Subject Cover for all common I-B.Tech.

1. Rajeev Gandhi Memorial College of
Engineering & Technology (Autonomous)
I-B.Tech., I-Semester
BASIC ELECTRICAL ENGINEERING
UNIT I : DC & AC Circuits
Dr.D.Lenine
Professor, Dept. of EEE
RGMCET, Nandyal

2. Syllabus
 Electrical Circuit Elements : R, L and C
 Ohm’s Law and its Limitations
 KCL & KVL
 Series, Parallel, Series-Parallel Circuits
 Super Position Theorem
 Simple Numerical Problems
DC
Circuits
 A.C. Fundamentals:
Equation of AC Voltage and current, Waveform, Time Period, Frequency, Amplitude, Phase,
Phase Difference, Average Value, RMS value, Form Factor, Peak Factor
 Voltage and Current Relationship With Phasor Diagrams in R, L, and C circuits
 Concept of Impedance, Active Power, Reactive Power and Apparent Power
 Concept of Power Factor
 Simple Numerical Problems
AC
Circuits
UNIT 1 : DC & AC Circuits

3. An Electrical Circuit is an interconnection of various circuit
elements where there is at least one closed path in which
current can flow. These circuit elements are categorized in to
Two types:
i. Active Elements
ii. Passive Elements
Electrical
Circuit
An Active Element is a circuit element which is capable of Supplying or Amplifying
Electrical Energy to the circuit connected.
Examples: Voltage Source, Current Source, Battery, Generator,
Transistor( BJT, FET), Op-Amps etc.
Active
Elements
A Passive Element is a circuit element which Dissipates or Stores the Electrical Energy.
Examples: Resistance (R), Inductance (L), Capacitance (C)
Passive
Elements
Definition of Electrical Circuit, Active Element & Passive Element D.C. Circuits
Flow of Energy
Active
Element
Passive
Element
Connecting
Wires

4. Active Element & Its Types D.C. Circuits
 Active elements are the elements of a circuit which
possess energy of their own and can impart it to other
element of the circuit.
 Active elements are of two types:
i. Voltage source
ii. Current source
A Voltage Source has a specified voltage across
its terminals, independent of current flowing
through it.
A Current Source has a specified current through
it independent of the voltage appearing across it.
Voltage
Source
Current
Source
Types of Active elements
+
_
D.C. Voltage Source D.C. Current Source
A.C. Voltage Source
Battery
+
_
A.C. Current Source
VDC IDC VDC
VAC IAC

5. Active Elements Types D.C. Circuits
VDC
t
V
+
_
VDC
D.C Voltage Source (or) Battery
IDC
t
I
IDC
D.C Current Source
The source in which voltage is constant (or) not
varying w.r.t time are known as D.C Voltage source.
The source in which current is constant (or) not
varying w.r.t time are known as D.C Current source.

6. Active Elements Types D.C. Circuits
Vm
-Vm
VAC
t
0
VAC
A.C Voltage Source
Im
-Im
IAC
t
0
IAC
A.C Current Source
The source in which voltage is not constant (or)
varying w.r.t time are known as A.C. Voltage
source.
The source in which current is not constant (or)
varying w.r.t time are known as A.C. Current
source.

7. Passive Elements & Its Types D.C. Circuits
 The Passive elements of an electric circuit do not possess
energy of their own. They receive energy from the Active
Elements. The passive elements are:
i. Resistance (R)
ii. Inductance (L)
iii. Capacitance (C)
 When electrical energy is supplied to a circuit element, it will
respond in one and more of the following ways:
 If the energy is consumed, then the circuit element is a
Pure Resistor.
 If the energy is stored in a magnetic field, the element is
a Pure Inductor.
 If the energy is stored in an electric field, the element is
a Pure Capacitor.
Resistance (R)
(OR)
Capacitor (C)
Inductance (L)
Types of Passive elements

8. Electrical Circuit Elements : Resistance (R) D.C. Circuits
 The property of a material to restrict the flow of electrons
is called resistance, denoted by “R”.
(OR)
 Resistance is that property of a circuit element which
opposes the flow of electric current and in doing so
converts electrical energy into heat energy.
Symbol of Resistance (R)
Unit of resistance is ohm (Ω)
Unit of conductance is mho(Ʊ)

