distance between – q and +
 The torque on an electric dipole in a uniform electric field
is given by:
r
r r
r
T  p E
 The potential energy of the system of an electric dipole in
a unifrom external electric field is given by:

r r
U  p  E
Atomic Description of Dielectrics
 The field in the presence of a dielectric equals
r
E
r
EO

 Charged dipoles can be viewed as creating another pair of
r
parallel plates establishing an electric field E
ind

 So, the net electric field in the dielectric has a magnitude
E  EO  Eind
