C H A P T E R 3 Resistive Network Analysis

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

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

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

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

Figure 3.12 A two-mesh circuit 4 v S 1 2 + _ i

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

Figure 3.14 Assignment of currents and voltages around mesh 3 2 + _ i – Mesh 2: KVL requires that = 0 where = ( ) , =

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

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

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

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

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

Figure 3.31 Illustration of Thevenin theorum + + Source v Load + v v Load T _ – –

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

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

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

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

Figure 3.47 R 1 + _ v S 3 2 O C –

Figure 3.48 R 1 + _ v S 3 2 O C – V i

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

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

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

Figure 3.63 Equivalence of Thevenin and Norton representations One-port network i N + _ Th é venin equivalent Norton equivalent

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

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

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

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

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

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

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

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

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