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**CIRCUIT ANALYSIS AND TECHNIQUES**

Mesh Current Method (Special Cases)

**Dependent Sources:**

In case that there is a dependent source in the
circuit, the mesh current equation must be adapted accordingly.

the mesh-current equation with respect to **i**_{3}
is:

the current **i**_{f}
now should be written with respect to node currents i.e.:

then proceed as before.

**The Current Source:**

A current source in mesh analysis can be
treated similarly with a voltage source in nodal analysis.

The above circuit can be described using **2
equations **because there are **4 essential nodes** and **5 essential
branches** ((b-(n-1)) = 2).

On the above figure, a variable **V** is added in
order to represent the unknown voltage across the current source.

**mesh A:**

............(16)

**mesh C:**

...........(17)

by adding (16) and (17) **V
**
is eliminated i.e.

.................(18)

using **
mesh B:**

...(19)

At this point the 2 required
equations have been found (18 & 19), but there are still 3 unknown currents.

Observing the current
source, a relation between currents i_{a} and i_{b} is formed:
**i**_{c} - i_{a} = 5

hence the equations (18) and
(19) are solved giving:

**i**_{a} = 1.75A

**i**_{b} = 1.25A

**i**_{c }= 6.75A

The equation (18) could have
been derived directly using the concept of a __supermesh__ which is
very similar to the __supernode__ of the node-voltage method.

The voltages around the __supermesh__
are expressed in terms of the node currents, i.e.

......(20)

(20) reduces to:

...........................................(21)

equation (18) is identical
to equation (21)