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Resistive Network Analysis By KCL

This chapter covers the analysis of resistive networks using Kirchhoff's Current Law (KCL), nodal analysis, mesh analysis, Thevenin's theorem, Norton's theorem, and the principles of superposition. It also explores the effects of source loading and includes practical examples.

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Resistive Network Analysis By KCL

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  1. 3 C H A P T E R Resistive Network Analysis

  2. By KCL : i – i – i = 0. In the node 1 2 3 voltage method, we express KCL by v – v v – v v – v a b b c b d – – = 0 R R R 2 1 3 R R v 1 3 b v v a d i i i 1 2 3 R 2 v c Figure 3.2 Use of KCL in nodal analysis

  3. Node a Node b R 2 i R R 1 3 S Node c v v a b R 2 i i 2 i 1 i 3 S i R R 1 3 S v = 0 c Figure 3.3 Illustration of nodal analysis

  4. Node 1 R 3 R 2 R R 1 4 I I 2 1 Node 2 R 3 R 2 R R 4 1 I I 2 1 Figure 3.5

  5. v v v R R a b c 1 3 + v R R i _ S 2 4 S Figure 3.8 Nodal analysis with voltage sources

  6. R R 1 3 + _ v i R i R 1 2 S 2 4 Figure 3.12 A two-mesh circuit

  7. Mesh 1: KVL requires that i R v v v v , – – = 0, where = 1 S 1 2 1 1 v ) R . i – i = ( 2 1 2 1 R R 3 1 + – v 1 + + v _ i v i R R 2 S 1 2 2 4 – Figure 3.13 Assignment of currents and voltages around mesh 1

  8. Mesh 2: KVL requires that v + v + v = 0 2 3 4 where v = ( i – i ) R , 2 2 1 2 v = i R , 3 2 3 v = i R 4 2 4 R R 1 3 + – v 3 – + + v i R v i R v _ S 1 2 2 4 2 4 + – Figure 3.14 Assignment of currents and voltages around mesh 3

  9. 5 2 + 10 V 2 A 4 + v _ i x i 1 2 – Figure 3.18 Mesh analysis with current sources

  10. + + _ _ = + v v B 2 B 2 R R R i i i B 1 B 2 + + _ _ v v B 1 B 1 The net current through R is the sum of the in- dividual source currents: . i + i = i B 1 2 B Figure 3.26 The principle of superposition

  11. 1.In order to set a voltage source equal to zero, we replace it with a short circuit. R R 1 1 + v i R i R _ S S S 2 2 A circuit The same circuit with v = 0 S 2. In order to set a current source equal tozero, we replace it with an open circuit. R R 1 1 + + v i v R R _ _ S S S 2 2 A circuit The same circuit with i = 0 S Figure 3.27 Zeroing voltage and current sources

  12. i + Linear v network – i Figure 3.28 One-port network

  13. i + + v v R R R _ S 1 2 3 – Source Load Figure 3.29 Illustration of equivalent-circuit concept

  14. Figure 3.31 Illustration of Thevenin theorum i i R T + + + Load Source Load v v v _ T – –

  15. i i Load Load + + Source i R v v N N – – – Figure 3.32 Illustration of Norton theorum

  16. R 3 a R R 1 2 b R 3 a || R R R 2 1 T b Figure 3.34 Equivalent resistance seen by the load

  17. What is the total resistance the i current will encounter in flowing S around the circuit? R a 3 + R R v i x S 1 2 – b R 3 R R i i 1 2 S S R = R || R + R T 1 2 3 Figure 3.35 An alternative method of determining the Thevenin resistance

  18. R R 3 1 i L + v R R S 2 _ L Figure 3.46

  19. R R 3 1 + + v v O C S R 2 _ – Figure 3.47

  20. R R 1 3 + – + 0 V + + v R v v O C 2 O C S _ – – i Figure 3.48

  21. R R R + R || R 1 3 3 1 2 i i L L R + + v R v R 2 R _ _ S 2 S L L R + R 1 2 A circuit Its Th é venin equivalent Figure 3.49 A circuit and its Thevenin equivalent

  22. One-port i SC network i R = R i SC N T N Figure 3.57 Illustration of Norton equivalent circuit

  23. Short circuit replacing the load v R R 3 1 R i + v 2 S S C _ i i 1 2 Figure 3.58 Computation of Norton current

  24. R T One-port v + i R T network N T _ Th é venin equivalent Nortonequivalent Figure 3.63 Equivalence of Thevenin and Norton representations

  25. R R 1 3 + v R i _ S 2 SC R 3 v S i R R 1 2 SC R 1 Figure 3.64 Effect of source transformation

  26. Node a a a a R + or or R i i R v _ S S S + v _ S b b b Node b The venin subcircuits é Norton subcircuits Figure 3.65 Subcircuits amenable to source transformation

  27. a Unknown Load network b An unknown network connected to a load a A Unknown network i “ ” r SC m b Network connected for measurement of short- circuit current a + Unknown V v r “ ” network m O C – b Network connected for measurement of open- circuit voltage Figure 3.71 Measurement of open-circuit voltage and short-circuit current

  28. Practical source R L Load R T + v R _ T L i L Source equivalent , what value of Given v and R R T T L will allow for maximum power transfer? Figure 3.73 Power transfer between source and load

  29. v + – i n t R T + v R _ T L i Source Load i + i n t i v R R N L T – Source Load Figure 3.74 Source loading effects

  30. Nonlinear element as a load. We wish to solve for v and i . x x R T i x + Nonlinear + v v _ x element T – Figeure 3.77 Representation of nonlinear element in a linear circuit

  31. i X v T v 1 T R Load-line equation: i = – v + T x R R x T T – 1 R T v v T x Figure 3.78 Load line

  32. i x curve of i-v “ exponential resistor ” v T R v T i = I e , v > 0 o Solution v 1 T Load-line equation: i = v + x x R R T T v v T x Figure 3.79 Graphical solution equations 3.48 and 3.49

  33. R T i i x x + + Linear Nonlinear + Nonlinear v v v network _ x load x load T – – Figure 3.80 Transformation of nonlinear circuit of Thevenin equivalent

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