Capacitors Presentation Presentations about capacitors What is capacitor Construction of capacitor by Mudasir Nadeem Institute of Chemical Sciences BZU Multan

1. Equipotential Surfaces
• An equipotential surface has the same potential at
every point on the surface
– Similar to topographic map, which
shows lines of constant elevation
• Since DV = 0 for each surface, W = 0
along the surface
– Thus electric field lines are perpendicular to the
equipotential surfaces at all points
• E points in the direction of the maximum decrease
in DV (E points from high to low potential)
– Similar to a topographic contour map (slope is steepest
perpendicular to lines of constant elevation)
– Electric field is thus sometimes called the potential
gradient (meaning grade or slope)

2. Equipotential Surfaces
• On a contour map a hill is steepest where the lines
of constant elevation are close together
• If equipotential surfaces are drawn such that the
potential difference between adjacent surfaces is
constant, then the surfaces are closer together
where the field is stronger

3. Examples of Equipotential Surfaces

4. Capacitance
• A capacitor is a device that stores electrical potential
energy by storing separated + and – charges
– 2 conductors separated by vacuum, air, or insulation
– + charge put on one conductor, equal amount of – charge
put on the other conductor
– A battery or power supply typically supplies
the work necessary to separate the charge
• Simplest form of capacitor is the
parallel plate capacitor
– 2 parallel plates, each with same area A,
separated by distance d
– Charge +Q on one plate, –Q on the other
– If plates are close together, electric field will be
uniform (constant) between the plates
Charging A Capacitor

5. Capacitance
• For a uniform electric field, the potential difference
between the plates is (see Example Problem #16.6)
DV = Ed
– E is proportional to the charge, and DV is proportional to E
 therefore the charge is proportional to DV
• The constant of proportionality between charge and
DV is called capacitance
– “Capacity” to hold charge for a given DV
– 1 F is very large unit: typical values of C are mF, nF, or pF
• Capacitance depends on the geometry of the plates
and the material between the plates
V
Q
C
D
 Units: C / V = Farad (F)
d
A
C 0

 (for plates separated by air)

6. Capacitors in Circuits and Applications
• Capacitors are used in a variety of electronic circuits
– Example of “circuit diagram” consisting of
capacitors and a battery shown at right
• Many practical uses of capacitors
– Some computer keyboard keys have
capacitors with a variable plate spacing below them
– Microphones using capacitors with one moving plate to
create an electrical signal
• Constant potential difference kept between plates by a battery
• As plate spacing changes, charge flows onto and off of plates
• The moving charge (current) is amplified to generate signal
– Tweeters (speakers for high-frequency sounds) are
microphones in reverse
– Millions of microscopic capacitors used in each RAM
computer memory chip
• Charged and discharged capacitors correspond to 1 and 0 states

7. Combinations of Capacitors
• Capacitors can be combined in circuits to give a
particular net capacitance for the entire circuit
• Parallel Combination
– Potential difference across each
capacitor is the same and equal to
DV of the battery
– Qtot = Q1 + Q2 + Q3 + …
– Total (equivalent) capacitance:
• Series Combination
– Magnitude of charge is the same on
all plates
– DV (battery) = DV1 + DV2 + DV3 + …
– Total (equivalent)
capacitance:




 3
2
1
eq C
C
C
C





3
2
1
eq
1
1
1
1
C
C
C
C

8. Example Problem
Solution (details given in class):
(a) 2.67 mF
(b) 24.0 mC (each 8.00-mF capacitor), 18.0 mC (6.00-mF
capacitor), 6.00 mC (2.00-mF capacitor)
(c) 3.00 V (each capacitor)
Find (a) the equivalent capacitance of the capacitors in the
circuit shown, (b) the charge on each capacitor, and (c) the
potential difference across each capacitor.

9. Energy Stored in a Charged Capacitor
• It’s easy to tell that a capacitor stores (releases)
energy when it charges (discharges)
• The energy stored by the capacitor = work required
to charge the capacitor (typically performed by a
battery or power supply)
• As more and more charge is transferred
between the plates, the charge, voltage,
and work done by battery increases
(DW = DVDQ)
• Total work done = total energy stored:
• Defibrillators typically release about 1.2 kJ of stored
energy from capacitor with DV ≈ 5 kV
 
C
Q
V
C
V
Q
E
2
2
1
2
1 2
2

D

D


10. Capacitors with Dielectrics
• A dielectric is an insulating material
– Rubber, plastic, glass, nylon
• When a dielectric is inserted between the conductors
of a capacitor, the capacitance increases
• Capacitance increases for a parallel-plate capacitor
in which a dielectric fills the entire space between the
plates
– k = dielectric constant (ratio of capacitance
with dielectric to capacitance without dielectric)
• For any given plate separation d, there is a maximum
electric field (dielectric strength) that can be
produced in the dielectric before it breaks down and
conducts
– See Table 16.1 for values of k and dielectric strength for
various materials
d
A
C 0
k


11. Capacitors with Dielectrics
• The molecules of the dielectric, when placed in the
electric field of a capacitor, become polarized
– Centers of positive and negative charges become
preferentially oriented in the field (see figure below at left)
– Creates a net positive (negative) charge on the left (right)
side of the dielectric (see figure below at right)
– This helps attract more charge to the conducting plates for
a given DV
– Since plates can store more charge for a given voltage,
the capacitance must increase (remember C = Q / DV )

12. Capacitors with Dielectrics
• To increase capacitance while keeping the physical
size reasonable, plates are often made of a thin
conducting foil that is rolled into a cylinder
– Dielectric material is sandwiched in between
• High-voltage capacitor commonly consists of
interwoven metal plates immersed in silicone oil
• Very large capacitances can be achieved with an
electrolytic capacitor at relatively low voltages
– Insulating metal oxide
layer forms on the
conducting foil and
serves as a (very thin)
dielectric