Are my KVLs incorrect for this circuit?

[pyroknife]

I attached the problem. I'm writing the KVL for each separate loop. For my purposes, I will only write the first two.

i1=1st loop (one on the left) current
i2=2nd loop current (loop in the middle)

Loop 1: 12-12*i1-10(i1-i2)-6*i1=0
Loop 2: -30(i2-i1)+10(i2-i1)=0

The solutions differ with mine however that for loop 2 they have -30(i2-i1)-10(i2-i1)=0

Am I wrong?

 

[Redbelly98]

Loop 2: -30(i2-i1)+10(i2-i1)=0

The solutions differ with mine however that for loop 2 they have -30(i2-i1)-10(i2-i1)=0

Am I wrong?

I agree more with the solution version -- apart from the fact that it's (i2-i3) that goes with the 30 ohm resistor.

The way I remember it is: when traversing around the loop, when going in the same direction as the current then it's a voltage drop, therefore you get a "-" sign. When going against the current direction it's a voltage rise, and therefore you get a "+" sign.

So, if we agree that we traverse the middle loop clockwise, and the currents are all defined as clockwise as well, then it should be "-" for all the i2 terms and "+" for i1 and i3 in the middle-loop equation.

Hope that helps.