9. Electrical Circuit Elements : Resistance (R) D.C. Circuits
Expression for Power:
 The power absorbed by the resistor is converted to heat is given by:
𝑷 = 𝑽𝑰 = 𝑰𝟐
𝑹 =
𝑽𝟐
𝑹
Watts
Expression for Energy Dissipation:
 Energy lost in a resistance in time “t” is given by :
𝑾 = 𝟎
𝒕
𝑷 . 𝒅𝒕 = 𝐏. 𝐭 = 𝐕. 𝐈. 𝐭 =
𝑽𝟐
𝑹
𝒕 = 𝑰𝟐
𝑹 t Joules
R
I
V
_
+
 According to Ohm’s law, the current is directly proportional to the voltage and inversely
proportional to the total resistance of the circuit.
𝑰 =
𝑽
𝑹
(or) 𝑹 =
𝑽
𝑰
Ohms (Ω)
 Reciprocal of resistance is called as Conductance. It is denoted as “G”.
𝑮 =
𝟏
𝑹
=
𝑰
𝑽
mhos (Ʊ)

10. Electrical Circuit Elements : Inductance (L) D.C. Circuits
Symbol of Inductance (L)
Unit of Inductance is Henry (H)
 Inductance is the property of a material which opposes any
change of magnitude and direction of electric current
passing through conductor.
 A Wire of certain length, when twisted into a coil becomes
a basic inductor.
 If current is made to pass through an inductor, an
electromagnetic field is formed.
 A Change in current produces change in the electromagnetic
field, which induces a voltage across the coil according to
Faraday’s law of electromagnetic induction.

11. Electrical Circuit Elements : Inductance (L) D.C. Circuits
 The amount of total magnetic flux (Ψ) produced by an inductor depends on current (I)
flowing through it and they have linear relationship.
i.e., Ψ α i ⇒ Ψ = L.i
 According to Faraday’s Law of Electromagnetic Induction:
𝑽 =
𝒅𝝍
𝒅𝒕
=
𝒅 𝑳. 𝒊
𝒅𝒕
= 𝑳
𝒅𝒊
𝒅𝒕
Expression for Power:
 Power absorbed by the inductor is given by:
𝑷 = 𝒗. 𝒊 = 𝑳𝒊.
𝒅𝒊
𝒅𝒕
Expression for Stored Energy:
 Energy stored in inductance in time “t” is given by:
𝑾 = 𝟎
𝒕
𝑷. 𝒅𝒕 = 𝟎
𝒕
𝑳𝒊.
𝒅𝒊
𝒅𝒕
. 𝒅𝒕 =
𝟏
𝟐
𝑳𝒊𝟐
i
V _
+
Magnetic Flux ()
L

12. Symbol of Capacitance (C)
Unit of Capacitance is Farad (F)
Electrical Circuit Elements : Capacitance (C) D.C. Circuits
 Any two conducting surfaces separated by an insulating
medium exhibit the property of a Capacitor.
 The conducting surfaces are called electrodes, and the
insulating medium is called dielectric.
 A capacitor stores energy in the form of an electric
field that is established by the opposite charges on
the two electrodes.

13. Electrical Circuit Elements : Capacitance (C) D.C. Circuits
 A Capacitor is said to have greater capacitance if it can store more charge per unit
voltage and capacitance i.e.,
𝒒 𝜶 𝒗 ⟹ 𝒒 = 𝑪. 𝒗
 The current flowing in the circuit is rate of flow of charge:
𝒊 =
𝒅𝒒
𝒅𝒕
=
𝒅 𝑪. 𝒗
𝒅𝒕
= 𝑪
𝒅𝒗
𝒅𝒕
Expression for Power:
 Power absorbed by the Capacitance is given by:
𝑷 = 𝒗. 𝒊 = 𝑪𝒗.
𝒅𝒗
𝒅𝒕
Expression for Stored Energy:
 Energy stored in Capacitance in time “t” is given by:
𝑾 = 𝟎
𝒕
𝑷. 𝒅𝒕 = 𝟎
𝒕
𝑪𝒗.
𝒅𝒗
𝒅𝒕
. 𝒅𝒕 =
𝟏
𝟐
𝑪𝒗𝟐
V
+ _
I
Holes
Electrons
+q -q
C

