Introduction to Electrical Systems Course Code: EE 111 Course Code: - - PowerPoint PPT Presentation

Introduction to Electrical Systems Course Code: EE 111 Course Code: EE 111 Department: Electrical Engineering Department: Electrical Engineering Instructor Name: B G Fernandes Instructor Name: B.G. Fernandes E‐mail id: bgf @ee iitb ac in E‐mail id: bgf @ee.iitb.ac.in

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 1/20

Sub‐Topics:

• Basic circuit elements
• Circuit laws.
• Series, parallel connections, Y‐Δ, Δ‐Y transformations

EE 111: Introduction to Electrical Systems B.G.Fernandes Mon, July 27 2009

Lecture 2 2/20

Review of DC Circuit Analysis & Network Theorems: Electric Circuit Closed path composed of active & passive elements

⇒

passive elements. Active Elements Capable of delivering power to

⇒

p g p some external device Two types Independent source Dependent source Independent source Independent V source Independent I source

Mon, July 27 2009

Independent I source

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 3/20

Independent V source Terminal V is INDEPENDENT f I fl i th h it

• f I flowing through it.

Non‐ideal Ideal

⇒ Battery ⇒ Battery

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 4/20

Independent I source : I is independent of ‘V’ it across it Dependent source: Source quantity depends on either ‘V’

Ideal Non‐ideal

• r ‘I’ existing at some other location in the circuit.

I I β

V V ∝

2 1

c b

I I β = vbe

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 5/20

Dependent V source : Voltage VX depends on either V1 or I1.

x

v k V =

1 1

k I

I dependent V source V dependent V source gain

k I =

2 1

I dependent V source

Some other part of circuit

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 6/20

Dependent I source: Current Ix depends on V1 I

• r I1

X

I k V =

3 1

V dependent I source k I =

4 1

I dependent I source

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 7/20

Passive Elements: bl f Capable of receiving power Can not independently deliver the energy R L & C

⇒ ⇒ ⇒ R, L & C ⇒

Resistor V

IR =

I GV =

• r

Conductance ‘Mho’ Power absorbed = V2/R or I2R W

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 8/20

Inductor:

di v L v L dt =

1 W LI =

2

1 2

Stores energy in the magnetic field

⇒

Requires very high ‘V’ Stores energy in the magnetic field I can not change instantaneously

⇒ ⇒

Requires very high V

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 9/20

Capacitor:

v idt C =

∫

1 C ∫

W CV 2 1 W CV =

2

2 ‘V’ cannot change instantaneously Requires very high I

⇒ ⇒

Requires very high I

⇒

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 10/20

Types of Electric circuits:

Active Network contains at least one active

⇒

element Passive network does not contain any active l

⇒

element

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 11/20

Terminologies used in Electric circuits:

Node: Point to which two or more circuit elements Node: Point to which two or more circuit elements are joined (a, b, c, d) Junction: Point in a network when 3 or more circuit elements are joined (b&d) Branch: Part of the circuit lies between two junction points (abd bcd) points (abd, bcd) Loop: Any closed path of network Loop: Any closed path of network (abda, bcdb, abcda) Mesh: Loop does not contain other loop within it

Mon, July 27 2009

Mesh: Loop does not contain other loop within it.

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 12/20

Mesh I That I which flows around the perimeter. Clockwise is +ve

⇒

Circuit Laws: Circuit Laws:

Kirchhoff’s Voltage law: In any closed path

V

∑

rise = fall

V

∑

V

∑

rise = fall

V

∑

V drop +ve V i

⇒

V rise ‐ve

Kirchhoff’s Current law: At any node

⇒

y

I

∑

Entering = Leaving

I

∑

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 13/20

Series Connection: When I flowing is same & there should b h be one mesh Parallel connection: ‘V’ across is same & connected across Parallel connection: V across is same & connected across the same node R 50Ω e.g: Req = 50Ω

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 14/20

Can not be resolved by series – parallel cobination.

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 15/20

Star – Delta (Y‐ Δ) transformation:

⇔

Nodes are unaffected

⇒

Equivalent resistance between any two terminals is same

⇒

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 16/20

Delta – Star transformation (Δ – Y) transformation: Rab is measured by applying V across AB, keep ‘C’ open

1 2 3 1 2 3

( ) ( )

b

R R R R R R R + = + =

• 1

2 3 1 2 3

( )

ab

R R R R R R R

Δ

+ + +

• ab

a b Y

R R R = +

Mon, July 27 2009

ab a b Y

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 17/20

1 2 3

( )

a b

R R R R R + + =

3 1 2

( )

b c

R R R R R + = +

• 1

2 3 a b

R R R + +

3 1 2 b c 2 1 3

( )

c a

R R R R R + = +

• 1

2 1 2 3 a

R R R R R R ∴ = + +

1 3 1 2 3 b

R R R R R R = + +

2 3 1 2 3 c

R R R R R R = + +

Any resistance of Y circuit = product of two adjacent Δ resistances / sum of 3 Δ resistances resistances / sum of 3 Δ resistances

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 18/20

Y‐ Δ transformation:

⇒

a c b b

R R R R = +

1 3

R R R

b ca b Y a c

R R R R

−

+ +

1 3 1 3 b ca

R R R

− Δ =

+

a b b c a c a c

R R R R R R R R + + = +

1 3

1 1

a c a b b c a c

R R R R R R R R R R + ∴ + = + +

Mon, July 27 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 19/20

1 1

a b

R R + + =

similarly

2 3 a b b c c a

R R R R R R R R + = + +

similarly 1 1 R R +

1 2

1 1

b c a b b c c a

R R R R R R R R R R + ⇒ + = + +

1 a b b c c a c

R R R R R R R R + + =

R R R R R R + + R R R R R R + +

2 a b b c c a b

R R R R R R R R + + =

3 a b b c c a a

R R R R R R R R + + =

R i t f Y i it S f ll d t f ll Resistance of Y circuit = Sum of all products of all possible pairs of the Y resistance/opposite resistance

• f Y

⇒

Mon, July 27 2009

• f Y

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 2 20/20