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Unformatted text preview: Gj k = Negative of the sum of the conductances directly
connecting nodes k and j , k = j
vk = Unknown voltage at node k
ik = Sum of all independent current sources directly
connected to node k , with currents entering the node
treated as positive
G is called the conductance matrix, v is the output vector; and i is the
input vector. Equation (3.22) can be solved to obtain the unknown node
voltages. Keep in mind that this is valid for circuits with only independent
current sources and linear resistors.
Similarly, we can obtain meshcurrent equations by inspection when
a linear resistive circuit has only independent voltage sources. Consider
the circuit in Fig. 3.17, shown again in Fig. 3.26(b) for convenience. The
circuit has two nonreference nodes and the node equations were derived
in Section 3.4 as  v v R1 + R3
−R3  −R3
R2 + R 3 eText Main Menu i1
v1
=
i2
−v2  Textbook Table of Contents  (3.24) Problem Solving Workbook Contents 96 PART 1 DC Circuits We notice that each of the diagonal terms is the sum of the resistances in
the related mesh, while each of the offdiagonal terms is the negative of
the resistance common to meshes 1 and 2. Each term on the righthand
side of Eq. (3.24) is the algebraic sum taken clockwise of all independent
voltage sources in the related mesh.
In general, if the c...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.
 Spring '12
 bkav

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