### 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 i3 is:

the current if 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 ia and ib is formed: ic - ia = 5

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

ia = 1.75A

ib = 1.25A

ic = 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)