Introduction to Electric Circuits

146 Nodal and mesh analysis 2Ii - 41 4i 1 Solution This is a square matrix of order 3. The elements in column I (n = 1) are all ...

7.3 Nodal voltage analysis 147 Solution In matrix form the equations may be written [A][I] = [B] where A=I521 _3102 _11 and B= I ...

148 Nodal and mesh analysis all the other nodes to it. By applying Kirchhoff's current law to each of these other nodes in turn, ...

7.3 Nodal voltage analysis 149 Setting the reference voltage to zero, V3 = 0, and then we have I- V~/R~ + V1/R2 + (V, - Vz)/R3 U ...

150 Nodal and mesh analysis This is of the form Ax = B so that Cramer's rule may be used to solve for V~ and V2. Circuits with v ...

7.3 Nodal voltage analysis 151 9 the coefficient of V1 is the sum of all the conductances connected to node 1, 9 the coefficie ...

152 Nodal and mesh analysis Finally V1 = A1/A --[(Vs1Gll(G 3 -Jr- a 4 "Jr- (~5) -lt- (Vs2G3G5)I/(GI -[- G2 Jr- (~3)((~3 -]- a 4 ...

7.3 Nodal voltage analysis 153 recourse to Kirchhoff's law by using the pattern noted in the bullet points leading to Equations ...

154 Nodal and mesh analysis To determine A~, we replace column 1 by the column vector on the right-hand side of Equation (7.10). ...

vs, l( 200V Figure 7.5 1 Y1 11 2 I3 Y3 ) - ( 4 7.3 Nodal voltage analysis 155 I Vs2 Y1 =(-j/3)S 210/-30V Y2 = (1/10)S Y3 = (-j/5 ...

156 Nodal and mesh analysis V2 = 105/--101.5~ ~ 194.8/--22.2 ~ The potential difference across the admittance Yz is 1/2 - V4 = V ...

7.3 Nodal voltage analysis 157 Figure 7.7 Vs, ) (5V) Is = 5A ,,.._ v- '~ 1 12 ~2 4 Q 3 R2 = 5fl I3 R1 = 2s R3 = 4~ I= 4 R4 = 1 ...

158 Nodal and mesh analysis 7.4 MESH CURRENT ANALYSIS Whereas in the nodal voltage method of analysis we used Kirchhoff's curren ...

7.4 Mesh current analysis 159 mesh currents being 11, 12 and 13. None of the other loops are meshes because they have other loop ...

160 Nodal and mesh analysis the three mesh currents or Cramer's rule can be used to solve the matrix equation (7.18). We note fr ...

7.4 Mesh current analysis 161 For mesh 2 1 The coefficient of the mesh current is the sum of the resistances around the mesh (=R ...

162 Nodal and mesh analysis Solution There are three meshes identified by the currents I~, I2 and 13. Applying KVL to mesh 1 and ...

7.4 Mesh current analysis 163 To find A 1 we replace column 1 of A by the column vector on the right-hand side of the matrix equ ...

164 Nodal and mesh analysis Solution There are two meshes whose currents are I~ and 12, respectively, and we note that the mesh ...

7.4 Mesh current analysis 165 Applying KVL to mesh 1 and taking the clockwise direction to be positive, we have V- R1/4- R4/5 = ...