Nodal analysis trying to find Voc

[jdawg]

Homework Statement

Find Voc

Homework Equations

The Attempt at a Solution

This is what I have:

(VA-9)/5 +VA/5 + 1.8 = 0
VA=0

-1.8 + VB/(60+10) +(VB-9)/20
VB=35

What I'm confused about is why you combine the 60 ohm and 10 ohm resistors for the VB nodal equation, but not the 25 ohm and 10 ohm resistor for the VA nodal equation. Is it because the grounding symbol is directly below the 25 ohm resistor? Thanks!

 

[gneill]

By adding the 60 and 10 ohm resistors together you've treated them as an isolated branch, ignoring the "tap" that is the terminal "b". This is okay as far as it goes because terminal b is open and no current can flow into or out of it. So it's not really a matter of the ground symbol being directly below V_A that prevents you from combining the 25 and 10 ohm resistors, but rather that it is a node that happens to be there. It just happens to be the reference node with a defined potential (0 V).

Note that what you have found is the potential at V_B with respect to the reference (ground) node, not the voltage Voc.

To remedy this you could add a node at b, maybe call it V_C. Then redo your node equations accordingly and solve for Voc = V_B - V_C. Alternatively, knowing the potential across the branch you can determine the current in the branch and hence determine the potential drop across the 60 ohm resistor.

 

[jdawg]

Thanks, great explanation!