Hi

In the attched mesh current example from the DC notes i have a problem with the negative sign in the second mesh equation. No matter how i look at this the second equation should read " I2R3 + (I1 -I2)R2 -B2 = 0 " and not " I2R3 - (I1 -I2)R2 -B2 = 0" as shown. I know that I'm wrong but I cannot figure out why. Can any one maybe explain. Your assistance will be greatly appreciated.

Many Thanks

Willie​

 

What they did was they wrote down the voltage across R2 and used it in both loop equations. Since they started with loop 1, they wrote it as (I1-I2)R2 with positive at the bottom. Since I1 enters this resistor from the bottom it appears as +(I1-I2)R2 in the loop 1 equation, but I2 enters from the top so it appears as -(I1-I2)R2 in the loop 2 equation.

Personally I don't like that because it requires you to write it down and try to remember...
The way I do is if I'm in loop 1, I keep I1 positive. If I'm in loop 2, I keep I2 positive.

So, loop 1 is:

I1R1 - B1 + (I1 - I2)R2 = 0

And loop 2:
I2R3 + (I2 - I1) R2 - B2 = 0

Notice that is equal to what they wrote... since +(I2 - I1) = -(I1 - I2)

 

Thank you. I have been sitting on this for hours.

Have a great day.