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 EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 1/20 2009

Sub ‐ Topics: • Basic circuit elements • Circuit laws. • Series, parallel connections, Y ‐Δ , Δ‐ Y transformations EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 2/20 2009

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 Independent I source EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 3/20 2009

Independent V source Terminal V is INDEPENDENT of I flowing through it. f I fl i th h it Non ‐ ideal Ideal ⇒ Battery ⇒ Battery EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 4/20 2009

Independent I source : I is independent of ‘V’ across it it Ideal Non ‐ ideal Dependent source: Source quantity depends on either ‘V’ or ‘I’ existing at some other location in the circuit. = β β I I I I c b v be ∝ V V 2 1 EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 5/20 2009

Dependent V source : Voltage V X depends on either V 1 or I 1 . = V dependent V source v k V 1 1 x = I dependent V source I dependent V source k I k I 2 1 gain Some other part of circuit EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 6/20 2009

Dependent I source: Current I x depends on V 1 or I 1 I = V dependent I source I k V 3 1 X = k I I dependent I source 4 1 EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 7/20 2009

Passive Elements: ⇒ Capable of receiving power bl f ⇒ Can not independently deliver the energy ⇒ R, L & C ⇒ R L & C = Resistor V IR = I GV or Conductance ‘Mho’ Power absorbed = V 2 /R or I 2 R W EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 8/20 2009

Inductor : di = v v L L dt 1 1 2 = W LI 2 ⇒ ⇒ Stores energy in the magnetic field Stores energy in the magnetic field ⇒ I can not change instantaneously Requires very high ‘V’ Requires very high V EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 9/20 2009

Capacitor : 1 C ∫ ∫ = v idt C 1 CV 2 2 = W W CV 2 ⇒ ‘V’ cannot change instantaneously ⇒ ⇒ Requires very high I Requires very high I EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 10/20 2009

Types of Electric circuits: ⇒ Active Network contains at least one active element ⇒ Passive network does not contain any active element l EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 11/20 2009

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 Mesh: Loop does not contain other loop within it. EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 12/20 2009

Mesh I That I which flows around the perimeter. ⇒ Clockwise is +ve Circuit Laws: Circuit Laws: Kirchhoff’s Voltage law : In any closed path ∑ ∑ ∑ ∑ rise = rise = fall fall V V V V ⇒ V drop +ve ⇒ V i V rise ‐ ve Kirchhoff’s Current law : At any node y ∑ ∑ Entering = Leaving I I EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 13/20 2009

Series Connection: When I flowing is same & there should b be one mesh h Parallel connection: ‘V’ across is same & connected across Parallel connection: V across is same & connected across the same node e.g: R eq = 50 Ω R 50 Ω EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 14/20 2009

Can not be resolved by series – parallel cobination. EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 15/20 2009

Star – Delta (Y ‐ Δ ) transformation: ⇔ ⇒ Nodes are unaffected ⇒ Equivalent resistance between any two terminals is same EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 16/20 2009

Delta – Star transformation ( Δ – Y) transformation: R ab is measured by applying V across AB, keep ‘C’ open + R R ( R ) = + + = � � 1 2 3 R R R R R R R R ( ( ) ) + + Δ ab b 1 1 2 2 3 3 R R R 1 2 3 = + R R R ab ab a a b b Y Y EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 17/20 2009

+ R R ( R ) + = 1 2 3 R R + + a a b b R R R 1 2 3 + = + � R R R ( R R ) b b c c 3 3 1 1 2 2 + = + � R R R ( R R ) c a 2 1 3 R R R R R R ∴ = = = 1 2 2 3 R 1 3 R R + + + + a c + + b R R R R R R R R R 1 2 3 1 2 3 1 2 3 Any resistance of Y circuit = product of two adjacent Δ resistances / sum of 3 Δ resistances resistances / sum of 3 Δ resistances EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 18/20 2009

Y ‐ Δ transformation: ⇒ R R = + + R R a c R R R R Δ = − + 1 1 3 3 b ca b b b R R Y R R − + b ca a c R R 1 3 + + + R R R R R R R R 1 1 ∴ + = = a c a b b c a c + + + R R R R R R R R R R 1 3 a b b c a c a c EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 19/20 2009

+ R R 1 1 + + = = similarly similarly a b + + R R R R R R R R a b b c c a 2 3 + + 1 1 1 1 R R R R ⇒ + = b c + + R R R R R R R R 1 2 a b b c c a + + R R R R R R = a b b c c a R 1 R + + + + c + + + + R R R R R R R R R R R R R R R R R R R R R R R R = = a b b c c a a b b c c a R R 2 3 R R b a ⇒ Resistance of Y circuit = Sum of all products of all R i t f Y i it S f ll d t f ll possible pairs of the Y resistance/opposite resistance of Y of Y EE 111: Introduction to Electrical Systems Mon, July 27 Lecture 2 B.G.Fernandes 20/20 2009