14. Summary of Electrical Circuit Elements : R, L, C D.C. Circuits
Resistance Inductance Capacitance
Representation R L C
Symbol
Units Ohms (or) Ω Henry (or) H Farad (or) F
Property
Dissipates
Heat Energy
Stores
Magnetic Field
Stores
Electric Field
V-I Equation 𝑽 = 𝑰 ∗ 𝑹 𝒗 = 𝑳 ∗
𝒅𝒊
𝒅𝒕
𝒊 = 𝑪 ∗
𝒅𝒗
𝒅𝒕
I-V Equation 𝑰 =
𝑽
𝑹
𝒊 =
𝟏
𝑳
𝒗 . 𝒅𝒕 𝒗 =
𝟏
𝑪
𝒊 . 𝒅𝒕
Formula
𝑹 =
𝑽
𝑰
𝑳 =
𝒗
𝒅𝒊
𝒅𝒕
𝑪 =
𝒊
𝒅𝒗
𝒅𝒕
Energy Dissipated
(or) Stored 𝑰𝟐
𝑹 𝒐𝒓
𝑽𝟐
𝑹
𝟏
𝟐
𝑳𝒊𝟐
𝟏
𝟐
𝑪𝒗𝟐

15. Ohm’s Law : Definition D.C. Circuits
R
I
V
_
+
 According to Georg Simon Ohm, the voltage “V”
across a resistor (R) is directly proportional to
the current “I” flowing through the resistor
provided the temperature do not change.
i.e., V α I (or) V = R.I
L
A
r
d

Resistance of a Conductor
R = Resistance (Ω)
L = Length of the Conductor (m)
A = Area of Cross Section of Conductor (m2)
ρ = Specific Resistivity of Conductor (Ω - m)
d = Diameter of Conductor (m)
r = Radius of Conductor (m)
 The resistance “R” of a conductor is given by the
equation:
𝐑 = 𝛒 .
𝐋
𝐀
Where,
Area of Cross Section, 𝐀 = 𝛑𝐫𝟐
=
𝛑
𝟒
𝐝𝟐
∵ 𝐫 =
𝐝
𝟐

16.  It is not applicable when the temperature changes, i.e., physical conditions must be
constant.
 It is not applicable for unilateral elements like diodes and transistors as they
allow the current to flow through in one direction only.
 It’s not applicable for non - linear elements.
Ohm’s Law : Limitations D.C. Circuits

17. Network Terminology : Definitions D.C. Circuits
Node:
A Node is that point in a network where two
elements are connected.
Junction:
A Junction is that point in a network where three or
more circuit elements are connected.
 A Node or Junction is denoted as “n”.
V1
R1
+
_ R2
+
_ V2
R3
Node Node
Junction
Junction
V1
R1
+
_
R2
+
_ V2
R3
Node Node
Junction
Junction
B1
B2
B3
B4
B5
Branch:
A Branch is that part of a network which lies between
two nodes. (B1, B2, B3, B4, B5).
 A Branch is denoted as “b”.

18. Network Terminology : Definitions D.C. Circuits
Loop:
A loop is any closed path which originates
from a particular node and terminating at the
same node of a network.
 A Loop is denoted as “l”.
V1
R1
+
_ R2
+
_ V2
R3
Loop 1 Loop 2
 The terms Loop (l), Branch (b) and Node (n) are related using the following equation:
l = b – n + 1

19. Kirchhoff's Laws D.C. Circuits
Gustav Robert Kirchhoff introduced two laws “To write network equations for
a given electric circuit”. These laws are known as:
1. Kirchhoff’s current law (KCL)
2. Kirchhoff’s voltage law (KVL)

