hi guys
i am a newbie
and i have 2 question which probably very easy for you guys..
so on the first picture i didnt understand why the i1 direction is like that..shouldnt it be the way i draw (with red ) and equation should be i1=i2+i3 or am i missing something ?

and can you guys explain me the second question..why the answer is 1A .i mean it should be 1A if that current source wasnt there..but doesnt it have any effect on the circut ?? can you explain me what does that current source and how should i solve question like these if there is a current source in it

 

For fig. 1: You can take current's direction in which ever way you want. Final result will come out negative if you took current in opposite direction. Just make sure that you flow in one direction in a loop( either clockwise or anticlockwise).
For Fig 2: You can analyse this circuit using superposition theorem. It becomes very straight forward.

 

Figure 2.
The 1 Ohm resistor is in parallel with 1 Volt voltage source. What does it mean? When branches are in parallel, all branches have the same voltage across them. So. There is 1 Volt across 1 Ohm resistor. Why? Because 1 Ohm resistor is in parallel with 1 Volt independent voltage source. Apply Ohm's Law: i=v/(1 Ohm)=1 Volt/(1 Ohm)=1 Ampere.

Figure 1.
Like dalam said. Before we do anything, we make some assumptions. One such assumption is the direction of the current. Unfortunately instructors don't inform their students that they made these assumptions. They just inform the students that current X is this way. They don't say why. They should start any solution with a statement, something like this: "I assume that current X is positive when it is in clockwise direction. If later I find that current X is negative, that means that the assumption that I am making here is wrong, AND that current X is positive when it is in counter clockwise direction." So like dalam said, initially, before you did any calculations, you pick whatever directions you like for your currents. It is really your choice. Later, once you calculate all the currents, you will see which currents came up positive and which came up negative.

 

As already stated, the direction of the symbolic currents is arbitrary -- you can flip a coin to determine which way you will draw it. But, once that is done, you then need to develop your system of equations and interpret the results in a way that is consistent with the directions chosen.

A voltage source is a source that produces or absorbs whatever current is necessary in order to maintain the indicated voltage across its terminals. By direct analogy, a current source is a source that produces or absorbs whatever voltage is necessary in order to maintain the indicated current through its terminals.

I don't like this particular example because you can get the correct answer via incorrect reasoning and thus think you have done it correctly. So ask yourself what the answer would be if the resistor were 10 ohms instead of just 1 ohm.