Mesh or Loop Analysis For Electric Circuits

Mesh Analysis :
This is also called Loop Analysis.This method uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network.

Mesh Analysis only works for planar circuits :circuits that can be drawn on a plane (like on a paper) with out any elements or wires cossing each other. In some cases a circuit that looks nonplanar can be made in to a planar circuit by moving some of the connecting wires.

The first step in the mesh Current method is to identify "loops" with in the circuit encompassing all components. Represent all the loops with different loop currents in one direction.The choice of each loop current's direction is entirely arbitrary.

The next step is to label all voltage drop polarities across resistors according to the assumed directions of the mesh currents.

Next write the KVL equations for each mesh and solve all the equations for mesh (loop)currents.

Example :

KVL equation for Loop1 : -28 + 2(I1+I2) + 4*I1 =0.
KVL equation for Loop2 : -2(I1+I2) + 7 - 1I2=0.
Solving these 2 equations we get I1=5A I2=-1A.
The solution of -1 amp for I2 means that our initially assumed direction of current was incorrect. In actuality, I2 is flowing in a counter-clockwise direction at a value of (positive) 1 amp.