Example method of two nodes

It is used when the circuit contains only two nodes (parallel connection).

Algorithm:
Positive current directions and voltages between two nodes are arbitrary;
Equation for determining inter-nodal voltage



where G - branch conductivity, J - current sources;

Rule: G • E and J are taken with a “+” sign if E and J are directed to a node with high potential;
The currents of the circuit are determined by the generalized Ohm's law.

Task
Determine the currents in the branches by the method of two nodes

Given:

R1 ÷ R3 = 10 Ohm, Е1 = 100 V, Е2 = 10 V


Let us set the directions of the currents arbitrarily. We write the equation for determining the voltage between the nodes. The potential φa> φb and set the direction of the voltage from a to b.

Decision:



Check under the first law of Kirchhoff: