Download ENT 163 05A-08

FUNDAMENTALS OF ELECTRICAL
ENGINEERING
[ ENT 163 ]
LECTURE #5a
CAPACITORS AND INDUCTORS
HASIMAH ALI
Programme of Mechatronics,
School of Mechatronics Engineering, UniMAP.
Email: [email protected]
CONTENTS
1.Introduction
2.Capacitors
Introduction
1. Two new important passive linear circuit elements: capacitors
and inductors.
2. Capacitors and inductors do not dissipate energy but store
energy.
3. Therefore capacitors and inductors are called storage
elements.
CAPACITORS
• A capacitor is a passive elements designed to store energy in its
electric field.
• Capacitors are the most important common electrical component
and extensively used in electronics, communication, computer, and
power system.
• Example, they are used in the tuning circuits of radio receivers and
as dynamics memory elements in computer system.
A capacitor consists of two conducting plates separated by
an insulator (or dielectric).
CAPACITORS
• Practically, the plates may be aluminum
foil ; dielectric may be air ceramic, paper
and mica.
• When a voltage source is connected to
the capacitor, the source deposits a
positive charge q, on one plate and a
negative charge –q on the other.
CAPACITORS
• Therefore the capacitor is said to store the electric charge.
q  Cv
q= amount of charge stored,
v= applied voltage and
C=capacitance of the capacitor
• Unit of capacitance= farad, F
Capacitance is the ratio of the change on one plate of a capacitor
to the voltage difference between the two plates, measured in
farads (F).
1 farad = 1 coulomb/ volt
CAPACITORS
• Capacitance, C of a capacitor depends on the physical dimensions
of the capacitor.
• Example: for parallel plate capacitor, the capacitance is given:
A
C
d
C= capacitance,
A= surface area of each plate
d= distance between plate
ε = permittivity of the dielectric
material between plates
CAPACITORS
• Three factors determine the value of capacitance:
a) The surface area of the plate – the larger the area, the greater
the capacitance.
b) The spacing between the plates – the smaller the spacing , the
greater capacitance.
c) The permittivity of the material – the higher the permittivity, the
greater the capacitance
Typical range value for capacitor: picofarad (pF)  microfarad (µF)
CAPACITORS
• According to passive sign convention, current is considered to flow
into the positive terminal of the capacitor when the capacitor is
being charges, and out of the positive terminal when the capacitor
is discharging.
• Current-voltage relationship of the capacitor:
dv
iC
dt
CAPACITORS
1. Voltage-current relation of the capacitor
t
t
1
v   idt
C 
or
1
v   idt  v(to )
C to
q (to )
v(to ) 
C
This equation shows that capacitor
voltage depends on the past history
of the capacitor current.
Means that the voltage across
the capacitor at time t0
CAPACITORS
•
The instantaneous power delivered to the capacitor is:
dv
p  vi  Cv
dt
•
The energy stored in the capacitor:
1 2
w  Cv
2
2
q
w
2C
CAPACITORS
1. Take note of the important properties of a capacitor:
1. From the voltage-current relation equation, note that
when the voltage across a capacitor is not charging with
time (i.e dc voltage), the current through the capacitor is
zero.
A capacitor is an open circuit to dc.
2. The voltage on the capacitor must be continuous. The
capacitor resists an abrupt change in the voltage across it.
The voltage on a capacitor cannot change abruptly.
CAPACITORS
1. The ideal capacitor does not dissipate energy. It takes power from
the circuit when storing energy in its field and returns previously
stored energy when delivering power to the circuit.
2. A real, nonideal capacitor has a parallel-model leakage resistance,
and can be neglected for most practical applications.
CAPACITORS
Example:
a) Calculate the charge stored on a 3-pF capacitor with 20V across it.
b) Find the energy stored in the capacitor.
CAPACITORS
Solution:
Further Reading
1. Fundamentals of Electric Circuits, 2nd Edition,McGrawhill
Alexander, C. K. and Sadiku, M. N. O.
2. Electric Circuit, 8th Edition, Pearson, Nillson and Riedel.
3. Circuits,Brooks/ Cole, A. Bruce Carlson.
4. http://www.scribd.com/word/full/2031941?access_key=key1vybbz6deqeinoosecmm