Hello, sir.

This type of problem is not my major, so I have no idea how to induct for (4), (5), (6) equations.

Please help me with your guidance.

 

The current law says that the sum of the currents going into an out of ANY node must be zero. You only need to pick a sign convention as follows:

1. Currents going in are positive and currents going out are negative, OR
2. Currents going in are negative and currents going out are positive.

It does not matter which convention you pick as long as you pick one of those two choices, and it is applied consistently within a given problem. In the solution the signs will take care of themselves.
That's about as simple as it gets. In all fields of science and engineering there are "balance" or "continuity" equations that say things cannot be created or destroyed and that what goes in must come out. It is an almost universal concept.

When you get a negative result for an unknown, it just means your initial assignment was the opposite of what it should have been.

 

Thanks for your direction of approach.
However I'm majoring in chemical engineering and this problem is so strange and awkward to me.

 

Thanks for your direction of approach.
However I'm majoring in chemical engineering and this problem is so strange and awkward to me.

OK. chemical engineering. when you have a chemical reaction you have things in and thing coming out. Is it possible to have something coming out that did not go in? No. Same for current. what goes in must come out and there needs to be a balance. Think of a node in a circuit as an analog to a chemical reaction. Write the condition for things to be in balance! It is: current out must equal current in. Rearranging the terms gets you to the sum of the currents in and out must equal zero.

 

OK. chemical engineering. when you have a chemical reaction you have things in and thing coming out. Is it possible to have something coming out that did not go in? No. Same for current. what goes in must come out and there needs to be a balance. Think of a node in a circuit as an analog to a chemical reaction. Write the condition for things to be in balance! It is: current out must equal current in. Rearranging the terms gets you to the sum of the currents in and out must equal zero.

Alright. First I'm gonna do my best in my way and coming back when I stuck again. Thanks, really appreciate.