I\'m having trouble with the problem in the following link. http://www.cramster.

Question

I'm having trouble with the problem in the following link.
http://www.cramster.com/solution/solution/1256079

I understand the first part of finding the current I = 4/9 = .44 Amps using Kurchoff's Loop Law, however I'm having trouble with the use of the Kurchoff's Second Law.

Vab = (Sum_of_Voltages) - (Sum_of_IR)
The cramster solution says:
12V - 10V - (0.44)(2 + 1 + 1) = Vab ---> Vab = .22V
What I don't understand is why for the sum of the resistances we only use the 2, 1, and 1 ohm resistors and forget to include the 3 ohm and 1 ohm resistor in the middle branch?
________
part b) If points a and b are connected by a wire with negligible resistance, find the current in the 12V battery.
Again, I get the first part right using Kurchoff's Loop Rule to obtain 1 = 2I + 2I_1 but don't understand how the second equation is derived. Why do we use the quantity (I -I_1) when using what appears to be the format for Kurchoff's Loop law?

Explanation / Answer

Kirchoff's second law states that the net voltage in a closed loop is zero. Here the loop considered does not contain the middle resistances so they are not considered. I think that should clear both of your doubts.

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