EE101 - Electrical Sciences
S. Sivasubramani
Assistant Professor
Electrical Engineering Department
Indian Institute of Technology Patna
Introduction
In EE101, you will learn
I
Circuit analysis techniques with DC as well as Sinusoidal
input.
I
Transient analysis of First order and second order circuits
I
Diode and its applications
I
Bipolar Junction Transistor (BJT) and how it is used as an
amplifier
I
Operational amplifier(Op-amp) and its applications
I
Digital circuit design
I
Magnetic circuits, Transformers and its equivalent circuit
model.
This course is very important for EE students.
For non EE students, the techniques and models used here will
help you solve problems in your domain.
Basic Definitions
I
I
Electric circuit : It is an interconnection of electrical
components.
Electric current : It is time rate of change of charge.
dq
i=
dt
It is measured in Ampere (A).
1 A = 1 coulomb/second
I
i
t
t
(a) Direct current
(b) Alternating current
Figure: Types of Current
I
Voltage (Potential difference): It is the energy required to
move a unit charge through an element.
v=
dw
dq
It is measured in volts (V).
1 volt = 1 joule/ coulomb
Like electric current, there are DC voltage and AC voltage.
I
Power: It is the time rate of expending or absorbing energy.
p=
dw
dw dq
=
=v i
dt
dq dt
It is measured in watts (W).
1 watts = 1 joule/second
The power is the product of voltage across an element and the
current through the element.
I If the product is positive, the element is absorbing power.
I If the product is negative, the element is delivering power.
By passive sign convention
1. If the current enters the positive terminal of voltage polarity,
p is positive and the element is absorbing power.
2. If the current leaves the positive terminal of voltage polarity, p
is negative and the element is delivering power.
i
i
+
+
v
v
−
−
(a) p = vi > 0
(b) p = vi < 0
Figure: Passive sign convention
Circuit Elements
There are two types of elements.
1. Active elements : They are capable of generating energy.
Example : Generators and Batteries.
2. Passive elements : They are not capable of generating
energy. Instead they can either absorb or store energy.
Example: Resistors, Inductors, Capacitors.
Active elements are modeled as either voltage source or current
source.
The voltage and current sources are further classified into
independent and dependent sources.
Ideal Independent Voltage Source
It is an active element that maintains its terminal voltage constant
irrespective of current it supplies.
Example : Batteries and Generators
i
−
+
V
V
V
(a)
v
(b)
Figure: Symbols
Figure: i-v characteristics
Test yourself
Draw the i − v characteristics.
i
i
+
R
v
−
+
V
v
V
Slope =
−
− VR
1
R
Ideal Independent Current Source
It is an active element that supplies a certain current irrespective
of its terminal voltage.
Example : Solar cells
i
I
I
v
Figure: Symbol
Figure: i-v characteristics
Test yourself
Draw the i − v characteristics.
i
i
+
I ×R
I
R
v
v
Slope =
−
−I
1
R
Ideal Dependent Voltage Source
An ideal dependent or controlled voltage source is an active
element. However its terminal voltage is controlled by another
voltage or current
−
+
v
Figure: Symbol
There are two types
1. Voltage Controlled Voltage Source
2. Current Controlled Voltage Source
1. Voltage Controlled Voltage Source (VCVS)
A
C
+
vo
−
+
vi
−
B
D
vo = kvi
2. Current Controlled Voltage Source (CCVS)
A
C
vo
B
−
+
ii
D
vo = rm ii
Ideal Dependent Current Source
An ideal dependent or controlled current source is an active
element. However its current is controlled by another voltage or
current
i
Figure: Symbol
There are two types
1. Voltage Controlled Current Source
2. Current Controlled Current Source
1. Voltage Controlled Current Source (VCCS)
A
+
vi
C
io
D
−
B
io = gm vi
2. Current Controlled Current Source (CCCS)
A
C
ii
io
D
B
io = kii
Resistor
R
i
+
v
−
By Ohm’s Law,
v = iR
Where R is the resistance in Ω.
i
Slope =
v
Figure: i − v characteristics
1
R
When R = 0,
+ i
v = iR
v =0 R=0
v =0
-
It acts as a short circuit.
When R = ∞,
+
i=0
v = iR
v R=∞
i =0
It acts as an open circuit.
-
Inductor
i
+
L
−
v
The voltage across an inductor using passive sign convention is
v =L
di
dt
where L is the inductance in henry (H).
The important properties of an inductor
1. An inductor acts like a short circuit to DC.
2. The current through an inductor can not change
instantaneously.
Test yourself
Draw the voltage across an inductor if the current through the
inductor is
i
t
v
t
Capacitor
C
i
−
+
v
The voltage across a capacitor using passive sign convention is
i =C
dv
dt
where C is the capacitance in farad (F).
The important properties of a capacitor
1. A capacitor acts like an open circuit to DC.
2. The voltage across a capacitor can not change
instantaneously.
Test yourself
Draw the current through a capacitor if the voltage across the
capacitor is
v
t
i
t
Branch
It is an element. It can be either voltage source or current source
or resistor.
Node
It is a point at which two or more branches are connected.
Loop
It is a closed path in a circuit. A loop is said to be independent if
it does not contain any other loop inside.
The number of independent loops (l) in a network can be found as
given below.
l =b−n+1
where b and n are branches and nodes of the network respectively.
Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
The algebraic sum of currents entering a node or a closed
boundary is zero.
i1
i3
i4
i2
i1 − i2 + i3 − i4 = 0
i1 + i3 = i2 + i4
KCL is based on conservation of charge.
KCL is true only when
1. there is no net charge accumulation at a node
2. the charge moves instantaneously
Kirchhoff’s Voltage Law (KVL)
The algebraic sum of voltages around a cosed path or loop is zero.
+
−
v1
VA
−VA + v1 + VB + v2 = 0
VB
−
v2
+
VA = v1 + VB + v2
KVL is based on conservation of energy.
KVL is true only when
1. there is no flux cutting the loop i.e., a conservative field.
Elements in Series
By Ohm’s law,
V1 = IR1 ,
V2 = IR2
R1
I
+
By KVL,
V
−
+
V = V1 + V2
V1
V = I (R1 + R2 ) = IReq
where Req = R1 + R2 .
If N resistors are connected in series,
Req = R1 + R2 + · · · + RN
I =
V1 =
V
R1 + R2
R1
V,
R1 + R2
V2 =
R2
V
R1 + R2
R2
−
+
V2
−
Elements in Parallel
By Ohm’s law,
I
V = I1 R1 = I2 R2
V
,
R1
I2 =
V
R2
V
−
+
I1 =
I1
R1
By KCL,
I = I1 + I2
I =
V
V
V
+
=
R1 R2
Req
R1 R2
.
R1 + R2
If N resistors are connected in parallel,
where Req =
I1 =
R2
I
R1 + R2
I2 =
R1
I
R1 + R2
1
1
1
1
=
+
+ ··· +
Req
R1 R2
RN
I2
R2