Greetings all 
First time poster here and I am very very rusty at Circuit theory. I am trying to get back into it, but am getting very frustrated at the same time. What may have been simple many years ago is just not clicking with me anymore.
I am working through problems in a Schaum's guide. I have attached the problem (diagram, Figure 327). They do provide the answer but not the steps. I am trying to find V_ab.
For this particular problem the answer is 20V. However, V_ab is in the middle of this circuit. The total resistance is 10 ohms, and the total voltage (I believe) is 35V (20 +25  15  10), which would lead to a current of 3.5A. If signs didn't matter, then the total voltage would be 70V, and the current would be 7A. So that's my first clarification  which one is correct?
As for V_ab  the way I understand it is the V_ab is the voltage drop from node a to node b, which is the same of the voltage drops across the components connected between nodes a and b either to the right or left of node a.
I assume that we are doing KVL in some sense, where the sum of all voltages in a loop must equal zero. While I am not clear here either, and in doing both right and left loops with both 3.5 A and 7A, I do not get 20V for V_ab.
I am trying to understand where I am going wrong so I can get better at this. Any guidance would be helpful.
Thanks!
10th
Mod: Added clip from PDF.
First time poster here and I am very very rusty at Circuit theory. I am trying to get back into it, but am getting very frustrated at the same time. What may have been simple many years ago is just not clicking with me anymore.
I am working through problems in a Schaum's guide. I have attached the problem (diagram, Figure 327). They do provide the answer but not the steps. I am trying to find V_ab.
For this particular problem the answer is 20V. However, V_ab is in the middle of this circuit. The total resistance is 10 ohms, and the total voltage (I believe) is 35V (20 +25  15  10), which would lead to a current of 3.5A. If signs didn't matter, then the total voltage would be 70V, and the current would be 7A. So that's my first clarification  which one is correct?
As for V_ab  the way I understand it is the V_ab is the voltage drop from node a to node b, which is the same of the voltage drops across the components connected between nodes a and b either to the right or left of node a.
I assume that we are doing KVL in some sense, where the sum of all voltages in a loop must equal zero. While I am not clear here either, and in doing both right and left loops with both 3.5 A and 7A, I do not get 20V for V_ab.
I am trying to understand where I am going wrong so I can get better at this. Any guidance would be helpful.
Thanks!
10th
Mod: Added clip from PDF.
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