 # Branch current method - example 1

In order to designate the currents and the voltages in an electric circuit the Kirchhoff’s current law equations (KCL) and the Kirchhoff’s voltage law equations (KVL) have to be written down. The number of equations for each Kirchhoff’s law is given by following formulas:
KCL equations=n-1
KVL equations=m-(n-1)
n-number of nodes in circuit
m-number of branches in circuit By looking at the examined electric circuit it can be noted that it is a direct current circuit (DC circuit). The subject electric circuit has two nodes and two meshes in its topology. The elements of circuit are: four voltage power supplies and five resistors. Since the circuit has two nodes (n=2), thereby, for the first Kirchhoff’s law (KCL) there is one current equation. The Kirchhoff’s current law says that the sum of currents which flow to and flow out of a node is equal to zero. It has to be remembered that the currents which flow into node are written down in the equation with sign “+”. The currents which flow out from a node are written down in the equation with sign “-“.

The number of Kirchhoff's current law equations is given by following formula below. Since in the result there is only one Kirchhoff's current equation it is written down. The considered circuit has three branches (m=3). The number of equations for Kirchhoff’s voltage law (KVL) is equal to two. Before the Kirchhoff’s voltage law (KVL) is written down. It has to be determined what convention of voltage’s signs is to be applied in the examined circuit. In this example, the plus sign “+” is assigned to voltages if their arrows direction are clockwise. If the voltages arrows are counterclockwise then the minus sign “-“ is assigned. The voltages of elements are marked by arrows. The voltage’s arrow direction is opposite to current flow's arrow direction. For the resistors, the Ohm law is employed. This law links current, voltage and resistance in one equation.

The general forms of the Ohm's law equation. It is worth noting that the Ohm's law ties a current in function of a voltage (I = f(V)) or a voltage in a function of a current (V = f(I)). The resistance R is assumed as constant in both these forms of the Ohm's law. In other words, the resistance in the Ohm's law is a coefficient of proportion. The Kirchhoff’s voltage equation for mesh 1: The Kirchhoff’s voltage equation for mesh 2: Based on the result three Kirchhoff’s equations it can be assumed that the electric circuit has been solved. This example has been limited only to write the Kirchhoff’s current equation (KCL) and the Kirchhoff’s voltage equations (KVL). The rest what can be done with the Kirchhoff's equations is a selection of values for parameters and computing of results for the selected unknowns. The three equations mean that the examined electric circuit can be solved for three unknowns.