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* ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY 3.3 Treating Voltage Sources in Nodal Analysis 1、Accompanied Voltage Sources 2、Unaccompanied Voltage Sources 1) Only an Unaccompanied Voltage Source in a Circuit 2) Two or More Unaccompanied Voltage Sources in a Circuit Contents FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY CASE 1 Accompanied Voltage Sources Source Transformation Approach Accompanied Voltage Sources 1/18 FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY Accompanied Voltage Sources Example 1 Use nodal analysis to find current and voltage in the circuit of Fig.1. Solution Fig.1 (1) (2) (3) 2/18 a b ● ● FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY Accompanied Voltage Sources Solving for gives Hence 3/18 FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY CASE 2 Unaccompanied Voltage Sources Only an Unaccompanied Voltage Source in a Circuit SUBCASE1 Approach Assign the One Polarity of the Voltage Source as the Reference Node Unaccompanied Voltage Sources / Subcase 1 4/18 FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY Unaccompanied Voltage Sources / Subcase 1 Example 2 For the circuit shown in Fig.2,find the four node voltages , , , . Solution Fig.2 5/18 (1) (2) (3) Equations for the Nodes 3 and 4: Auxiliary Equations: ● ● ● ● ● 1 2 3 4 0 FUNDAMENTALS OF ELECTRIC CIRCUITS ELECTRICAL ENGNEERING SCHOOL OF WUHAN UNIVERSITY Unaccompanied Voltage Sources / Subcase 1 From Eqs.(1) ,(2)and(3) we obtain , Applying KVL around the left loop gives By voltage division, we get 6/18 FUNDAMENTALS OF ELECTRIC