We also know that when we're doing mesh analysis, the first thing we do is assign

meshes, and then mesh currents associated with those meshes.

So that we can then sum up the voltages around the meshes to create the equations

that can be solved simultaneously to determine the mesh currents.

So, we're going to start with assigning our meshes.

Our first mesh we're going to assign in a clockwise fashion,

on the left hand side, and we're going to call the current on it I-sub-1.

And you might imagine that the next mesh is going to be on

the right side of our circuit.

It's going to have a mesh current I2.

We immediately notice that I2 is equal to I sub x,

because it's the current flowing down through the 2 kilometer resistor.

So, we can write that down to help us out,

because I sub x Introduces a third unknown variable.

We have an unknown, current I sub 1, we have an unknown current, I sub 2,

and we have an unknown current, I sub x.

But this is our first equation, which is independent of our other equations,

it's a constrain equation that relates I1, I2, and Ix.