Understanding Current Flow in a Circuit with a Current Source

[CoolDude420]

Homework Statement

Say I have the following hypotehtical circuit,

Ignore the open circuit at the bottom.

Would I be correct in saying that all of the input current i goes to the resistor R or would it be split? Because I know for a current source that it has to produce that current i5 no matter what.

Homework Equations

The Attempt at a Solution

 

[gneill]

What circuit law could you appeal to in order to find out?

 

[CoolDude420]

What circuit law could you appeal to in order to find out?

KCL?

i = i1 + i5

where i1 is the current through resistor.

Well that answered my question.

 

[gneill]

KCL?

i = i1 + i5

where i1 is the current through resistor.

Well that answered my question.

 

[CoolDude420]

Thank you. Apologies for the stupid question. I forgot the basics.

 

[gneill]

No worries. You got the answer by your own efforts with just one vagueish hint, so that's a win!

 

[CoolDude420]

No worries. You got the answer by your own efforts with just one vagueish hint, so that's a win!

Sorry. I'm just having some second doubts in relation to a different question but on the same topic.

For this circuit, I was told that ALL the current $$g_mv_{gs,2}$$ flows through resistor $$r_{o2}$$. Now that doesn't make sense if I apply KCL at the the middle node on the right side(S2, D1).
KCL at S2, D1 $$ g_mv_{gs,2} + i_{r_{o1}}= i_{r_{o2}} + g_mv_{gs,1}$$
Rearranging,
$$ g_mv_{gs,2} = i_{r_{o2}} + g_mv_{gs,1} - i_{r_{o1}}$$

That is telling me that in fact, not all of the current is going through r_o2. See the related thread,
https://www.physicsforums.com/threads/cascode-amplifier-small-signal-model.940510/#post-5951679

It made sense at the time, but I am having doubts about it now.

 

[gneill]

The current generator must "draw in" the same current that it "pushes out", and the only path for that drwin-in current is via that resistor.

For this circuit, I was told that ALL the current $$g_mv_{gs,2}$$ flows through resistor $$r_{o2}$$. Now that doesn't make sense if I apply KCL at the the middle node on the right side(S2, D1).
KCL at S2, D1 $$ g_mv_{gs,2} + i_{r_{o1}}= i_{r_{o2}} + g_mv_{gs,1}$$
Rearranging,
$$ g_mv_{gs,2} = i_{r_{o2}} + g_mv_{gs,1} - i_{r_{o1}}$$

That is telling me that in fact, not all of the current is going through r_o2. See the related thread,

And if $i_{r_{o2}} = g_mv_{gs,2}$, what does the equation tell you?

 

[CoolDude420]

The current generator must "draw in" the same current that it "pushes out", and the only path for that drwin-in current is via that resistor.
View attachment 221998And if $i_{r_{o2}} = g_mv_{gs,2}$, what does the equation tell you?

Ah.. I get it now. So the current source is fixing the current in that branch no matter what and if other currents were to flow into ro2 then, that fixed branch current wouldn't be fixed anymore.