20. Kirchhoff's Current Law (KCL) : Statement D.C. Circuits
Kirchhoff’s Current Law (KCL) states that “The algebraic sum of the currents meeting at a
junction in an electrical circuit is zero”.
(OR)
Kirchhoff’s Current Law (KCL) states that “ In an electrical circuit the sum of incoming
currents is equal to sum of outgoing currents at a junction”.
I1 I2
I3
I4
I5
Junction
For Incoming Currents : +Ve Sign
For Outgoing Currents : -Ve Sign
I1 + I4 + I5 = I2 + I3
I1 - I2 - I3 + I4 + I5 = 0
𝒏=𝟏
𝑵
𝑰𝒏 = 𝟎 Where N is the number of branches connected to the Junction and
In is the nth current entering (or leaving) the Junction.

21. Kirchhoff's Voltage Law (KVL) : Statement D.C. Circuits
Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around a loop is
equal to zero.
(OR)
Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltage sources is equal to
algebraic sum of voltage drops that are present in a loop.
𝒏=𝟏
𝑵
𝑽𝒏 = 𝟎
Where N is the number of Elements in a Loop and
Vn is the nth Element Voltage in a Loop.
Vin
R1
+
_ R2
Loop
+
+
_
_
V1
V2
From the circuit diagram: Vin – V1 – V2 = 0
(OR)
Vin = V1 + V2

22. Series Connection of Resistances D.C. Circuits
+ _
V
R1 R3
R2
A B
I I
V1 V2 V3
+ _
V
R eq.
A B
I I

 The circuit in which resistances are connected end to end so that there is only one path
for current to flow is called a Series Circuit.
 Consider three resistances R1, R2, R3 ohms connected in series across a Voltage Source of
“V” volts as shown in above figure.
 There is only one path for current “I” i.e. current is same throughout the circuit.

23. Series Connection of Resistances D.C. Circuits
+ _
V
R1 R3
R2
A B
I I
V1 V2 V3
+ _
V
Req.
A B
I I

According to Ohm’s law, Voltage across the resistances
R1, R2, R3, Req. is written as:
For Resistance R1 ∶ 𝑽𝟏 = 𝑰. 𝑹𝟏
For Resistance R2 ∶ 𝑽𝟐 = 𝑰. 𝑹𝟐
For Resistance R3 ∶ 𝑽𝟑 = 𝑰. 𝑹𝟑
For Resistance Req.: 𝑽 = 𝑰. 𝑹𝒆𝒒.
Apply Kirchhoff’s Voltage Law (KVL)
for the circuit:
V = V1 + V2 + V3 (Eq.1)
Eq.1 is rewritten as:
𝑰. 𝑹𝒆𝒒. = 𝑰. 𝑹𝟏 + 𝑰. 𝑹𝟐 + 𝑰. 𝑹𝟑
𝑰. 𝑹𝒆𝒒. = 𝑰. 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑
𝑹𝒆𝒒. = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑
Where 𝑹𝒆𝒒. = Equivalent resistance

24. Series Connection of Resistances D.C. Circuits
+ _
V
R1 R3
R2
A B
I I
V1 V2 V3
+ _
V
Req.
A B
I I

When a number of resistances are
connected in series, equivalent
resistance (𝑹𝒆𝒒.) is equal to sum of the
individual resistances (𝑹𝟏, 𝑹𝟐, 𝑹𝟑).
𝑹𝒆𝒒. = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑
The main characteristics of a series circuit are :
i. The current in each resistor is the same.
ii. The equivalent resistance in the circuit is equal to the sum of individual resistances.
iii. The total power dissipated in the circuit is equal to the sum of powers dissipated in
individual resistances.
𝐏𝐝𝐢𝐬𝐬𝐢𝐩𝐚𝐭𝐞𝐝 = 𝐏𝑹𝟏
+ 𝐏𝑹𝟐
+ 𝐏𝑹𝟑
= 𝐈𝟐
. 𝐑𝟏 + 𝐈𝟐
. 𝐑𝟐 + 𝐈𝟐
. 𝐑𝟑

