I'm working on his problem and I know the answer and how it is derived. There is an older thread on this specific problem; however, I do not understand why the answer was derived in such a fashion.
My approach to the problem using nodal analysis was to add the three currents stemming from the top node and set them equal to zero.
I set the node where all three resistors meet to be the reference node. Substituting the currents with voltages and resistance yielded:
(30V/2kΩ) + (20V/5kΩ) + (Vo/4kΩ) = 0
The correct answer is derived from the following equation:
((30V-Vo)/2kΩ) + ((20V-Vo)/5kΩ) + (Vo/4kΩ) = 0
I don't understand why Vo is supposed to be subtracted from each of the voltage sources when it is not between the path from the non-reference node to the node. I find I have problems similar to this in many circuit problems. I do well in subjects from understanding why things work the way that they do, and it seems that in this subject I seldom understand what assumptions can be made or why. Any help is greatly appreciated!
My approach to the problem using nodal analysis was to add the three currents stemming from the top node and set them equal to zero.
I set the node where all three resistors meet to be the reference node. Substituting the currents with voltages and resistance yielded:
(30V/2kΩ) + (20V/5kΩ) + (Vo/4kΩ) = 0
The correct answer is derived from the following equation:
((30V-Vo)/2kΩ) + ((20V-Vo)/5kΩ) + (Vo/4kΩ) = 0
I don't understand why Vo is supposed to be subtracted from each of the voltage sources when it is not between the path from the non-reference node to the node. I find I have problems similar to this in many circuit problems. I do well in subjects from understanding why things work the way that they do, and it seems that in this subject I seldom understand what assumptions can be made or why. Any help is greatly appreciated!
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