EE101 - Electrical Sciences

S. Sivasubramani

Assistant ProfessorElectrical Engineering Department

Indian Institute of Technology Patna

Introduction

In EE101, you will learn

I Circuit analysis techniques with DC as well as Sinusoidalinput.

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 anamplifier

I Operational amplifier(Op-amp) and its applications

I Digital circuit design

I Magnetic circuits, Transformers and its equivalent circuitmodel.

This course is very important for EE students.For non EE students, the techniques and models used here willhelp you solve problems in your domain.

Basic DefinitionsI Electric circuit : It is an interconnection of electrical

components.I Electric current : It is time rate of change of charge.

i =dq

dt

It is measured in Ampere (A).

1 A = 1 coulomb/second

t

I

(a) Direct current

t

i

(b) Alternating current

Figure: Types of Current

I Voltage (Potential difference): It is the energy required tomove 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

dt=

dw

dq

dq

dt= v i

It is measured in watts (W).

1 watts = 1 joule/second

The power is the product of voltage across an element and thecurrent 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, pis negative and the element is delivering power.

−

+

v

i

(a) p = vi > 0

−

+

v

i

(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 generatingenergy. Instead they can either absorb or store energy.Example: Resistors, Inductors, Capacitors.

Active elements are modeled as either voltage source or currentsource.

The voltage and current sources are further classified intoindependent and dependent sources.

Ideal Independent Voltage Source

It is an active element that maintains its terminal voltage constantirrespective of current it supplies.

Example : Batteries and Generators

+−V

(a)

V

(b)

Figure: Symbols

v

i

V

Figure: i-v characteristics

Test yourself

Draw the i − v characteristics.

+−V

R

i

+

−

v v

i

−VR

V

Slope = 1R

Ideal Independent Current Source

It is an active element that supplies a certain current irrespectiveof its terminal voltage.

Example : Solar cells

I

Figure: Symbolv

i

I

Figure: i-v characteristics

Test yourself

Draw the i − v characteristics.

I

i

+

−

vR v

i

−I

I × R

Slope = 1R

Ideal Dependent Voltage Source

An ideal dependent or controlled voltage source is an activeelement. However its terminal voltage is controlled by anothervoltage 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)

B

−

+

vi

A

D

+−vo

C

vo = kvi

2. Current Controlled Voltage Source (CCVS)

B

ii

A

D

+−vo

C

vo = rmii

Ideal Dependent Current Source

An ideal dependent or controlled current source is an activeelement. However its current is controlled by another voltage orcurrent

i

Figure: Symbol

There are two types

1. Voltage Controlled Current Source

2. Current Controlled Current Source

1. Voltage Controlled Current Source (VCCS)

B

−

+

vi

A

C

io

D

io = gmvi

2. Current Controlled Current Source (CCCS)

B

ii

A

C

io

D

io = kii

Resistor

R

+ −v

i

By Ohm’s Law,v = iR

Where R is the resistance in Ω.

v

i

Slope = 1R

Figure: i − v characteristics

When R = 0,

v = iR

v = 0

It acts as a short circuit.

i

v = 0 R = 0

+

-

When R =∞,

v = iR

i = 0

It acts as an open circuit.

i

v R =∞

+

-

= 0

Inductor

L

+ −v

i

The voltage across an inductor using passive sign convention is

v = Ldi

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 changeinstantaneously.

Test yourselfDraw the voltage across an inductor if the current through theinductor is

t

i

t

v

Capacitor

C

+ −v

i

The voltage across a capacitor using passive sign convention is

i = Cdv

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 changeinstantaneously.

Test yourselfDraw the current through a capacitor if the voltage across thecapacitor is

t

v

t

i

BranchIt is an element. It can be either voltage source or current sourceor resistor.

NodeIt 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 ifit does not contain any other loop inside.

The number of independent loops (l) in a network can be found asgiven 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 closedboundary is zero.

i1

i2i3

i4 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.

VA

+ −v1

VB

+− v2

−VA + v1 + VB + v2 = 0

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 SeriesBy Ohm’s law,

V1 = IR1, V2 = IR2

By KVL,

V = V1 + V2

V = I (R1 + R2) = IReq

where Req = R1 + R2.

+−V

IR1

+ −V1

R2

+ −V2

If N resistors are connected in series,

Req = R1 + R2 + · · ·+ RN

I =V

R1 + R2

V1 =R1

R1 + R2V , V2 =

R2

R1 + R2V

Elements in Parallel

By Ohm’s law,

V = I1R1 = I2R2

I1 =V

R1, I2 =

V

R2

By KCL,

I = I1 + I2

I =V

R1+

V

R2=

V

Req

where Req =R1R2

R1 + R2.

+−V

I

R1

I1

R2

I2

I1 =R2

R1 + R2I

I2 =R1

R1 + R2I

If N resistors are connected in parallel,

1

Req=

1

R1+

1

R2+ · · ·+ 1

RN