Базовые элементы электрических цепей

The method is effectively used when there are few nodes, but many branches.

I = (U +E)/Z = (φ1- φ2 +E)/Z

Express all currents through the potentials of the nodes

φ1, φ2, φ3, φ4:

Next, we write down the first Kirchhoff's law for nodes 1, 2 and 3. Для узла 1: +I1-I2+I3 = 0 Для узла 2: +I2+I4-I5 =0 Для узла 3: -I3+I5+I6 = 0

Substitute currents expressed in terms of potentials into these equations. Perform term-by-term division by Z and transfer the terms of the equation containing the EMF to the right side. We replace the resistances with conductivities G and combine the coefficients for each φ, and equate φ4 to 0:

φ1 (G1+G2+G3) - φ2G2 - φ3G3 = E1G1 φ1 G2 - φ2 (G2+G4+G5)+ φ3G5 = -E4G4 -φ1 G3 - φ2G5 + φ3 (G3+G5+G6)= -E6G6