The next thing we do when we're performing Mesh Analysis is we, some of the voltages

around our meshes ultimately, so that we can find the values for I sub 1,

I sub 2 and I sub 3 or mesh or loop currents.

So when we look at this first mesh and we try to do that,

we see that we have, we can certainly sum the 12 volt source and

we can certainly sum the voltage across the 2 kilo ohm resistor, but

we don't know the voltage drop across the 2 milliamp source.

Sure we can assign another variable, maybe the 2 milliamps for

the voltage that drops across the source.

That adds another variable to the problem.

And instead of having just three unknowns, I1 through I3,

we also have a fourth unknown, V2 milliamps.

So in order to avoid that,

we use this concept of supermesh in order to solve the problem.

So if we're trying to find the solutions to I1,

I2 and I3 in Mesh Analysis, and we have a current source

which is tied between two adjacent loops or

meshes, then we need to use this concept of supermesh to solve the problem.

And what supermesh allows us to do is it allows us to

avoid that current source when we're summing the voltages around the loop.

So our supermesh that we're going to find is the one in red,

where we avoid that 2 milliamp source, yet

we still create another independent equation, so we have that third equation.