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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 1 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I C H A P T E R 3 Resistive Network Analysis

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 2 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.2 Use of KCL in nodal analysis

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 3 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.3 Illustration of nodal analysis Va/R1+(Va-Vb)/R2 =Is Vb/R3+(Vb-Va)/R2=0 Or Va(1/R1+1/R2)+Vb(-1/R2)=Is Va(-1/R2) +Vb(1/R2+1/R3)=0 or, in matrix form

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 4 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.5 Example 3.1 R1=1K, R2=2K, R3=10K,R4=2K I1=10mA, I2=50mA, V1/R1+(V1-V2)/R2+(V1-V2)/R3=I1 V2/R4+(V2-V1)/R2+(V2-V1)/R3=-I2 Or (1/R1+1/R2+1/R3)V1+ (-1/R2-1/R3)V2=I1 (-1/R2-1/R3)V1 + (1/R2+1/R3+1/R4)V2= I2 Plugging the numbers 1.6 V1- 0.6 V2=10 -0.5V1 +1.1 V2=-50 By solving the above Eq. V1=-13.57 V2=-52.86

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 5 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.8 Nodal analysis with voltage sources Va=Vs (Vs-Vb)/R1-vb/R2-(Vb-Vc)/R3=0 (Vb-Vc)/R3+Is-Vc/R4=0 Or (1/R1+1/R2+1/R3)Vb+(-1/R3)Vc=Vs/R1 (-1/R3)Vb+ (1/R3+1/R4)Vc=Is Or in Matrix form

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 6 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.13 Assignment of currents and voltages around mesh 1 R 3 R 4 v S R 1 R 2 + _i 1 i 2 v 2 v 1 +– + – Mesh 1: KVL requires that v S – v 1 – v 2 = 0, where v 1 = i 1 R 1, v 2 = ( i 1 – i 2 )R 1.

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 7 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.14 Assignment of currents and voltages around mesh 3

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 8 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.12 A two-mesh circuit R 3 R 4 v S R 1 R 2 + _ i 1 i 2 I1R1+(I1-I2)R2=Vs (I2-I1)R2 + I2R3 + I2R4=0 Or The advantage of Mesh Current Method is that it uses resistances in the equations, rather than conductances. But Node Voltage Method is physically more sensible.

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 9 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.18 Mesh analysis with current sources 2 4 10 V 5 2 A i 1 v x i 2 + _ + – 5I1 +Vx =10 -Vx+2I2+4I2=0 I1-I2=2 Adding Eqs. 1 and 2 will delete Vx 5I1 +6 I2 =10 I1-I2=2 I1=2 A I2=0 P3.1-3.20

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 10 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.26 The principle of superposition R v B2 + _ + _ v B1 i = R + _ v B 1 i B 1 The net current through R is the sum of the in- dividual source currents: i = i B1 +i B 2. R v B 2 + _ i B2 +

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 11 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.27 Zeroing voltage and current sources

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 12 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.28 One-port network Linear network i v + – i

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 13 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.29 Illustration of equivalent-circuit concept R 3 + _ v S R 2 i v + – R 1 LoadSource

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 14 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.31 Illustration of Thevenin theorum i i Load v + – Source Load v + – + _ R T v T

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 15 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.32 Illustration of Norton theorem v + – R N i N i v + Source – – i Load

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 16 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.34 Equivalent resistance seen by the load

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 17 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.35 An alternative method of determining the Thevenin resistance R 2 a b R 3 R 1 v x + – i S R 3 R T =R 1 ||R 2 + R 3 R 1 i S R 2 i S What is the total resistance the current i S will encounter in flowing around the circuit?

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 18 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.46 R 2 R 1 + _ v S R L R 3 i L

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 19 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.47 R 1 + _ v S R 3 R 2 v O C + –

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 20 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.48 R 1 + _ v S R 3 R 2 v OC + – v OC + – +– 0V i

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 21 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.49 A circuit and its Thevenin equivalent

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 22 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.57 Illustration of Norton equivalent circuit i SC i N R T =R N i One - port network

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 23 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.58 Computation of Norton current R 2 R 1 + _ v S R 3 i SC i 1 i 2 Short circuit replacing the load v

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 24 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.63 Equivalence of Thevenin and Norton representations

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 25 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.64 Effect of source transformation R 2 R 1 v S R 3 i SC + _ R 3 R 2 v S i R 1 R 1

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 26 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.65 Subcircuits amenable to source transformation

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 27 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.71 Measurement of open-circuit voltage and short-circuit current

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 28 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.73 Power transfer between source and load

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 29 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.74 Source loading effects v T v int + _ R L +– R T i i N vR L + – i int R T SourceLoad SourceLoad

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 30 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.77 Representation of nonlinear element in a linear circuit R T + _ i x v T v x + – Nonlinear element Nonlinear element as a load. We wish to solve for v x andi x.

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 31 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.78 Load line i X v x 1 R T Load-line equation:i x =– v T R T v x + v T –1 R T v T R T

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 32 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.79 Graphical solution equations 3.48 and 3.49 i x v x i=I o e v,v > 0 i-v curve of “exponential resistor ” Solution 1 R T Load-line equation:i x = v T R T v x + v T R T v T

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© The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 33 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 3.80 Transformation of nonlinear circuit of Thevenin equivalent i x v x + – Linear network load R Nonlinear T + _ v T v x + – i x load Nonlinear

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