Solve Mesh Analysis Problem with a Current Source

[julz127]

Homework Statement

[PLAIN]http://img718.imageshack.us/img718/3519/circuith.png

This is a circuit I've simulated in pSpice, I can't get the currents to match up with my hand calculations using mesh analyses. Specifically, I'm not entirely sure how to handle the current source.

Homework Equations

Mesh 1 is far left, mesh 2 is the center and mesh the is the far right.

Mesh 1.

$18 = 15i_{1} + 30(i_{1} - i_{2})$

Mesh 2.

$0 = 10i_{2} + 20(i_{2} - i_{3}) + 30(i_{2} - i_{1})$

Mesh 3.

$30 = 40i_{3} + 20(i_{3} - i_{2})$

finally, putting all this in a matrix ( I'm using an online calculator, to eliminate the possibility of an error here, but I do know how to do it by hand ).

I get,

$i_{1} = 0.407A$
$i_{2} = 0.010A$
$i_{3} =-0.580A$

Thanks

 

[gneill]

For the 10Ω resistor term in the second mesh, include the current of the current source as though it were another mesh's current. Thus
$$0 = 10(i_{2} - I1) + 20(i_{2} - i_{3}) + 30(i_{2} - i_{1})$$
where I1 is the value of the current source.

 

[julz127]

Thanks for the reply, however I managed to solve the circuit just a few minutes after I posted it.

I realized that I've been looking at this whole mesh analyses technique the wrong way.

A huge 'lightbulb' moment. Feels good man.