Loop analysis is an alternative means of
analysing a circuit. It is based on the mesh current technique. In this case, if
the link currents are known then all the tree branch currents can be calculated.
In this case ** the current sources of the circuit are included, and the
voltage sources of the circuit are excluded.**

The independent equations that describe the circuit can be derived using the link currents as variables, by defining a loop current around each fundamental loop of the circuit.

An example circuit is shown in *figure A*
together with its graph in *figure B* respectively:

*figure A : the circuit*

*figure B : the graph of
figure A*

The tree is defined as shown in figure C (is the group of the black branches), together with the cotree (is the group of the green branches or links).

*figure C : tree & cotree*

There are **4 nodes** and **6 branches**,
therefore (6-(4-1)) = **3 equations** are needed in order for the circuit to
be analysed.

Three fundamental loops should be identified now:

*figure D : loops & loop
currents*

Loop |
Branches |
Associated Current |

a |
a-b-d-f |
i |

b |
b-e-a |
i |

c |
c-d-b |
i |

**For loop A :**

.......(1)

**For loop B :**

By observing loop B it is clear that** i _{b}
= 7A**, because of the current source that exists on the link branch

**For loop C :**

.................(2)

from (1) =>

.................................................(3)

from (2) =>

=>

**i _{a} = 2A**

**i _{c} = 2.5A**