a question regarding NODE equation..

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i watched an MIT lecture
and he presents there an example
in which he constructs node e2 equation in a very weird way
some how he decides the directions of the current
i dont know how
???

i think i understand the system of how he does the
he takes out e2 and subtracts by the voltage from the line
and divides by it resistor
but why the I1 is negative

i dont know why he does this equation like this
and not the normal KCL method
????

The way he does it is fine. He assumes all the currents are flowing away from the node that is being analyzed and ends up with a list of equations with an equal amount of unknowns. The current direction (indicated by the sign) will resolve to the true direction after solving. A positive sign indicates the current is flowing in the direction originally assumed while a negative sign indicates it is flowing in the opposite direction assumed.

but..

but there is not I variables
if KCL we suppose to have each current represented by I

how did he substitute that?

If you notice in his equation each item IS a current, i.e. (e2-Vo)/Ru. Since the current source is a known current, he just uses its value, or I.

i cant understand..

i cant understand the reason why he subtracts e2-V0??

its always e2 - (the other voltage)

why is that??