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DC Network Analysis

# Branch Current Method

The **branch current method** is a circuit analysis technique of determining
the current in each branch of a circuit using Kirchhoff's and Ohm's laws.

Note: A branch is a section of a circuit that has a complete path for current.

Let's use this circuit to illustrate the method:

The first step is to assign a current in each circuit branch in an **arbitrary
(assumed)** direction. There are three branches in this circuit and consequently
three currents to consider. We will label the three currents as *I*_{1},
*I*_{2}, and *I*_{3}, respectively (see the figure below).

The next step is to apply Kirchhoff's voltage law for each loop of the circuit. In this step, the voltage drops across all resistors are expressed using branch currents and Ohm's law. The directions (from + to -) of the voltage drops across resistors are considered to be equal to the assigned current directions. We can write two such equations for two loops in this circuit.

Left loop (*R*_{1}, *R*_{2}, *V*_{1}):

Right loop (*R*_{2}, *R*_{3}, *V*_{2}):

Third step, Kirchhoff's current law is applied to all nodes except the ground reference. The ground reference node is usually the node with most connections. We will choose the bottom node as the reference (see the figure below).

Kirchhoff's current law applied to the top (A) node:

Fourth and last step is to solve the equations resulting from previous steps for the branch currents.

Solutions:

Note: Negative sign of *I*_{3} means that our *assumed*
direction for *I*_{3} is opposite of its real direction.