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Write down the nodal equation in a matrix form and determine the current flowing through branch AC.

Physics
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Here is the circuit.
1 Attachment
The answer is 2.6A. I've worked it out first by using KCL and Ohm's law at the Nodes. At that point I've considered current direction. Then, using Cramer's rule I got 12A. If we don't take into consideration current direction, i.e take it all to be positive, you obtain the answer 2.61A.
However, i don't understand why we don't take the current directions in this case while using KCL. Can anyone explain me the reason why.

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Other answers:

KCL - Kirchoff's current law
you dont take signal if current is entering in node or leaving it?
Yes. We don't consider whether it is leaving or entering the node, then we get the answer.
if you dont using the signal then you will find in your ans a negative current
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if you do all you currents like this all will be positive,but when you do the equations some value will be negative get it?
So that's why we take it that all the current is moving away from the node..??
yes, you dont have to know first, the direction of current ,if you find a negative value the current is entering in node instead leaving
Okay..!! Thanks for your help..!! Fan + medal..!! :)
you are welcome

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