Engineering Current variable given through junction crossing

[Practical Cat]

Homework Statement

Find Vab as a function of load current device

Relevant Equations

none

I'm supposed to solve this using nodal analysis. No biggie! I'm just not sure how to handle ia. I've never seen a current indicated in a junction crossing. I searched the web and my textbook and found zilch. I asked a GSI and was informed it is indeed written where is supposed to be. Within the node V3. Which has me puzzled. Best I could think of is it's specifically the sum of the 30k 25k & 15Valpha branch currents. Within my mind this interpretation is in superposition; it's flat wrong, and reasonable enough but odd and arcane if indeed correct. I can manage solving once I know how to approach ia, but can anyone weigh in on the spooky current?

 

[gneill]

It would appear to me that $i_a$ must equal the sum of

$15 i_{s1} + 2 mA + I_L + \frac{V_3}{35k\Omega}$

This presumes that the bottom "rail" is the assumed ground node as shown in the original circuit diagram.

This is not a problem I'd like to face on a midterm

 

[DaveE]

You could substitute a 0V voltage source for any connection in that network, for example the connection that carries i_a. That may help clarify your thinking about this problem. It's not just any connection, it's the one that they defined as having i_a, the current in question. Because they asked about the current between the connections in this node, you have to treat it as two separate nodes with no voltage difference.