i cant understand those kirshgof equations..

[transgalactic]

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when i go round the I1 current when i go threw the diamond shape
battery from - to + i get in the equation +Vr
but when i go from + to - (opposite) on the 100v battery i get +100 in the second equation(the value is taken as positive again)

why???

 

[jacob.zurasky]

Diamond is a dependent source. Its value is whatever the voltage Vr is across that other resistor. And yes, it should be -Vr. KVL equations are written clock-wise and if you hit the - first, its -. So it should be -100 in the second equation as well.
The equations should be:

I1: -Vr + 4I1 + 4(I1 - I3) + 4(I1 - I2) = 0

I2: -100 + 4(I2 - I1) + 4(I2 - I3) + 20 = 0

-Jacob