Question

Nodal Analysis by Inspection [G1 + G2 -G2] [v1] = [I1 - I2] [ -G2 G2 + G3] [v2] [ I2 ] [G11 G12 ... G1N] [v1] [i1] [G21 G22 ... G2N] [v2] = [i2] [ : : : : ] [ : ] [ : ] [GN1 GN2 ... GNN] [vN] [iN] Where: Gkk = Sum of the resistances in mesh k Gkj = Gjk = Negative of the sum of the resistances in common with meshes 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

          Nodal Analysis by Inspection
[G1 + G2 -G2] [v1] = [I1 - I2]
[ -G2 G2 + G3] [v2] [ I2 ]
[G11 G12 ... G1N] [v1] [i1]
[G21 G22 ... G2N] [v2] = [i2]
[ : : : : ] [ : ] [ : ]
[GN1 GN2 ... GNN] [vN] [iN]
Where:
Gkk = Sum of the resistances in mesh k
Gkj = Gjk = Negative of the sum of the resistances in common with meshes 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

Nodal Analysis by Inspection
[G1 + G2 -G2] [v1] = [I1 - I2]
[ -G2 G2 + G3] [v2] [ I2 ]
[G11 G12 ... G1N] [v1] [i1]
[G21 G22 ... G2N] [v2] = [i2]
[ : : : : ] [ : ] [ : ]
[GN1 GN2 ... GNN] [vN] [iN]
Where:
Gkk = Sum of the resistances in mesh k
Gkj = Gjk = Negative of the sum of the resistances in common with meshes 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

Added by Juana B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/15/2023

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Nodal Analysis by Inspection [G1 + G2 -G2][v1] = [I1 - I2] [-G2 G2 + G3][v2] [I2] Where: Gkk = Sum of the resistances in mesh k Gkj = Gjk = Negative of the sum of the resistances in common with meshes 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