CIRCUIT ANALYSIS AND TECHNIQUES Mesh-Current Method

Using the Mesh-Current method, a circuit can be described in b-(n-1) equations. On the above circuit there are three resistors. An unknown  current passes through each resistor (i.e. three unknown currents in total have to be estimated).

But on the above circuit there are two meshes with currents ia and ib. By applying Kirchoff's current law =>  Using the above two equations, currents ia and ib could be found. Having found the values of these currents, the unknown circuit currents could now be found.

Example By observing the above figure find:

• i1 and i2
• the power associated with each voltage source
• the voltage across the 6 ohm resistor

On the above circuit there are 3 essential nodes and 5 essential branches.

Number of equation needed: b-(n-1)=3 equations

Mesh A:  ...............................(11)

Mesh B:  ........................(12)

Mesh C  .........................(13)

from (11)=> ................................(14)

from (13)=> ..........................(15)

substituting (14) and (15) into (12) =>  ia = 3.04A

ic = -2.35A  Since ia is the current in the 50V source =>

P(40V) = 50 x 3.04 = 152W

Since ic is the current in the 125V source =>

-2.35 x 125 = -293.75W

Note that ic was defined as flowing into the 125V source, then the source is actually providing power.

The current in the 6 ohm resistor is => => voltage drop = 6 x 1.13 = 6.78V