Misunderstanding about the choices of current values in KCL

[kookamlok]

_【Moved from general forum. Homework template is missing._】

By KCL,
-ID2 + (-I2) = 0

0 = ID2 + I2

Q1: Do you think this equation is correct? (i assume it is correct because it came from my professor's notes)

Q2: Which node do you think this equation is used for making this equation with values currents which is going in and out to the selected partcular node? (I would guess node at V2 but why the input current will be 0 according to 0 = ID2 + I2?)

Q3: why will my professor choose this node? (to be honest, i have no clue. I will ask my professor later but want to see your opinion.)

 

[NascentOxygen]

Hi kookamlok.

These equations can arise in cases such as where you have been provided with the labelled figure in white, and asked to find something in terms of the current coloured in blue, I₂.

You can see that I₂ is the current I_D2 but opposite in direction, so you can write
I₂ = –I_D2

Alternatively, you could consider the point in the wire near where you see the voltage label V₂, and sum the currents into (or out of) that point.

There is a current –I_D2 directed in from the left, and a current –I₂ directed up from the ground. KCL says these must sum to zero. (Otherwise there would have to be current spilling out of the wire, or something equally preposterous).

 

[CWatters]

I would guess node at V2..

It must be node V₂ because that's the only node that involves only I_D2 and I₂. If you applied KCL at node V₁ it would feature I_D1.

but why the input current will be 0 according to 0 = ID2 + I2?)

Not sure what you mean by input current but the zero arises because KCL states that the sum of currents going into (or out of) a node equals zero. It so happens that in this case I_D2 and I₂ have been defined in opposite directions so you can rearrange your equation to ..

I_D2 = -I₂

When applying KCL you must first decide if current entering or leaving a node is going to be defined as positive (+ve). This can be an arbitrary decision but you must be consistent. It looks like your professor decided that current entering a node would be +ve when he wrote..

-ID2 + (-I2) = 0

Both I_D2 and I₂ are -ve in his equation because on the drawing they are shown leaving node V₂. That only makes sense if he defined current entering a node as +ve.

Here is KCL for node V₁...

(+I_D1) + (+I_D2) + (-V₁/1k) = 0

I have tried to be very explicit with the signs because this is the greatest source of error when applying KCL.
I_D1 is +ve because it's entering node V₁.
Likewise for I_D2.
The last term -V₁/1k is negative because I have made the reasonable assumption that V₁ stands for the voltage across the 1K resistor and it's polarity is as shown by the arrow that I have added in this version of your drawing. This implies the current in the 1k resistor is flowing downwards out of V₁ so it's -ve. In some cases you have to add your own arrows to a drawing to define what you mean by a positive voltage.