25. Parallel Connection of Resistances D.C. Circuits
 When one end of each resistance is joined to a common point and the other end of each
resistance is joined to another common point so that there are many paths for current
flow, it is called a Parallel Circuit.
 Consider three resistances R1, R2 and R3 ohms connected in Parallel across Voltage source of
“V” volts as shown in above figure.
 The Voltage across each resistance is the same (V volts) and Number of Current Paths equal to
Number of Resistances.
 The total current “I” divides into three parts :
“I1 flowing through R1” , “I2 flowing through R2” and “I3 flowing through R3”.
R1
+ _
V
R3
R2
A B
I I
+ _
V
R eq.
A B
I I

I I
I1
I2
I3

26. Parallel Connection of Resistances D.C. Circuits
R1
+ _
V
R3
R2
A B
I I
+ _
V
R eq.
A B
I I

I I
I1
I2
I3
According to Ohm’s law, Current through
resistances R1, R2, R3, Req. is written as:
For Resistance R1 ∶ 𝐈𝟏 =
𝐕
𝐑𝟏
For Resistance R2 ∶ 𝐈𝟐 =
𝐕
𝐑𝟐
For Resistance R3 ∶ 𝐈𝟑 =
𝐕
𝐑𝟑
For Resistance Req.: 𝐈 =
𝐕
𝐑𝒆𝒒.
Apply Kirchhoff’s Current Law (KCL)
for the circuit:
I = I1 + I2 + I3 (Eq.1)
Eq.1 is rewritten as:
𝐕
𝐑𝐞𝐪.
=
𝐕
𝐑𝟏
+
𝐕
𝐑𝟐
+
𝐕
𝐑𝟑
𝐕
𝐑𝐞𝐪.
= 𝐕.
𝟏
𝐑𝟏
+
𝟏
𝐑𝟐
+
𝟏
𝐑𝟑
𝟏
𝐑𝐞𝐪.
=
𝟏
𝐑𝟏
+
𝟏
𝐑𝟐
+
𝟏
𝐑𝟑
Where 𝑹𝒆𝒒. = Equivalent resistance

27. Parallel Connection of Resistances D.C. Circuits
R1
+ _
V
R3
R2
A B
I I
+ _
V
R eq.
A B
I I

I I
I1
I2
I3
When a number of resistances are connected
in parallel, the Reciprocal of Equivalent
Resistance (Req.) is equal to the sum of
the Reciprocals of the Individual
Resistances.
𝟏
𝐑𝐞𝐪.
=
𝟏
𝐑𝟏
+
𝟏
𝐑𝟐
+
𝟏
𝐑𝟑
The main characteristics of a parallel circuit are :
i. The voltage across each resistor is the same.
ii. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the
individual resistances.
iii. The total power dissipated in the circuit is equal to the sum of powers dissipated in
individual resistances.
𝐏𝐝𝐢𝐬𝐬𝐢𝐩𝐚𝐭𝐞𝐝 = 𝐏𝑹𝟏
+ 𝐏𝑹𝟐
+ 𝐏𝑹𝟑
=
𝑽𝟐
𝑹𝟏
+
𝑽𝟐
𝑹𝟐
+
𝑽𝟐
𝑹𝟑

28. Summary Table : Series and Parallel Connection of Resistances D.C. Circuits
Series Connection of Resistances Parallel Connection of Resistances
Same Current flows through each resistance Same Voltage exists across all the resistances in
parallel.
Voltage across each resistance is different Current through each resistance is different
Sum of voltages across all the resistances is
equal to supply voltage.
V= 𝐕𝟏 + 𝐕𝟐 + 𝐕𝟑 + … … + 𝐕𝐧
Sum of currents through all the resistances is equal to
supply current.
I= 𝐈𝟏 + 𝐈𝟐 + 𝐈𝟑 + … … + 𝐈𝐧
Equivalent Resistance is :
𝑹𝒆𝒒 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + … … + 𝑹𝒏
Equivalent Resistance is :
𝟏
𝑹𝒆𝒒
=
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
+ … … +
𝟏
𝑹𝒏
The equivalent resistance is largest than
each of the resistance in series
𝑹𝒆𝒒 > 𝑹𝟏, 𝑹𝒆𝒒 > 𝑹𝟐, … … , 𝑹𝒆𝒒 > 𝑹𝒏
The equivalent resistance is smaller than the smallest of
all the resistances in parallel
+ _
V
R1 Rn
R2
A B
I I
V1 V2 Vn
Rn
R2 B
I I
I
I1
I2
In
+ _
V
R1
A I

