In this problem, we can identify several meshes.

We have a mesh on the left-hand side of the circuit, which is the left loop,

if you will, but also the mesh on the right-hand side, which is the right mesh,

or right loop of the circuit.

We also have mesh which is around the outside of the circuit, and

so we have three different meshes.

They're not independent of one another because

the outside mesh composes the left and the right meshes, so

we're going to write mesh equations for two different meshes.

Mesh 1 and Mesh 2 for this problem.

So, first of all, we're going to identify the meshes.

This is our Mesh 1 and this is the mesh current associated with Mesh 1,

and this is Mesh 2, the right-hand side mesh, and

we're going to assign currents for Mesh 2 to I sub 2.

So, we have two meshes, Mesh 1 and Mesh 2, and mesh currents I1 and I2.

So, the first step in writing the Mesh equation is to

use the passive sign convention to assign polarity is across the different elements.

Our voltage sources already have polarities assigned so

we don't have to do that.

But we have to identify polarities for the resistors and

the voltage drop across the resistors.

So using the passive sign convention, if we start with the left most loop and

we're looking at the current I1 It flow through R1.

And positive sign convention tells us that the positive current flows

into the positive polarity of the voltage drop across those resistors.

So this would be identified like this, as V R1.

So V R1. We also have when

we continue around that loop, past resistor one,

we have resistor three So we have a voltage drop across it, V R3.

And if we continue around that mesh, we have R2 at the bottom of that loop.

And the voltage drop, again using the passive sign convention is V R2

across the resistor at the bottom of the left hand loop.