Nodal potentials method

The proposed method is the most effective of the proposed methods, while the accuracy of the calculations is of course lost, this method is incorporated into the engineering programs of the EWB MULTISIM, TINA, definitions of the circuit parameters.
The current in any branch of the circuit can be found by the generalized Ohm's law. For this it is necessary to determine the potentials of the nodes of the circuit.
If the scheme contains n-nodes, then the equations will be (n-1):
Ground any node of the circuit φ = 0;
It is necessary to determine the (n-1) potentials;
Equations are compiled according to the first Kirchhoff law according to the type:


where I11 ... I (n-1), (n-1) the node currents in the branches with EMF connected to this node, Gkk is the sum of the conductances of the branches in node k, called the intrinsic conductivity, Gkm is the sum of the conductances of the branches connecting the nodes k and m, taken with a “-” sign, called mutual conductivity between nodes;
The currents in the circuit are determined by the generalized Ohm's law.
Example:



Ground the node C, i.e. φс = 0



Defining the potentials of φа and φb, we find the currents of the circuit. The compilation of formulas for calculating currents is carried out in accordance with the rules of EMF signs and voltages, when calculating according to the generalized Ohm's law.



The correctness of the calculation of currents is checked using the laws of Kirchhoff and the power balance