29. Series - Parallel Connection of Resistances D.C. Circuits
 From the figure, it is observed that R2 and R3 are connected in parallel with each other
and that both together are connected in series with R1.
 One simple rule to solve such circuits is to first reduce the parallel branches to an
equivalent series branch and then solve the circuit as a simple series circuit.
+ _
V
R1
I1
I2
I3
R2
R3
I1
 As the name suggests, an electrical circuit contains a combination of resistances
connected in series and parallel circuits.

30. Series - Parallel Connection of Resistances D.C. Circuits
+ _
V
R1
I1
I2
I3
R2
R3
I1
Referring to the series-parallel circuit shown in figure:
RP for parallel combination =
𝐑𝟐.𝐑𝟑
𝐑𝟐+ 𝐑𝟑
Total circuit resistance = 𝑹𝟏 +
𝐑𝟐.𝐑𝟑
𝐑𝟐+ 𝐑𝟑
Voltage Across Resistance “R1”= 𝑰𝟏. 𝑹𝟏
Voltage Across Parallel Combination of “R2” & “R3” = 𝑰𝟏.
𝑹𝟐.𝑹𝟑
𝑹𝟐+ 𝑹𝟑

31. In a multisource network consisting of linear bilateral elements, the voltage across or
current flowing through any given element of the network is equal to the algebraic sum of the
voltage across or current flowing through that element produced by each source acting alone,
when all the remaining sources replaced by their respective internal resistances.
Superposition Theorem – Statement D.C. Circuits

32. Explanation of Superposition Theorem D.C. Circuits
+
_
V1
R1 R2
R3
A
B
I
IS
+
_
V1
R1 R2
R3
A
B
IS is Replaced by
Internal Resistance
i.e., Open Circuit
I1
 Consider a network, shown in figure 1, having two voltage
sources V1 and V2.
 The current in resistance R3 which is between terminals A-B,
using superposition theorem is calculated as given below.
Step 1:
Let voltage source V1 is acting alone. At this time, other sources
must be replaced by their internal resistances.
As internal resistance of current source Is is not given, it must
be replaced by Open Circuit (O.C.). Hence the circuit is modified
as shown in figure 2.
Using network techniques, obtain the current flowing through
resistance R3 which is denoted as I1.
Figure 1
Figure 2

33. A
B
V1 is Replaced by
Internal Resistance
i.e., Short Circuit
R1 R2
R3
I2
IS
Step 2:
Let current source Is is acting alone. At this time, other sources
must be replaced by their internal resistances.
As internal resistance of voltage source V1 is not given, it must be
replaced by Short Circuit (S.C.). Hence the circuit is modified as
shown in figure 3.
Using network techniques, obtain the current flowing through
resistance R3 which is denoted as I2.
Explanation of Superposition Theorem D.C. Circuits
Figure 3
Step 3:
According to superposition theorem, the total current (I) through resistance R3 is equal to the
sum of currents ( I1 and I2) through resistance R3, when only one source (either V1 or Is) is
acting alone.
𝑰 𝑽𝟏 𝒂𝒏𝒅 𝑰𝒔 𝒂𝒓𝒆 𝒂𝒄𝒕𝒊𝒏𝒈 𝒔𝒊𝒎𝒖𝒍𝒂𝒕𝒏𝒆𝒐𝒖𝒔𝒍𝒚 = 𝑰𝟏 𝑽𝟏 𝒂𝒄𝒕𝒊𝒏𝒈 𝒂𝒍𝒐𝒏𝒆 + 𝑰𝟐 𝑰𝒔 𝒂𝒄𝒕𝒊𝒏𝒈 𝒂𝒍𝒐𝒏𝒆