Chapter 4
Introduction to AC Circuits
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Objectives
• To identify the main features of the AC source.
• To determine the behavior of the different circuit elements in the AC
domain.
• To introduce frequency domain (complex domain analysis).
• To apply circuit analysis techniques in the frequency domain.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Circuit Elements
• The main elements in the AC circuits are: Resistors R, Capacitors C
and Inductors L.
• Capacitors and inductors are energy storing elements.
• Capacitors store electrical energy while inductors store magnetic
energy.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Michael Faraday (1791–1867), an English
chemist and physicist, Faraday realized his
boyhood dream by working with the
great chemist Sir Humphry Davy at the
Royal Institution, where he worked for 54
years.
The unit of capacitance, the farad, was
named in his honor.
Joseph Henry (1797–1878), an American
physicist, discovered inductance and
constructed an electric motor.
Joseph Henry discovered electromagnetic
induction before Faraday but failed to publish
his findings. The unit of inductance, the
henry, was named after him.
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Capacitors
A capacitor is a passive element designed to store energy in its electric
field
A capacitor consists of
two conducting plates
separated by an insulator
(or dielectric).
• The plates may be aluminum foil
• The dielectric may be air, ceramic,
paper, or mica.
Circuit Symbol
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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• When a voltage source v is
connected to the capacitor.
• The source deposits a positive
charge q on one plate.
• Negative charge −q on the other.
The capacitor is said to store the
electric charge.
The amount of charge stored,
represented by q, is directly
proportional to the applied voltage v
so that
Q
C=
V
farad (F),
C, is known as the capacitance of the
capacitor.
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Electronics and Electrical Engineering Department
The unit is
“Farad”
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C=
Q
V
Capacitance is the ratio of the charge on one plate of a
capacitor to the voltage difference between the two plates,
measured in farads (F).
1 farad = 1 coulomb/volt.
capacitance C of a capacitor, it does not depend on q or v.
It depends on the physical dimensions of the capacitor.
………………..Applied for parallel plates
A is the surface area of each plate, the larger the area, the greater the
capacitance.
d is the distance between the plates, smaller the spacing, the greater the
capacitance.
ε
is the permittivity of the dielectric material between the plates. the higher the
permittivity, the greater the capacitance.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Capacitors are commercially available in different values and types.
Typically, capacitors have values in the picofarad (pF) to microfarad
( F)
used to block dc,
pass ac, shift
phase, store
energy, start
motors, and
suppress noise.
current direction when the capacitor is being charged
current direction when the capacitor is discharging.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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To obtain the current-voltage relationship of the capacitor, we take
the derivative of both sides of the equation
C=
Q
V
Since
dq
c = dt
dv
dt
=
i
dv
dt
Then
This is the current-voltage relationship for a capacitor, assuming the positive
sign convention.
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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• The current drop across the terminals is related to the voltage
by
dv
i=C
dt
v
i
• If the voltage is constant (DC voltage) the capacitor behaves
as an open circuit.
v = constant
dv
=0
dt
i=0
• The voltage cannot change instantaneously across the
terminals of a capacitor.
dv
≠∞
dt
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
i≠∞
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C
V
This type of capacitor is said to be linear
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Series-parallel Combinations
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Electronics and Electrical Engineering Department
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Parallel
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Example
Find Cab?
Solution
6µF × 4µF
= 2.4 µF
4 µF + 6µF
3 µF
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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The inductor
• An inductor is a passive electrical device that stores energy
in a magnetic field, typically by combining the effects of many
loops of electric current.
They are used in power
supplies, transformers,
radios, TVs, radars,
and electric motors.
• The inductance is measured in Henrys (H)
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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An inductor consists of a
coil of conducting wire.
Inductance is the property whereby an inductor exhibits
opposition to the change of current flowing through it,
measured in henrys (H).
L is the inductance of the coil
N is the number of turns,
is the length,
A is the cross-sectional area.
is the permeability of the core.
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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The voltage-current relationship for equation
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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The current-voltage relationship for equation
is
OR
i(t0) is the total current for − < t < t0
i(− ) = 0. (because there must be a
time in the past when there was no
current in the inductor.
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Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Series combinations
v1
v2
v3
v
v1 = L1
di
dt
i
di
v2 = L2
dt
v3 = L3
v = v1 + v2 + v3 = ( L1 + L2 + L3 )
Leq = L1 + L2 + L3 +
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
di
dt
di
dt
+ Ln
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Parallel Combinations
i
i2
i1
i1(to)
v
i3
i2(to)
1 1
1
i = i1 + i2 + i3 =
+ +
L1 L2 L3
1
i=
Leq
t
to
i3(to)
t
to
vdt + i (to )
1
1 1
1
= + +
Leq L1 L2 L3
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
1 t
i1 (t ) =
vdt + i1 (to )
t
L1 o
1 t
i2 (t ) =
vdt + i2 (to )
t
L2 o
1 t
i3 (t ) =
vdt + i3 (to )
t
L3 o
vdt + i1 (to ) + i2 (to ) + i3 (to )
1
1 1
1
= + + +
Leq L1 L2 L3
1
+
Ln
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Example
Find Lab?
Leq1 = 20 // 30 = 12 H
Leq 2 = 12 + 8 = 20 H
a
5H
14 H
15 H
b
60 H
80 H
10 H
30 H
20 H
8H
Leq 3 = 20 // 80 = 16 H
Leq 4 = 14 + 16 = 30 H
Leq 5 = 30 // 60 = 20 H
Lab = 10 + 5 = 15 H
Leq 6 = 10 + 20 = 30 H
Leq 7 = 30 // 15 = 10 H
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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Example
Find Cab?
Ans. :
6 µF × 4µF
= 2.4 µF
4 µF + 6 µF
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT708: Electronics for Biotechnology
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