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Theoretical foundations of electrical engineering

Problems with Node voltage method (Node potential method) – nodal solution

Given
Е1=9 V;
Е2=13 V;
Е3=15 V;
J=1,4 А;
R1=12 ohms;
R2=16 ohms;
R3=9 ohms;
R4=5 ohms;
R5=10 ohms
Find
Currents in the branches by the node potential method (nodal solution)::

Solution



We make matrix equation of the nodal potentials
(Y)(U)=(I), where:
(Y) — conductance matrix of the branches;
(U) — matrix of unknown potentials;
(I) — matrix of entering and leaving currents from nodes.
Note that the known matrix is a matrix of currents therefore sources of the electromotive force switched on in series with resistors need to be replaced with the current sources of the E/R value connected in parallel to resistors. The potential of a point can be written once Ua=E2=13 V:

Node voltage method (Node potential method) – nodal solution
Node voltage method (Node potential method) – nodal solution

Knowing nodes potentials, we use the Ohm’s law and find currents in the branches:
Node voltage method (Nodal potential method) – nodal solution

For the sixth branch it is possible to write down the Kirchhoff's first law:

Ответ: I1=0,852 А; I2=-0,076 А; I3=0,929 А; I4=0,684 А; I5=1,158 А; I6=0,926 А.
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